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[method.ovchinnikov.co](./#overview)[Overview](./#overview)[Settings and conventions](./#settings)[A. How pool shares earn returns](./#earnings)[B. Rebalancing gains, trading losses and fees](./#harvesting)[C. What the simulator can explain](./#simulation)[D. Testing different sequences of market moves](./#resampling)[E. Tests of the YB proposal](./#proposal)[F. The re-peg gate](./#repeg)[G. When price_scale detaches](./#detachment)[H. Choosing parameters means choosing bets](./#bets)[Concerns about the evidence](./#concerns)[Common misunderstandings](./#misunderstandings)[Glossary](./#glossary)

YieldBasis $\cdot$ pool economics and simulator trust

The study text and chart tables are available below. Interactive charts load when the data are ready.

[Previous YB-policy pages $\cdot$ archive](/yb-policy/) $\cdot$ [Agent-readable study](agents.md) $\cdot$ [All page text and chart tables](PAGE-TEXT.md) $\cdot$ [llms.txt](llms.txt)


# The proposal and eight findings {#overview}

**The proposal reduces the money supplied to the pool.**

This funding is called [financing](./#glossary/financing). The proposal also changes how outside prices guide trading fees. It changes how those prices guide [re-pegs](./#glossary/re-peg), moves of the pool’s central price.

The tests separate the financing cut from the pool’s performance. The [YB position](./#glossary/yb-position), a holder of pool shares and debt, borrows to buy its shares. The debt uses [crvUSD](./#glossary/crvusd), the stablecoin used as cash in these pools. Interest on that debt funds [donations](./#glossary/donation), capital supplied to the pool.

The pool concentrates trading capacity around its central price, called [price_scale](./#glossary/price_scale). The proposal concerns [WETH](./#glossary/weth), the token form of [ETH](./#glossary/eth) used in these pools. [The team’s forum post describes the proposal in full.](https://forum.yieldbasis.com/t/oracle-reports-for-yieldbasis-pools-a-new-price-scale-and-fee-policy-for-the-weth-market/40)

[LevAMM](./#glossary/levamm) is the contract that manages borrowing and pool shares. Its fee appears in the table.

Current and proposed settings for the WETH comparison
| Setting | Deployed current settings | Proposal | 
| --- | --- | --- |
| Donations each year, % of pool value | 5% | About 1.2% | 
| Recorded profit protected from spending on price adjustments | 45% | About 42.9% | 
| LevAMM fee | 1.3% | 1.5% | 
| Prices used for fees and price adjustments | The pool’s rules based on its traded prices | Messages carrying prices from outside the pool | 

[LP/xyk](./#glossary/lp-xyk) measures growth beyond a reference pool after the donation charge. The measure uses market prices to value each share.

The reference pool follows the same prices and charges no fees. Its trades keep the product of its two asset quantities constant. [Settings and conventions](./#settings) defines the yearly growth rate and each group of settings.

## Eight findings
- [Replaying](./#glossary/replay) recorded inputs closely reproduces the live pools’ returns. The simulator receives recorded market prices and supplied user activity.

  The largest replay-minus-live LP/xyk difference is 0.32 [percentage points](./#glossary/percentage-point) per year over 128 days. [Replay evidence](./#simulation/live).

- The original test finds a gain on the history used to choose settings. The only supplied trading in that test is [arbitrage](./#glossary/arbitrage), trading to profit from price differences.

  The full proposal beats deployed current settings by +1.65 percentage points per year of LP/xyk. With recorded operation times, every tested variant puts the proposal behind.

  The proposal-minus-current results range from [−0.18, −0.04] percentage points per year. [Original and timing tests](./#proposal/test).

- The financing change helps early and hurts later in tests starting from observed WETH states. Changing financing alone raises LP/xyk above deployed current settings at 7 days. It lowers LP/xyk at 90 days.

  The full proposal gives slower growth in each share’s [market value](./#glossary/market-value) than deployed current settings. The result holds at every reported period, from 7 through 90 days. [Financing evidence](./#proposal/channels).

- Customers would pay more under the proposal for WETH trades of the recorded sizes. The median cost against the outside market price is 145 [basis points](./#glossary/basis-point) under the proposal. Under deployed current settings, the median is 6.5 basis points.

  A basis point is a hundredth of a percentage point. [Customer-cost evidence](./#proposal/demand).

- On unused data, selected settings show no reliable growth advantage for the YB position over alternatives with the same financing. Those alternatives share the donation rate and the fraction of profit reserved. On older history, the selected settings’ mean advantage is negative. [Tests on unused and older data](./#proposal/selection).

- Removing the profit floor changes outcomes differently across Bitcoin pools on the same September price history. The floor sets the minimum protected accounting value.

  Compared with keeping the floor, removal changes yearly growth in each [LP](./#glossary/lp) share’s market value as shown below. An LP share represents ownership of part of the pool.

  
  | Pool | Change in yearly growth, percentage points | 
  | --- | --- |
  | [WBTC](./#glossary/wbtc) | +10.70 | 
  | [cbBTC](./#glossary/cbbtc) | −4.37 | 

  [Profit-floor evidence](./#repeg/removal).

- On rebuilt WETH histories, a floor that can be reset meets the [detachment](./#glossary/detachment) rarity limits at some donation rates. Detachment means losing trading capacity at the market price. These histories only reorder the original price moves.

  The deployed gate, the rule allowing or blocking price adjustments, passes at none of the tested rates through 6% yearly donations.

  Settings that reduce detachment do not reliably grow wealth faster than their named controls. Forcing the pool to stay [centred](./#glossary/centred-pool) does not reliably grow wealth faster than its own control either. [Donation tests](./#detachment/donations) and [wealth comparisons](./#detachment/funded).

- On the team’s tested grid, higher past holder returns mostly came from one market term. Each re-peg setting is a bet on whether a price move lasts. [What choosing parameters means](./#bets/mechanism).

Some common beliefs about these pools do not hold up. [Common misunderstandings](./#misunderstandings) lists them, each with its evidence.

## Where to start

For the findings, start with [the proposal and its parts](./#proposal/test). Then read [financing](./#proposal/channels), [the profit floor](./#repeg/protection) and [detachment](./#detachment/measure).

For the foundations, start with [what a pool share is worth](./#earnings/measure). Continue through [harvesting, trading losses and fees](./#harvesting/rebalancing), [simulation](./#simulation/live) and [rebuilt histories](./#resampling/why). Then read the proposal results.

[next $\to$](./#settings)


# Settings and conventions {#settings}

**Each comparison names the rules, funding and activity used in the test.**

A group of settings specifies the pool’s price rules and [financing](./#glossary/financing), the money supplied to the pool. The profit gate decides whether the pool may move its central price. A [re-peg](./#glossary/re-peg) is such a move.

[Donations](./#glossary/donation) supply outside capital to the pool. Reserved profit is the share of recorded profit protected from spending. [LevAMM](./#glossary/levamm) is the contract that manages borrowing and pool shares.

## Deployed WETH reference settings

| Setting | Meaning | 
| --- | --- |
| Pool and history | [WETH](./#glossary/weth) proposal tests on the tuning or older histories. Some tests start from named observed WETH states. | 
| Financing | With a simulated position, annual donations are 5% of pool value. Reserved profit is 45%. The LevAMM fee is 1.3%. Recorded-flow tests use the donation coins and operations stated with each test. | 
| Gate | The deployed floor protects cumulative recorded profit. | 
| Used for | The reference settings for proposal tests. | 

## Observed-state gate comparison

| Setting | Meaning | 
| --- | --- |
| Pool and history | The named WETH or Bitcoin pool and starting date. | 
| Financing | The financing and fees attached to that pool. Only the settings named by the experiment change. | 
| Gate | Kept, removed or reset, as stated. | 
| Used for | Gate tests starting from observed states in the re-peg chapter. | 

## Current price rule with shared financing settings

| Setting | Meaning | 
| --- | --- |
| Pool and history | Named observed WETH starting states or rebuilt WETH price histories. | 
| Financing | Reserved profit is 42.91%. The LevAMM fee is 1.50%. Each result states the donation rate. | 
| Gate | The deployed gate, unless the test explicitly resets the floor. | 
| Used for | The WETH test changing financing alone. Also, [detachment](./#glossary/detachment) scans and reruns of histories. The control restores annual donations to 5% when comparing growth with settings that reduce detachment. | 

## Proposal

| Setting | Meaning | 
| --- | --- |
| Pool and history | WETH tuning and older histories, or the named observed pool state. | 
| Financing | Where financing is simulated, annual donations are 1.1976%. Reserved profit is 42.913386%. The LevAMM fee is 1.50%. | 
| Gate | The deployed gate unless the experiment changes it. | 
| Used for | The full proposal in tests of its parts and of different time periods. Recorded-flow tests state whether donated coins stay fixed. | 

## Proposal with a resettable floor

| Setting | Meaning | 
| --- | --- |
| Pool and history | Rebuilt WETH histories. | 
| Financing | The shared reserved-profit and LevAMM settings above. Each result states the donation rate. | 
| Gate | An allowed move may spend below the protected floor. The rule then lowers that floor. The absolute floor remains. | 
| Used for | Detachment scans and comparisons of reduced detachment, repairs, quotes and funded attachment. Each test names the original or faster price averages. | 

## What “financing only” changes

A financing-only test keeps current price rules and changes the funding settings. With a simulated [YB position](./#glossary/yb-position), the changes cover donations, reserved profit and the LevAMM fee. The YB position owns pool shares and owes debt.

With recorded activity, the test scales the supplied donation coins and changes reserved profit. Recorded LevAMM operations keep their fees.

## Histories and supplied activity

| History | Dates or length | 
| --- | --- |
| Live pools: actual pools and observed setting changes | 26 May 2026 to 1 October 2026 [UTC](./#glossary/utc) | 
| History used to choose settings | 2025-03-24 to 30 September 2026 | 
| Rebuilt WETH histories for detachment tests | 556 days, from a common starting template | 

Older-history tests state their dates beside the results. UTC is the common time standard used here.

- Real-flow [replay](./#glossary/replay) copies the recorded times and amounts of user operations.
- [Pings](./#glossary/ping) copy only the times. Simulated [arbitrage](./#glossary/arbitrage) and the YB position can still trade.
- Arbitrage-only tests supply the update opportunities stated on their pages.

Arbitrage means trading to profit from price differences. These input choices answer different questions about the same pool rules.

## Yearly rates

First divide final value by starting value. The natural logarithm of that ratio is the log change. To obtain the yearly rate, multiply by 100 and divide by elapsed years. A year contains 365 days in these calculations.

Differences between yearly rates use [percentage points](./#glossary/percentage-point) per year, abbreviated pp/yr. A positive proposal-minus-control difference means faster growth under the proposal for the named measure. [M](./#glossary/m), [LP/xyk](./#glossary/lp-xyk), internal accounting and the holder’s remaining wealth measure different outcomes.

The post’s claimed LP/xyk advantage is +1.65 pp/yr over current settings in the original test. That test uses the tuning history and arbitrage-only activity. The claim provides a useful scale for other LP/xyk differences.

Growth of the YB position in [ETH](./#glossary/eth) needs its own named measure. Internal accounting and shares valued at market prices also need their own measures. ETH is the native asset of the Ethereum network.

Trade costs in [basis points](./#glossary/basis-point) use different units from yearly return differences. Event probabilities, repair percentages and the live harvesting and curvature totals also use different units.

## Whose value is measured
- M compares [market value](./#glossary/market-value) per [LP](./#glossary/lp) share with a fee-free constant-product reference pool. Market value uses prices outside the pool.
- LP/xyk takes M’s yearly growth and subtracts the realised log charge for donations.
- The holder’s remaining wealth subtracts [crvUSD](./#glossary/crvusd) debt from the market value of its LP assets. The result uses ETH or [BTC](./#glossary/btc) units.

A constant-product pool trades while keeping the product of its asset quantities constant. The reference follows the same market prices. BTC denotes Bitcoin.

An ETH amount measures a change in wealth. A rate in pp/yr measures a difference in yearly growth rates.

## When a price-gap stall starts

The pool’s central price is called [price_scale](./#glossary/price_scale). A price-gap [stall](./#glossary/stall) occurs when its distance from the market price exceeds 5% for at least 24 uninterrupted hours. The rule uses the absolute percentage distance and checks each [blockchain block](./#glossary/blockchain-block).

“Both attached” means neither compared pool has such a stall in the window. Brief gaps can still occur. Noise tests, September gate tests, live-chart shading and funded-attachment groups use this rule.

## When trading depth is seriously reduced

Trading depth is the capacity available for small trades. The detachment chapter compares depth at the market with an equally funded pool [centred](./#glossary/centred-pool) on that price. Both pools use the same curve shape.

“Serious” means that less than 75.00% of the reference depth remains. The [episode-counting rule](./#detachment/measure) differs from the price-gap stall rule.

## What uncertainty means

A middle outcome range describes differences across histories. A [confidence interval](./#glossary/confidence-interval) describes uncertainty in a stated mean or probability. A [standard error](./#glossary/standard-error) also describes uncertainty in an estimate.

Overlapping windows share market moves. Their effective count estimates how much independent market history the test contains. Intervals from rebuilt histories describe variation obtained from the original price history.

[← previous](./#overview)[next $\to$](./#earnings/measure)


# A. How pool shares earn returns {#earnings}

**A pool share’s value depends on prices, trading and outside funding.**

- [A1 What a pool share is worth](./#earnings/measure) — [Market value](./#glossary/market-value) tells us what a pool share is worth at prices outside the pool.
- [A2 Where a pool share’s return comes from](./#earnings/equation) — A pool share’s return comes from price changes, pool operations and outside funding.
- [A3 What contributed to the live pools’ returns](./#earnings/live) — In the live pools, fees almost fully repay the losses from trades at outdated prices.


# A1 What a pool share is worth {#earnings/measure}

**[Market value](./#glossary/market-value) tells us what a pool share is worth at prices outside the pool.**

A [liquidity pool](./#glossary/liquidity-pool) holds cash and an asset whose price can change. An [LP](./#glossary/lp), a liquidity provider, owns a share of both. Value the coins at prices outside the pool, then divide by the number of shares.

[LP/xyk](./#glossary/lp-xyk) measures growth beyond a reference pool after the [donation](./#glossary/donation) charge. Donations are capital supplied from outside the pool. The reference pool starts with equal values in cash and the risky asset. It charges no fees and keeps the product of its asset quantities constant.

> **Common misunderstanding:** “Donations are earnings of the pool.”
>
> **What is true.**
>
> Donations bring outside capital into the pool. Interest paid by the YB holder funds them. LP/xyk subtracts the donation charge, so donated value never counts as the pool's own earnings.

**Measure:** LP/xyk, in [percentage points](./#glossary/percentage-point) per year after the donation charge.

**Compared:** An actual LP share with the fee-free constant-product reference pool.

**Same for both:** The market-price history.

**Higher means:** More growth beyond the reference pool after the donation charge.

[M](./#glossary/m) divides market value per share by the reference pool’s price factor. LP/xyk takes M’s yearly [log growth](./#glossary/log-growth) and subtracts the donation charge. First divide final value by starting value. The natural logarithm of that ratio gives the log change.

Measuring each share separates existing holders’ gains from new deposits. Both policies share the reference pool when compared on the same dates. That reference therefore cancels from their growth difference. Different donation charges still change their LP/xyk difference.

**More detail**

The formula calculates the market value of each share compared with the reference pool.

$M=(x+Py)/(2\sqrt{P}\,\text{LP supply})$

| Symbol | Meaning | 
| --- | --- |
| x | Cash held | 
| y | Risky asset held | 
| P | The risky asset’s price outside the pool | 

To calculate LP/xyk, first divide final M by starting M. Take the natural logarithm of that ratio. Multiply by 100 and divide by elapsed years. Subtract the realised yearly log charge for donated shares over the same period.

### A worked example

This example keeps the number of LP shares fixed. [crvUSD](./#glossary/crvusd) is the cash asset. [ETH](./#glossary/eth) is the asset whose price changes.

| At the start | Amount | 
| --- | --- |
| Cash | 1,000,000 crvUSD | 
| ETH held | 500 ETH | 
| Price of ETH | 2,000 crvUSD per ETH | 
| Total pool value | 2,000,000 crvUSD | 

At a final price of 8,000 crvUSD per ETH, compare the following values.

| Investment | Final value, crvUSD | 
| --- | --- |
| Fee-free reference pool | 4,000,000 | 
| Example pool, with the same share count | 4,200,000 | 

The example pool beats the reference pool by 5%, before any donation deduction.

**More detail**

| Investment or difference | Final value, crvUSD | 
| --- | --- |
| Holding the opening coins | 5,000,000 | 
| Fee-free reference pool | 4,000,000 | 
| Shortfall of the reference pool against holding | 1,000,000 | 

That shortfall is called [impermanent loss](./#glossary/impermanent-loss). M records the example pool’s 5% gain over the reference. M’s absolute level depends on the chosen unit for shares.

### Market value and internal accounting

Market value prices the actual coins at prices outside the pool. [Virtual price](./#glossary/virtual-price) is the pool’s separate accounting index for each share. The [invariant](./#glossary/invariant), a value identifying the pool’s reserve curve, helps determine that index. The calculation also uses [price_scale](./#glossary/price_scale), the pool’s central price.

The accounting index can stay high while the share’s market value grows more slowly than the fee-free reference pool.

Two ways to value a pool share
| Measure | How the value is calculated | Question answered | 
| --- | --- | --- |
| Market value per LP share | External market price | What the assets are worth outside the pool | 
| Virtual price | Capital from the invariant, adjusted using price_scale | The accounting index protected by the spending rule | 

LP/xyk uses market value and subtracts the donation charge. Virtual price uses the invariant per share. Donations can support the accounting budget. They supply outside capital rather than earnings from the pool.

**More detail**

Moving price_scale changes virtual price without changing the coins’ total market value at that instant. A [burn](./#glossary/burn) removes shares from supply. Burning donated shares at the same time can raise the value of each remaining share. Later trades can change market value.

The [profit floor](./#repeg/protection) limits the accounting change.

The [shared conventions](./#settings) explain the yearly return rates.

[← previous](./#settings)[next $\to$](./#earnings/equation)


# A2 Where a pool share’s return comes from {#earnings/equation}

**A pool share’s return comes from price changes, pool operations and outside funding.**

An [LP](./#glossary/lp) share represents ownership of part of the pool. [LP/xyk](./#glossary/lp-xyk) measures its growth beyond a reference pool after the [donation](./#glossary/donation) charge. The same contribution names and colours appear throughout the site.

The reference pool charges no fees and follows the same prices. Its trades keep the product of its asset quantities constant.

| Contribution to LP/xyk | What it measures | 
| --- | --- |
| Harvesting | The gain from restoring chosen asset proportions at current market prices. | 
| Price direction | The effect of holding more or less than half the pool’s value in the risky asset. | 
| Approximation remainder | The difference needed to recover the exact return on the assets held. | 
| Pool operations, including fees | Changes caused by trades, deposits, withdrawals and removal of shares. | 
| Subtract the donation charge | Remove the outside capital supplied through donated shares. | 

Add harvesting, direction, the approximation remainder and the effect of pool operations. Then subtract the donation charge to obtain LP/xyk.

Price moves change the value of coins already held. Harvesting and direction approximate that change compared with the reference pool. The remainder makes the calculation exact.

Pool operations then change value per share. Each operation’s contribution includes its fees. Subtracting the donation charge removes the outside capital supplied.

[Arbitrage](./#glossary/arbitrage) traders profit from price differences. Their trades are one group of pool operations. Customer activity supplies native fees: fees from users’ trades and other operations. [Financing](./#glossary/financing) supplies outside capital to the pool.

The [live-return chart](./#earnings/live) uses the pool’s changing holdings. The simple formula uses only the proportions at the start.

**More detail**

For each market-price move, value the existing coins at the new price. Subtract the reference pool’s growth to obtain the return above that reference.

- For harvesting, multiply the risky asset’s share of pool value by the cash share. Multiply half that product by the squared log-price move.
- For direction, subtract half from the risky share. Multiply that difference by the log-price move.
- The remainder closes the gap to the exact return on the coins held.
- Add the contributions across [blockchain blocks](./#glossary/blockchain-block) and convert the sum to a yearly rate.

The [shared conventions](./#settings) explain the yearly return rates.

[← previous](./#earnings/measure)[next $\to$](./#earnings/live)


# A3 What contributed to the live pools’ returns {#earnings/live}

**In the live pools, fees almost fully repay the losses from trades at outdated prices.**

Arbitrageurs trade to profit from differences between market and pool prices. Their trades can take value from the pool before fees. That loss is called [LVR](./#glossary/lvr). Fees paid by these traders repay almost all of it in the live pools.

[LP/xyk](./#glossary/lp-xyk) measures growth of each pool share beyond a reference pool after the [donation](./#glossary/donation) charge. The reference pool charges no fees and follows the same prices. Its trades keep the product of its asset quantities constant.

**Measure:** Each contribution to LP/xyk, in [percentage points](./#glossary/percentage-point) per year.

**Compared:** The selected live pool with its fee-free constant-product reference pool.

**Same for both:** The selected period and observed market prices.

**Higher means:** A larger contribution to LP/xyk.

- [WETH](./#glossary/weth) grows faster than the reference after the donation charge: LP/xyk is +4.48 pp/yr over the full study period.
- The losses and fees almost cancel. [Arbitrage](./#glossary/arbitrage) trades contribute −18.78 pp/yr before fees. Those traders’ fees contribute +18.33 pp/yr.
- WETH’s LP/xyk deducts 4.98 pp/yr for capital supplied through donated shares.

| Live study period | Date | 
| --- | --- |
| Start | 26 May 2026 [UTC](./#glossary/utc) | 
| End | 1 October 2026 UTC | 

Expressing returns as yearly rates makes different periods comparable. The conversion does not predict that the same return will continue.

> **Common misunderstanding:** “A yearly rate tells us next year's return.”
>
> **What is true.**
>
> Yearly rates make periods of different lengths comparable. A rate measured over a few months does not predict the next year. The market's direction changes results from one window to the next.

Pool: WETH, WBTC, cbBTC or tBTC.

Period: Full study period, May, observed days, June, July, August or September.

Each bar shows one contribution to WETH LP/xyk, in percentage points per year. LP/xyk measures growth per share above the same-price reference pool, after the donation charge. The final bar adds the contributions. User-activity contributions already include their fees.

The selected period starts on 26 May 2026. It ends on 1 October 2026.

Monthly gains or losses from holding risky assets are much larger than the post’s claimed gain. That contribution changes sign. The trading-loss and fee bars nearly cancel. The result from coins held changes with the amount of risky assets held.

For [tBTC](./#glossary/tbtc), the contribution from price direction is −13.73 pp/yr in June and +14.34 pp/yr in July. Price direction therefore accounts for a large part of the measured return in those months.

### Harvesting and user activity

Native activity means customer trading and other user operations. Over the live WETH period, this activity supplies +1.95 pp/yr in fees. Including the effects of execution, its contribution is +1.25 pp/yr. That last figure already includes the fees.

The contribution from user activity already includes its fees.
| Pool | Harvesting after arbitrage losses and fees, pp/yr | Fees from user activity, pp/yr | User activity including fees, pp/yr | Donation charge, pp/yr | Contribution from price direction, pp/yr | 
| --- | --- | --- | --- | --- | --- |
| WETH | +2.95 | +1.95 | +1.25 | −4.98 | +0.86 | 
| [WBTC](./#glossary/wbtc) | +2.00 | +0.74 | +0.43 | −0.62 | −5.12 | 
| [cbBTC](./#glossary/cbbtc) | +1.95 | +1.05 | +1.05 | −0.57 | −0.31 | 
| tBTC | +1.83 | +0.54 | +0.27 | −0.52 | −4.84 | 

- Harvesting after arbitrage adds the fees to harvesting and subtracts losses from trades at outdated prices.
- The user-activity contribution adds its fees to its effect on execution.
- Total LP/xyk also includes price direction, other operations and the donation charge.

**More detail**

| Native activity | Meaning | 
| --- | --- |
| Customer swaps | Customer trades between the pool’s assets | 
| [LT](./#glossary/lt) deposits and withdrawals | Changes in capital using the YieldBasis liquidity token | 
| [VirtualPool](./#glossary/virtualpool) operations | Operations through a contract that routes trades | 

The study groups contracts with unknown purposes with arbitrage. Changing that grouping changes the split but preserves total return. Each chart bar measures its group’s contribution to the value of each [LP](./#glossary/lp) share.

“Other operations” includes VirtualPool activity, creation of donated shares, maintenance and remaining liquidity operations.

The [shared conventions](./#settings) explain the yearly return rates.

[← previous](./#earnings/equation)[next $\to$](./#harvesting/rebalancing)

**Chart data $\cdot$ WETH $\cdot$ Full study period $\cdot$ 26 May 2026 to 1 October 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +3.40 | 
| Price direction | +0.86 | 
| Approximation remainder | +0.000 | 
| Arbitrage trades before fees | −18.78 | 
| Fees from arbitrageurs | +18.33 | 
| Price adjustments and share removal | +4.40 | 
| Customer trades, including fees | +0.22 | 
| LT deposits, including fees | +0.96 | 
| LT withdrawals, including fees | +0.06 | 
| Other operations, including fees | +0.001 | 
| Donation charge | −4.98 | 
| LP/xyk | +4.48 | 

**Chart data $\cdot$ WETH $\cdot$ June $\cdot$ 1 June 2026 to 1 July 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +5.49 | 
| Price direction | +3.63 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −30.94 | 
| Fees from arbitrageurs | +31.94 | 
| Price adjustments and share removal | +3.65 | 
| Customer trades, including fees | +0.52 | 
| LT deposits, including fees | +1.35 | 
| LT withdrawals, including fees | +0.09 | 
| Other operations, including fees | +0.001 | 
| Donation charge | −4.98 | 
| LP/xyk | +10.76 | 

**Chart data $\cdot$ WETH $\cdot$ July $\cdot$ 1 July 2026 to 1 August 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +2.55 | 
| Price direction | +0.34 | 
| Approximation remainder | +0.000 | 
| Arbitrage trades before fees | −12.05 | 
| Fees from arbitrageurs | +11.57 | 
| Price adjustments and share removal | +4.42 | 
| Customer trades, including fees | +0.01 | 
| LT deposits, including fees | +0.50 | 
| LT withdrawals, including fees | +0.02 | 
| Other operations, including fees | +0.002 | 
| Donation charge | −4.98 | 
| LP/xyk | +2.40 | 

**Chart data $\cdot$ WETH $\cdot$ August $\cdot$ 1 August 2026 to 1 September 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +3.00 | 
| Price direction | −0.28 | 
| Approximation remainder | +0.000 | 
| Arbitrage trades before fees | −19.53 | 
| Fees from arbitrageurs | +17.86 | 
| Price adjustments and share removal | +5.13 | 
| Customer trades, including fees | +0.24 | 
| LT deposits, including fees | +0.31 | 
| LT withdrawals, including fees | +0.05 | 
| Other operations, including fees | +0.002 | 
| Donation charge | −4.98 | 
| LP/xyk | +1.80 | 

**Chart data $\cdot$ WETH $\cdot$ September $\cdot$ 1 September 2026 to 1 October 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +2.88 | 
| Price direction | −0.20 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −15.31 | 
| Fees from arbitrageurs | +14.74 | 
| Price adjustments and share removal | +5.03 | 
| Customer trades, including fees | +0.01 | 
| LT deposits, including fees | +1.90 | 
| LT withdrawals, including fees | +0.09 | 
| Other operations, including fees | −0.003 | 
| Donation charge | −4.96 | 
| LP/xyk | +4.18 | 

**Chart data $\cdot$ WETH $\cdot$ May $\cdot$ 26 May 2026 to 1 June 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +2.12 | 
| Price direction | +0.85 | 
| Approximation remainder | +0.000 | 
| Arbitrage trades before fees | −6.16 | 
| Fees from arbitrageurs | +5.55 | 
| Price adjustments and share removal | +1.03 | 
| Customer trades, including fees | +0.80 | 
| LT deposits, including fees | +0.05 | 
| LT withdrawals, including fees | +0.03 | 
| Other operations, including fees | +0.006 | 
| Donation charge | −5.02 | 
| LP/xyk | −0.75 | 

**Chart data $\cdot$ WBTC $\cdot$ Full study period $\cdot$ 26 May 2026 to 1 October 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +2.18 | 
| Price direction | −5.12 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −8.28 | 
| Fees from arbitrageurs | +8.10 | 
| Price adjustments and share removal | +0.57 | 
| Customer trades, including fees | +0.02 | 
| LT deposits and withdrawals, including fees | +0.41 | 
| Other operations, including fees | −0.001 | 
| Donation charge | −0.62 | 
| LP/xyk | −2.73 | 

**Chart data $\cdot$ WBTC $\cdot$ May $\cdot$ 26 May 2026 to 1 June 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +1.61 | 
| Price direction | −1.21 | 
| Approximation remainder | +0.000 | 
| Arbitrage trades before fees | −2.05 | 
| Fees from arbitrageurs | +1.92 | 
| Price adjustments and share removal | +0.11 | 
| Customer trades, including fees | +0.01 | 
| LT deposits and withdrawals, including fees | +0.22 | 
| Other operations, including fees | +0.002 | 
| Donation charge | −0.41 | 
| LP/xyk | +0.20 | 

**Chart data $\cdot$ WBTC $\cdot$ June $\cdot$ 1 June 2026 to 1 July 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +3.60 | 
| Price direction | −7.60 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −14.62 | 
| Fees from arbitrageurs | +14.58 | 
| Price adjustments and share removal | +0.35 | 
| Customer trades, including fees | +0.13 | 
| LT deposits and withdrawals, including fees | +0.54 | 
| Other operations, including fees | +0.000 | 
| Donation charge | −0.44 | 
| LP/xyk | −3.46 | 

**Chart data $\cdot$ WBTC $\cdot$ July $\cdot$ 1 July 2026 to 1 August 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +1.56 | 
| Price direction | +8.33 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −8.63 | 
| Fees from arbitrageurs | +8.34 | 
| Price adjustments and share removal | +0.44 | 
| Customer trades, including fees | +0.01 | 
| LT deposits and withdrawals, including fees | +0.11 | 
| Other operations, including fees | −0.003 | 
| Donation charge | −0.41 | 
| LP/xyk | +9.75 | 

**Chart data $\cdot$ WBTC $\cdot$ August $\cdot$ 1 August 2026 to 1 September 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +1.78 | 
| Price direction | −13.49 | 
| Approximation remainder | +0.000 | 
| Arbitrage trades before fees | −6.89 | 
| Fees from arbitrageurs | +6.54 | 
| Price adjustments and share removal | +0.50 | 
| Customer trades, including fees | −0.02 | 
| LT deposits and withdrawals, including fees | +0.77 | 
| Other operations, including fees | −0.001 | 
| Donation charge | −0.78 | 
| LP/xyk | −11.59 | 

**Chart data $\cdot$ WBTC $\cdot$ September $\cdot$ 1 September 2026 to 1 October 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +1.92 | 
| Price direction | −8.67 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −4.26 | 
| Fees from arbitrageurs | +4.23 | 
| Price adjustments and share removal | +1.10 | 
| Customer trades, including fees | −0.01 | 
| LT deposits and withdrawals, including fees | +0.25 | 
| Other operations, including fees | +0.000 | 
| Donation charge | −0.92 | 
| LP/xyk | −6.35 | 

**Chart data $\cdot$ cbBTC $\cdot$ Full study period $\cdot$ 26 May 2026 to 1 October 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +2.22 | 
| Price direction | −0.31 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −9.59 | 
| Fees from arbitrageurs | +9.32 | 
| Price adjustments and share removal | +0.55 | 
| Customer trades, including fees | +0.01 | 
| LT deposits and withdrawals, including fees | +1.04 | 
| Other operations, including fees | −0.004 | 
| Donation charge | −0.57 | 
| LP/xyk | +2.67 | 

**Chart data $\cdot$ cbBTC $\cdot$ May $\cdot$ 26 May 2026 to 1 June 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +1.61 | 
| Price direction | −1.19 | 
| Approximation remainder | +0.000 | 
| Arbitrage trades before fees | −2.10 | 
| Fees from arbitrageurs | +1.98 | 
| Price adjustments and share removal | +0.15 | 
| Customer trades, including fees | +0.10 | 
| LT deposits and withdrawals, including fees | +0.04 | 
| Other operations, including fees | +0.005 | 
| Donation charge | −0.41 | 
| LP/xyk | +0.18 | 

**Chart data $\cdot$ cbBTC $\cdot$ June $\cdot$ 1 June 2026 to 1 July 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +3.56 | 
| Price direction | −12.51 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −13.03 | 
| Fees from arbitrageurs | +12.75 | 
| Price adjustments and share removal | +0.34 | 
| Customer trades, including fees | +0.02 | 
| LT deposits and withdrawals, including fees | +0.14 | 
| Other operations, including fees | +0.000 | 
| Donation charge | −0.44 | 
| LP/xyk | −9.17 | 

**Chart data $\cdot$ cbBTC $\cdot$ July $\cdot$ 1 July 2026 to 1 August 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +1.55 | 
| Price direction | +13.41 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −8.26 | 
| Fees from arbitrageurs | +7.96 | 
| Price adjustments and share removal | +0.47 | 
| Customer trades, including fees | +0.00 | 
| LT deposits and withdrawals, including fees | +0.08 | 
| Other operations, including fees | −0.003 | 
| Donation charge | −0.41 | 
| LP/xyk | +14.81 | 

**Chart data $\cdot$ cbBTC $\cdot$ August $\cdot$ 1 August 2026 to 1 September 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +1.83 | 
| Price direction | −3.15 | 
| Approximation remainder | +0.000 | 
| Arbitrage trades before fees | −7.49 | 
| Fees from arbitrageurs | +7.07 | 
| Price adjustments and share removal | +0.39 | 
| Customer trades, including fees | +0.01 | 
| LT deposits and withdrawals, including fees | +0.23 | 
| Other operations, including fees | +0.001 | 
| Donation charge | −0.46 | 
| LP/xyk | −1.58 | 

**Chart data $\cdot$ cbBTC $\cdot$ September $\cdot$ 1 September 2026 to 1 October 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +2.11 | 
| Price direction | +0.81 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −11.20 | 
| Fees from arbitrageurs | +11.07 | 
| Price adjustments and share removal | +1.09 | 
| Customer trades, including fees | −0.03 | 
| LT deposits and withdrawals, including fees | +3.99 | 
| Other operations, including fees | −0.014 | 
| Donation charge | −0.98 | 
| LP/xyk | +6.83 | 

**Chart data $\cdot$ tBTC $\cdot$ Full study period $\cdot$ 26 May 2026 to 1 October 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +2.16 | 
| Price direction | −4.84 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −7.82 | 
| Fees from arbitrageurs | +7.49 | 
| Price adjustments and share removal | +0.50 | 
| Customer trades, including fees | +0.01 | 
| LT deposits and withdrawals, including fees | +0.27 | 
| Other operations, including fees | −0.003 | 
| Donation charge | −0.52 | 
| LP/xyk | −2.76 | 

**Chart data $\cdot$ tBTC $\cdot$ May $\cdot$ 26 May 2026 to 1 June 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +1.61 | 
| Price direction | −1.28 | 
| Approximation remainder | +0.000 | 
| Arbitrage trades before fees | −2.06 | 
| Fees from arbitrageurs | +1.89 | 
| Price adjustments and share removal | +0.13 | 
| Customer trades, including fees | +0.00 | 
| LT deposits and withdrawals, including fees | +0.09 | 
| Other operations, including fees | +0.005 | 
| Donation charge | −0.41 | 
| LP/xyk | −0.03 | 

**Chart data $\cdot$ tBTC $\cdot$ June $\cdot$ 1 June 2026 to 1 July 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +3.55 | 
| Price direction | −13.73 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −12.78 | 
| Fees from arbitrageurs | +12.27 | 
| Price adjustments and share removal | +0.36 | 
| Customer trades, including fees | +0.04 | 
| LT deposits and withdrawals, including fees | +0.15 | 
| Other operations, including fees | +0.000 | 
| Donation charge | −0.44 | 
| LP/xyk | −10.58 | 

**Chart data $\cdot$ tBTC $\cdot$ July $\cdot$ 1 July 2026 to 1 August 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +1.54 | 
| Price direction | +14.34 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −8.60 | 
| Fees from arbitrageurs | +8.22 | 
| Price adjustments and share removal | +0.46 | 
| Customer trades, including fees | +0.03 | 
| LT deposits and withdrawals, including fees | +0.49 | 
| Other operations, including fees | −0.013 | 
| Donation charge | −0.42 | 
| LP/xyk | +16.05 | 

**Chart data $\cdot$ tBTC $\cdot$ August $\cdot$ 1 August 2026 to 1 September 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +1.77 | 
| Price direction | −12.70 | 
| Approximation remainder | +0.000 | 
| Arbitrage trades before fees | −6.52 | 
| Fees from arbitrageurs | +6.12 | 
| Price adjustments and share removal | +0.39 | 
| Customer trades, including fees | −0.02 | 
| LT deposits and withdrawals, including fees | +0.35 | 
| Other operations, including fees | 0.000 | 
| Donation charge | −0.45 | 
| LP/xyk | −11.05 | 

**Chart data $\cdot$ tBTC $\cdot$ September $\cdot$ 1 September 2026 to 1 October 2026**

Contribution to LP/xyk, pp/yr
| Contribution | Contribution to LP/xyk, pp/yr | 
| --- | --- |
| Harvesting | +1.93 | 
| Price direction | −8.35 | 
| Approximation remainder | 0.000 | 
| Arbitrage trades before fees | −4.53 | 
| Fees from arbitrageurs | +4.47 | 
| Price adjustments and share removal | +0.85 | 
| Customer trades, including fees | −0.02 | 
| LT deposits and withdrawals, including fees | +0.09 | 
| Other operations, including fees | +0.001 | 
| Donation charge | −0.80 | 
| LP/xyk | −6.35 |


# B. Rebalancing gains, trading losses and fees {#harvesting}

**Rebalancing earns gains that trading losses and fees can change.**

- [B1 How rebalancing earns a gain](./#harvesting/rebalancing) — Restoring equal asset values earns extra growth compared with the reference pool.
- [B2 Why outdated prices cost the pool money](./#harvesting/lvr) — Trading at outdated prices costs the pool value before fees.
- [B3 How fees repay the trading loss](./#harvesting/fees) — Trading fees repay almost all the pool’s losses from trades at outdated prices.
- [B4 What prices and starting holdings explain](./#harvesting/formula) — A simple formula explains most of the [WETH](./#glossary/weth) pool’s return, given the recorded market prices.
- [B5 Two common misunderstandings about harvesting](./#harvesting/parameters) — Two common beliefs about [volatility harvesting](./#glossary/volatility-harvesting) do not hold up.


# B1 How rebalancing earns a gain {#harvesting/rebalancing}

**Restoring equal asset values earns extra growth compared with the reference pool.**

Rebalancing means trading to restore chosen proportions of the assets. A portfolio holding equal values sells after price rises and buys after falls. [Volatility harvesting](./#glossary/volatility-harvesting) is the return from restoring those proportions at current market prices.

The example compares rebalancing with holding the opening coins. The formula later compares growth with a different reference: a fee-free constant-product pool. That pool trades while keeping the product of its asset quantities constant.

[LVR](./#glossary/lvr) measures losses from trading at outdated pool prices. Reserve trades are the trades that rebalance the pool’s holdings. It compares them with execution at current market prices.

### An illustrative rise and fall

**Measure:** Ending wealth, as a percentage of starting wealth.

**Compared:** Rebalancing after the rise with holding the opening coins.

**Same for both:** The illustrative price rise and fall.

**Higher means:** More wealth at the end of the example.

The example starts with equal values in cash and the risky asset. The asset price rises 10%, then the portfolio restores equal values. The price then falls 10% from its new level. A fall by the same percentage does not undo the rise.

> **Common misunderstanding:** “A 10% fall undoes a 10% rise.”
>
> **What is true.**
>
> Percentage moves compound. After a 10% rise, a 10% fall leaves the price at 99% of its start. Each percentage change applies to the price reached after the move before it.

Illustrative ending values
| Strategy | Final value divided by starting value | 
| --- | --- |
| Hold the starting coins | 0.9950 | 
| Rebalance after the rise | 0.9975 | 

Rebalancing ends with more wealth: 99.75% of starting value, compared with 99.50% from holding the coins. The difference is 0.25% of starting value. This example illustrates the mechanism rather than estimating a YB outcome.

> **Common misunderstanding:** “Harvesting [volatility](./#glossary/volatility) guarantees a gain.”
>
> **What is true.**
>
> In this rise-and-fall example, rebalancing loses less than holding the opening coins. It ends at 99.75% of starting wealth. Holding ends at 99.50%. Both lose money.

**More detail**

**Measure:** [Log growth](./#glossary/log-growth) above the reference pool over the observed period.

**Compared:** Continuous rebalancing to equal values with the fee-free constant-product reference pool.

**Same for both:** The price history.

**Higher means:** More harvesting above that reference.

First divide final value by starting value. Take the natural logarithm of that ratio for the log change. The model rebalances continuously at current market prices. Its yearly log growth exceeds the square-root-price reference by annual price variance divided by 8.

The reference pool’s price factor follows the square root of the market price. For an observed period, the corresponding premium is [QV](./#glossary/qv) divided by 8. QV sums squared log-price changes across [blockchain blocks](./#glossary/blockchain-block).

Convert that period’s total to a yearly rate before comparing returns. Beating the strategy of holding opening coins also depends on the final price.

The [shared conventions](./#settings) explain the yearly return rates.

[← previous](./#earnings/live)[next $\to$](./#harvesting/lvr)


# B2 Why outdated prices cost the pool money {#harvesting/lvr}

**Trading at outdated prices costs the pool value before fees.**

An automated market maker, or [AMM](./#glossary/amm), trades under programmed rules. An arbitrageur trades to profit from price differences. The trader buys coins the pool offers too cheaply or sells coins the pool buys too dearly.

[LVR](./#glossary/lvr) is the loss from making reserve trades at outdated prices. It compares those trades with the same trades at current market prices. The measure excludes fees, which repay part of the loss.

**Measure:** Loss from execution, as a fraction of pool value before fees.

**Compared:** Reserve trades at outdated pool prices with the same trades at current market prices.

**Same for both:** The price moves.

**Higher means:** More LVR, the loss from trading at outdated prices.

**More detail**

A constant-product pool keeps the product of its two asset quantities constant. For a small price move, take the logarithm of the price ratio. Square that change and divide by 8.

The result approximates the execution loss as a fraction of pool value when the pool charges no fees. The comparison uses the same rebalance at the new market price.

Adding these losses across the period gives [QV](./#glossary/qv) divided by 8. QV sums squared log-price changes. Divide by elapsed years for a yearly rate.

The [shared conventions](./#settings) explain the yearly return rates.

[← previous](./#harvesting/rebalancing)[next $\to$](./#harvesting/fees)


# B3 How fees repay the trading loss {#harvesting/fees}

**Trading fees repay almost all the pool’s losses from trades at outdated prices.**

Arbitrageurs trade to profit from differences between pool and market prices. [LVR](./#glossary/lvr) measures the pool’s loss on those trades before fees. Across the live pools, fees cover 95.8% to 97.9% of these losses.

> **Common misunderstanding:** “[Arbitrage](./#glossary/arbitrage) traders drain the pool's [LPs](./#glossary/lp).”
>
> **What is true.**
>
> Arbitrage does take value from the pool. LVR measures that loss before fees. On the live pools, fees repay 95.8% to 97.9% of it.

**Measure:** Fees received, as a percentage of losses from arbitrage trades before fees.

**Compared:** [Arbitrage fees](./#glossary/arbitrage-fees) with arbitrage execution losses for each live pool.

**Same for both:** The live study period.

**Higher means:** The fees repay more of the loss from outdated prices.

| Study period | Date | 
| --- | --- |
| Start | 26 May 2026 | 
| End | 1 October 2026 | 

### Why a fee creates a no-trade range

The typical fee in the live [WETH](./#glossary/weth) period is about 1.5% of trade value. A buyer needs a price advantage larger than the buying fee to profit. A seller needs an advantage larger than the selling fee.

The [fee band](./#glossary/fee-band) is the range where those advantages cannot cover fees. The range extends on both sides of the market price. Traders keep only the extra price advantage beyond the fee once a move crosses that range.

Execution loss equals the fees received plus the trader’s remaining profit. When moves between [blockchain blocks](./#glossary/blockchain-block) are small compared with the fee, that remaining profit is small. Fees therefore repay most of LVR.

**Measure:** Profit after fees divided by fees paid, expressed as a percentage.

**Compared:** The fee-band model’s estimate with the observed pool result.

**Same for both:** The live study period.

**Higher means:** Traders retain more profit for each unit of fee paid.

Profit retained by arbitrageurs after fees
| Pool | Model: profit after fees / fees paid, % | Observed: profit after fees / fees paid, % | 
| --- | --- | --- |
| WETH | 8.0 | 2.5 | 
| [WBTC](./#glossary/wbtc) | 4.2 | 2.2 | 
| [cbBTC](./#glossary/cbbtc) | 4.4 | 3.0 | 
| [tBTC](./#glossary/tbtc) | 4.4 | 4.4 | 

**More detail**

The model lets the gap between pool and market prices move with the market. Arbitrage then pushes the gap back at either fee boundary. The accumulated corrections represent reserve trades.

On the Bitcoin histories, simulated arbitrageurs retain 4.7% to 4.9% of fees paid. Identified live bots retain 2.5% to 3.6%. The simulator assumes immediate trading without transaction costs or competition.

The table uses a broader arbitrage group that includes contracts with unknown purposes.

**More detail: limits of the fee-band model**

The shortcut cannot resolve the difference between proposed and current rules. It compares the proposal-minus-current arbitrage return after fees with the simulator’s measured difference.

| Period | Shortcut error, % of the simulator’s measured difference | 
| --- | --- |
| 7 days | 74% | 
| 30 days | 85% | 

The shortcut explains why fees almost offset execution losses. Its errors are too large to resolve the difference between the policies.

The [shared conventions](./#settings) explain the yearly return rates.

[← previous](./#harvesting/lvr)[next $\to$](./#harvesting/formula)


# B4 What prices and starting holdings explain {#harvesting/formula}

**A simple formula explains most of the [WETH](./#glossary/weth) pool’s return, given the recorded market prices.**

WETH is the token form of [ETH](./#glossary/eth) used in these pools. [LP/xyk](./#glossary/lp-xyk) measures growth beyond a reference pool after the [donation](./#glossary/donation) charge. The reference pool charges no fees and follows the same prices. Its trades keep the product of its two asset quantities constant.

**Measure:** LP/xyk, in [percentage points](./#glossary/percentage-point) per year.

**Compared:** The formula’s estimate with the observed WETH pool return.

**Same for both:** The starting states, selected periods and recorded market prices.

**Higher means:** A higher estimated return.

Accuracy means that the estimate is close to the observed value. The formula uses price moves and the starting share of value held in the risky asset. It adds harvesting to the contribution from price direction.

[Skill](./#glossary/skill) measures how much prediction error a method removes. The comparison here uses the [squared error](./#glossary/squared-error) from predicting zero LP/xyk. Squared error is the square of the difference between the predicted and observed values.

The formula removes most of that error for WETH. Its improvement is strong over a week but weaker over a month for the combined Bitcoin wrapper pools.

Improvement over predicting zero LP/xyk
| Pools and formula | Period | Squared error removed, % | 
| --- | --- | --- |
| WETH, simple formula | 7 days | 64.6% | 
| WETH, simple formula | 30 days | 87.1% | 
| Bitcoin wrapper pools, full formula | 7 days | 75.6% | 
| Bitcoin wrapper pools, full formula | 30 days | 21.9% | 

A [wrapper token](./#glossary/wrapper-token) represents another asset on this blockchain. The [prediction-accuracy page](./#simulation/skill) explains the scoring comparison.

At equal starting asset values, the contribution from price direction vanishes. The formula then gives [QV](./#glossary/qv) divided by 8. QV sums squared log-price changes. This estimates LP/xyk when the other return contributions largely offset each other.

**More detail**
- For harvesting, multiply the risky asset’s starting share of pool value by the cash share. Multiply half that product by QV.
- For direction, subtract half from the starting risky share. Multiply that difference by the period’s log-price change.
- Add these contributions above the square-root-price reference. Multiply by 100 and divide by elapsed years to express the estimate in pp/yr.

Period: 7 days or 30 days.

The simple formula explains most of the WETH result. Each point compares estimated and observed LP/xyk for a 7-day period. Both axes use percentage points per year. The point’s tooltip gives its starting date.

The diagonal marks equal estimated and observed returns. The formula’s parameters were not fitted to these outcomes.

The return equation also distinguishes [LVR](./#glossary/lvr), losses from trading at outdated prices. [Arbitrage fees](./#glossary/arbitrage-fees) are the fees paid by traders profiting from price differences.

The [shared conventions](./#settings) explain the yearly return rates.

[← previous](./#harvesting/fees)[next $\to$](./#harvesting/parameters)

**Chart data $\cdot$ WETH: the formula estimate and observed return $\cdot$ 7-day periods**

LP/xyk over the selected period, pp/yr
| Start date | Formula estimate of LP/xyk, pp/yr | Observed LP/xyk, pp/yr | 
| --- | --- | --- |
| 2026-06-02 | +10.28 | +29.62 | 
| 2026-06-03 | +10.28 | +29.75 | 
| 2026-06-04 | +10.16 | +28.80 | 
| 2026-06-05 | +9.24 | +21.91 | 
| 2026-06-06 | +6.41 | +11.69 | 
| 2026-06-07 | +5.16 | +4.74 | 
| 2026-06-08 | +4.23 | +3.67 | 
| 2026-06-09 | +3.80 | +1.16 | 
| 2026-06-10 | +3.57 | +2.44 | 
| 2026-06-11 | +3.49 | +1.32 | 
| 2026-06-12 | +3.36 | +0.78 | 
| 2026-06-13 | +3.32 | +0.62 | 
| 2026-06-14 | +3.49 | +1.20 | 
| 2026-06-15 | +3.40 | +0.91 | 
| 2026-06-16 | +3.32 | +5.00 | 
| 2026-06-17 | +3.24 | +5.20 | 
| 2026-06-18 | +3.42 | +4.83 | 
| 2026-06-19 | +4.07 | +6.68 | 
| 2026-06-20 | +4.93 | +10.15 | 
| 2026-06-21 | +4.87 | +9.84 | 
| 2026-06-22 | +4.99 | +10.24 | 
| 2026-06-23 | +5.26 | +9.37 | 
| 2026-06-24 | +5.17 | +6.33 | 
| 2026-06-25 | +4.86 | +7.51 | 
| 2026-06-26 | +4.36 | +5.23 | 
| 2026-06-27 | +3.60 | +2.41 | 
| 2026-06-28 | +3.66 | +2.45 | 
| 2026-06-29 | +3.60 | +2.89 | 
| 2026-06-30 | +3.50 | +4.12 | 
| 2026-07-01 | +3.55 | +5.14 | 
| 2026-07-02 | +3.34 | +2.99 | 
| 2026-07-03 | +2.98 | +2.81 | 
| 2026-07-04 | +2.89 | +2.71 | 
| 2026-07-05 | +2.78 | +2.57 | 
| 2026-07-06 | +2.68 | +1.58 | 
| 2026-07-07 | +2.53 | +1.57 | 
| 2026-07-08 | +2.48 | +0.94 | 
| 2026-07-09 | +2.42 | +2.31 | 
| 2026-07-10 | +2.46 | +2.95 | 
| 2026-07-11 | +2.49 | +2.28 | 
| 2026-07-12 | +2.39 | +2.69 | 
| 2026-07-13 | +2.39 | +3.80 | 
| 2026-07-14 | +2.38 | +1.65 | 
| 2026-07-15 | +2.21 | +1.70 | 
| 2026-07-16 | +2.12 | +0.05 | 
| 2026-07-17 | +2.02 | −0.61 | 
| 2026-07-18 | +1.90 | +1.71 | 
| 2026-07-19 | +1.87 | +1.25 | 
| 2026-07-20 | +1.87 | +2.03 | 
| 2026-07-21 | +1.84 | +1.38 | 
| 2026-07-22 | +1.98 | +0.87 | 
| 2026-07-23 | +2.21 | +2.13 | 
| 2026-07-24 | +2.20 | +2.81 | 
| 2026-07-25 | +2.23 | +1.84 | 
| 2026-07-26 | +2.29 | +2.05 | 
| 2026-07-27 | +2.32 | +1.02 | 
| 2026-07-28 | +2.11 | +1.87 | 
| 2026-07-29 | +1.94 | +2.20 | 
| 2026-07-30 | +1.66 | +1.97 | 
| 2026-07-31 | +1.58 | +0.63 | 
| 2026-08-01 | +1.51 | +0.38 | 
| 2026-08-02 | +1.41 | +0.67 | 
| 2026-08-03 | +1.26 | +0.67 | 
| 2026-08-04 | +1.20 | +0.23 | 
| 2026-08-05 | +1.10 | −1.80 | 
| 2026-08-06 | +1.07 | −1.33 | 
| 2026-08-07 | +1.05 | −0.43 | 
| 2026-08-08 | +0.94 | −1.83 | 
| 2026-08-09 | +0.93 | −2.84 | 
| 2026-08-10 | +0.92 | −3.54 | 
| 2026-08-11 | +0.86 | −3.52 | 
| 2026-08-12 | +0.81 | −2.28 | 
| 2026-08-13 | +2.85 | −3.10 | 
| 2026-08-14 | +3.63 | −0.88 | 
| 2026-08-15 | +5.09 | +0.32 | 
| 2026-08-16 | +6.17 | +5.53 | 
| 2026-08-17 | +6.95 | +7.98 | 
| 2026-08-18 | +7.64 | +9.15 | 
| 2026-08-19 | +8.16 | +10.57 | 
| 2026-08-20 | +6.32 | +11.04 | 
| 2026-08-21 | +5.88 | +9.94 | 
| 2026-08-22 | +4.84 | +9.16 | 
| 2026-08-23 | +3.81 | +5.12 | 
| 2026-08-24 | +3.42 | +2.63 | 
| 2026-08-25 | +2.99 | +1.74 | 
| 2026-08-26 | +2.73 | +1.98 | 
| 2026-08-27 | +2.70 | +1.34 | 
| 2026-08-28 | +2.65 | +0.78 | 
| 2026-08-29 | +2.88 | +1.42 | 
| 2026-08-30 | +2.90 | +0.86 | 
| 2026-08-31 | +2.68 | +3.26 | 
| 2026-09-01 | +2.51 | +3.30 | 
| 2026-09-02 | +2.44 | +2.67 | 
| 2026-09-03 | +2.38 | +2.79 | 
| 2026-09-04 | +2.29 | +2.75 | 
| 2026-09-05 | +2.56 | +0.50 | 
| 2026-09-06 | +2.56 | +1.27 | 
| 2026-09-07 | +2.53 | −1.84 | 
| 2026-09-08 | +2.80 | +0.52 | 
| 2026-09-09 | +3.35 | +3.68 | 
| 2026-09-10 | +3.76 | +3.48 | 
| 2026-09-11 | +3.75 | +3.74 | 
| 2026-09-12 | +3.30 | +7.20 | 
| 2026-09-13 | +3.45 | +7.48 | 
| 2026-09-14 | +3.62 | +9.60 | 
| 2026-09-15 | +3.97 | +9.17 | 
| 2026-09-16 | +3.60 | +5.94 | 
| 2026-09-17 | +3.32 | +6.57 | 
| 2026-09-18 | +3.40 | +6.81 | 
| 2026-09-19 | +3.19 | +5.66 | 
| 2026-09-20 | +3.01 | +4.10 | 
| 2026-09-21 | +2.79 | +3.21 | 
| 2026-09-22 | +2.40 | +1.34 | 
| 2026-09-23 | +2.27 | +3.55 | 
| 2026-09-24 | +2.11 | +4.31 | 

**Chart data $\cdot$ WETH: the formula estimate and observed return $\cdot$ 30-day periods**

LP/xyk over the selected period, pp/yr
| Start date | Formula estimate of LP/xyk, pp/yr | Observed LP/xyk, pp/yr | 
| --- | --- | --- |
| 2026-06-02 | +5.55 | +10.89 | 
| 2026-06-03 | +5.51 | +10.56 | 
| 2026-06-04 | +5.38 | +9.95 | 
| 2026-06-05 | +5.08 | +8.12 | 
| 2026-06-06 | +4.40 | +5.76 | 
| 2026-06-07 | +4.23 | +4.89 | 
| 2026-06-08 | +4.06 | +4.89 | 
| 2026-06-09 | +3.93 | +4.68 | 
| 2026-06-10 | +3.81 | +4.28 | 
| 2026-06-11 | +3.68 | +3.86 | 
| 2026-06-12 | +3.58 | +3.61 | 
| 2026-06-13 | +3.53 | +3.40 | 
| 2026-06-14 | +3.62 | +4.15 | 
| 2026-06-15 | +3.65 | +4.25 | 
| 2026-06-16 | +3.61 | +4.95 | 
| 2026-06-17 | +3.55 | +4.40 | 
| 2026-06-18 | +3.45 | +4.08 | 
| 2026-06-19 | +3.35 | +4.06 | 
| 2026-06-20 | +3.31 | +4.14 | 
| 2026-06-21 | +3.36 | +4.26 | 
| 2026-06-22 | +3.37 | +4.44 | 
| 2026-06-23 | +3.33 | +3.79 | 
| 2026-06-24 | +3.26 | +3.04 | 
| 2026-06-25 | +3.10 | +3.35 | 
| 2026-06-26 | +2.84 | +2.79 | 
| 2026-06-27 | +2.59 | +2.25 | 
| 2026-06-28 | +2.65 | +2.28 | 
| 2026-06-29 | +2.67 | +2.25 | 
| 2026-06-30 | +2.62 | +2.10 | 
| 2026-07-01 | +2.57 | +2.22 | 
| 2026-07-02 | +2.48 | +2.03 | 
| 2026-07-03 | +2.35 | +2.05 | 
| 2026-07-04 | +2.30 | +1.92 | 
| 2026-07-05 | +2.29 | +2.15 | 
| 2026-07-06 | +2.28 | +2.09 | 
| 2026-07-07 | +2.19 | +1.60 | 
| 2026-07-08 | +2.11 | +1.17 | 
| 2026-07-09 | +2.06 | +1.42 | 
| 2026-07-10 | +1.99 | +1.55 | 
| 2026-07-11 | +1.92 | +1.45 | 
| 2026-07-12 | +1.92 | +1.60 | 
| 2026-07-13 | +1.91 | +1.30 | 
| 2026-07-14 | +1.85 | +0.92 | 
| 2026-07-15 | +1.78 | +0.85 | 
| 2026-07-16 | +1.71 | +0.46 | 
| 2026-07-17 | +1.63 | +0.20 | 
| 2026-07-18 | +1.55 | +0.09 | 
| 2026-07-19 | +1.56 | +0.15 | 
| 2026-07-20 | +1.54 | −0.12 | 
| 2026-07-21 | +1.96 | −0.18 | 
| 2026-07-22 | +2.11 | +0.24 | 
| 2026-07-23 | +2.40 | +0.52 | 
| 2026-07-24 | +2.60 | +1.63 | 
| 2026-07-25 | +2.73 | +1.55 | 
| 2026-07-26 | +2.91 | +2.00 | 
| 2026-07-27 | +3.01 | +1.87 | 
| 2026-07-28 | +3.00 | +2.07 | 
| 2026-07-29 | +3.02 | +2.36 | 
| 2026-07-30 | +3.02 | +2.16 | 
| 2026-07-31 | +2.97 | +2.17 | 
| 2026-08-01 | +3.01 | +1.74 | 
| 2026-08-02 | +3.07 | +1.92 | 
| 2026-08-03 | +3.11 | +2.10 | 
| 2026-08-04 | +3.14 | +1.95 | 
| 2026-08-05 | +3.19 | +2.03 | 
| 2026-08-06 | +3.30 | +2.03 | 
| 2026-08-07 | +3.28 | +2.22 | 
| 2026-08-08 | +3.28 | +2.41 | 
| 2026-08-09 | +3.33 | +2.54 | 
| 2026-08-10 | +3.38 | +2.56 | 
| 2026-08-11 | +3.42 | +2.55 | 
| 2026-08-12 | +3.46 | +3.09 | 
| 2026-08-13 | +3.65 | +2.46 | 
| 2026-08-14 | +3.64 | +2.62 | 
| 2026-08-15 | +3.65 | +2.41 | 
| 2026-08-16 | +3.76 | +3.32 | 
| 2026-08-17 | +3.95 | +4.25 | 
| 2026-08-18 | +4.09 | +4.18 | 
| 2026-08-19 | +4.15 | +4.50 | 
| 2026-08-20 | +3.75 | +4.86 | 
| 2026-08-21 | +3.59 | +4.57 | 
| 2026-08-22 | +3.31 | +4.57 | 
| 2026-08-23 | +3.25 | +4.17 | 
| 2026-08-24 | +3.17 | +3.77 | 
| 2026-08-25 | +3.08 | +3.58 | 
| 2026-08-26 | +3.04 | +3.62 | 
| 2026-08-27 | +3.02 | +3.61 | 
| 2026-08-28 | +2.92 | +3.21 | 
| 2026-08-29 | +2.83 | +3.18 | 
| 2026-08-30 | +2.92 | +3.29 | 
| 2026-08-31 | +2.90 | +3.99 | 
| 2026-09-01 | +2.88 | +4.18 |


# B5 Two common misunderstandings about harvesting {#harvesting/parameters}

**Two common beliefs about [volatility harvesting](./#glossary/volatility-harvesting) do not hold up.**

Volatility harvesting is the return from restoring chosen asset proportions at current market prices. The tests compare the proposal with deployed current settings on the same [WETH](./#glossary/weth) price histories.

> **Common misunderstanding:** “The new parameters make the pool harvest more [volatility](./#glossary/volatility).”
>
> **What is true.**
>
> Harvesting is largest when the pool holds equal value in its two assets. The new parameters keep the pool only slightly closer to that balance. Small improvements near equal values barely change harvesting. Changing settings cannot create more market price variation.
>
> The proposal keeps [price_scale](./#glossary/price_scale), the pool’s central price, closer to the market. Across the tested starts and activity setups, the average distance shrinks by 0.48 to 0.68 [percentage points](./#glossary/percentage-point) of price.
>
> Harvesting barely changes over the 7- and 30-day periods. The change is at most 0.0021 percentage points per year in either direction.

**Measure:** Harvesting contribution, in percentage points per year.

**Compared:** The proposal minus deployed current settings.

**Same for both:** The observed WETH starting states, market prices and supplied activity.

**Higher means:** More harvesting under the proposal.

Each line joins deployed current settings, shown as a circle, to the proposal, shown as a diamond. Colours distinguish the supplied activity. The vertical axis starts at zero. The tests start from observed WETH states.

The period is 7 days. Harvesting uses yearly rates.

Harvesting barely changes over 30 days. Horizontal movements show closer tracking of the market price. Vertical movements show almost no change in harvesting. Colours and marker shapes match the shorter-period chart.

**More detail**

The asset proportions limit harvesting for a given amount of market price variation. A [stall](./#glossary/stall) can create a large imbalance and reduce harvesting. Restoring equal values restores that missing contribution.

Changes under the proposal: proposal minus current settings
| Activity supplied | Period | Change in mean price gap, percentage points | Change in harvesting, pp/yr | Change from price direction, pp/yr | Interval for direction change, pp/yr | 
| --- | --- | --- | --- | --- | --- |
| [Pings](./#glossary/ping) with a simulated [YB position](./#glossary/yb-position) | 7 days | −0.675800 | +0.001933 | −0.010973 | −1.376649 to +1.147373 | 
| Pings with a simulated YB position | 30 days | −0.479595 | −0.000669 | +0.325482 | −0.069831 to +0.703944 | 
| Real flow replayed | 7 days | −0.666958 | +0.001605 | −0.295438 | −1.690270 to +0.871133 | 
| Real flow replayed | 30 days | −0.557300 | +0.000038 | +0.205130 | −0.137703 to +0.572510 | 
| Real flow replayed, including [unlabelled contracts](./#glossary/unlabelled-contracts) | 7 days | −0.666605 | +0.002026 | −0.425958 | −1.692198 to +0.769435 | 
| Real flow replayed, including unlabelled contracts | 30 days | −0.646436 | +0.001345 | −0.143585 | −0.529150 to +0.284486 | 

Pings supply operation times without copying user asset transfers. The simulated YB position owns pool shares and owes debt. Simulated [arbitrage](./#glossary/arbitrage) and YB trades can still change the pool’s holdings.

Real-flow [replay](./#glossary/replay) copies recorded user operations. An additional setup includes contracts whose purposes were not identified. Each row uses the stated activity setup.

Every uncertainty interval for the change from price direction allows both a gain and a loss on these WETH periods. A stall changes holdings and can change both direction and harvesting.

> **Common misunderstanding:** “[Concentrated liquidity](./#glossary/concentrated-liquidity) harvests A times more volatility.”
>
> **What is true.**
>
> Here, “A times” is the multiplier claimed in the misunderstanding. Greater concentration makes the pool trade more after a small price move. The pool loses more to arbitrageurs, traders profiting from price differences. These traders also pay more fees, which repay most of that loss.
>
> The harvesting premium at equal asset values stays the same on that price history. The arbitrage cost left unpaid by fees can rise.

**Measure:** Loss on arbitrage trades before fees, divided by the same-path constant-product premium.

**Compared:** Each live pool’s execution loss with the fee-free reference pool’s [QV](./#glossary/qv) premium.

**Same for both:** The live market-price history and period.

**Higher means:** More execution loss before fees for each unit of that premium.

QV adds squared log-price changes. Dividing QV by 8 gives the equal-value premium on this price history.

Fees, trading losses and holdings on the live WETH history
| Live WETH contribution | Percentage points per year | 
| --- | --- |
| [Arbitrage fees](./#glossary/arbitrage-fees) received | +18.33 | 
| Arbitrage trades before fees | −18.78 | 
| Arbitrage trades including fees | −0.450 | 
| Holding the changing mix of assets, including price direction | +4.26 | 
| Equal-value premium: QV divided by 8 | 3.407 | 

The bars compare losses from arbitrage trades, fees and estimated harvesting for each live pool over the main study period. Arbitrage losses are shown before fees. A separate bar includes those fees. All contributions use percentage points per year.

Harvesting uses the asset proportions before each market move. The separate contribution from price direction is outside this harvesting term.

Trading losses compared with the price-history premium
| Pool | Constant-product LVR: QV divided by 8, pp/yr | Observed loss before fees / same-path QV premium | Arbitrage including fees, pp/yr | 
| --- | --- | --- | --- |
| WETH | 3.407 | 5.51 | −0.450 | 
| [WBTC](./#glossary/wbtc) | 2.286 | 3.62 | −0.176 | 
| [cbBTC](./#glossary/cbbtc) | 2.286 | 4.20 | −0.276 | 
| [tBTC](./#glossary/tbtc) | 2.287 | 3.42 | −0.330 | 

[LVR](./#glossary/lvr) measures losses from trading at outdated prices before fees. The QV divided by 8 reference has no concentration multiplier. That simple reference already explains most of WETH’s result.

**More detail**

In the simplified [centred](./#glossary/centred-pool)-pool model, LVR before fees equals the [concentration factor](./#glossary/concentration-factor) times the QV divided by 8 scale. Subtract the portion of LVR left unpaid by fees from the harvesting premium.

This unpaid portion divides arbitrage profit by execution loss. The fee-band table instead divides profit by fees. The observed loss-to-QV ratio compares losses with a price-history reference. That ratio does not directly estimate the curve’s concentration parameter.

### What tracking changes

Tracking changes how price rises and falls affect the pool’s value. It also changes the trading depth, capacity available for small trades, at the market price. A pool has most depth near price_scale.

When that centre follows the market, a small order moves the price less than in an equally funded [off-centre](./#glossary/off-centre) pool. Off-centre means that the two assets have unequal [market values](./#glossary/market-value). Whether better quotes attract more trades depends on [customer responses](./#simulation/limits).

Near equal values, better tracking barely changes harvesting. The customer benefit works through fees from [native flow](./#glossary/native-flow), customer trading and other user activity. Avoiding stalls preserves the ability to rebalance. The study did not separately measure the size of this benefit to native flow.

Concentration increases the small arbitrage profit left after fees. It also makes the pool move off-centre faster when price_scale lags behind the market.

For the same lag, greater concentration can increase gains or losses from price direction. It can also make a stall more likely. The stall outcome also depends on [financing](./#glossary/financing) and the gate.

In the live WETH period, user activity contributes +1.25 pp/yr to [LP/xyk](./#glossary/lp-xyk) after execution effects. LP/xyk measures growth beyond a reference pool after the [donation](./#glossary/donation) charge.

- The activity includes customer trades.
- It includes [LT](./#glossary/lt) deposits and withdrawals. LT is the YieldBasis liquidity token.
- It also includes [VirtualPool](./#glossary/virtualpool) operations. VirtualPool is a contract routing trading operations.

For recorded-size WETH customer trades, the proposal’s median cost against the outside market price is 145 [basis points](./#glossary/basis-point). Under deployed current settings, the cost is 6.5 basis points. A basis point is a hundredth of a percentage point.

The [quote test](./#proposal/demand) keeps supplied activity fixed. Each comparison uses the activity named in its setup. Predicting customer responses requires a separate model.

The [shared conventions](./#settings) explain the yearly return rates.

[← previous](./#harvesting/formula)[next $\to$](./#simulation/live)

**Chart data $\cdot$ Closer tracking barely changes harvesting $\cdot$ 7 days**

Harvesting, pp/yr
| Supplied activity | Settings | Mean centre-to-market gap, % | Harvesting, pp/yr | 
| --- | --- | --- | --- |
| Pings with a simulated YB position | Deployed current settings | 0.953012 | 3.488914 | 
| Pings with a simulated YB position | Proposal | 0.277213 | 3.490847 | 
| Real flow replayed | Deployed current settings | 0.953749 | 3.489014 | 
| Real flow replayed | Proposal | 0.286791 | 3.490620 | 
| Real flow replayed, including unlabelled contracts | Deployed current settings | 0.947997 | 3.488717 | 
| Real flow replayed, including unlabelled contracts | Proposal | 0.281393 | 3.490743 | 

**Chart data $\cdot$ Closer tracking barely changes harvesting $\cdot$ 30 days**

Harvesting, pp/yr
| Supplied activity | Settings | Mean centre-to-market gap, % | Harvesting, pp/yr | 
| --- | --- | --- | --- |
| Pings with a simulated YB position | Deployed current settings | 0.980788 | 3.175154 | 
| Pings with a simulated YB position | Proposal | 0.501193 | 3.174485 | 
| Real flow replayed | Deployed current settings | 0.969661 | 3.175366 | 
| Real flow replayed | Proposal | 0.412360 | 3.175404 | 
| Real flow replayed, including unlabelled contracts | Deployed current settings | 0.961739 | 3.175264 | 
| Real flow replayed, including unlabelled contracts | Proposal | 0.315303 | 3.176609 | 

**Chart data $\cdot$ Trading losses, fees and harvesting**

Contribution to growth, pp/yr of pool value
| Comparison | Fees from arbitrageurs $\cdot$ Contribution to growth, pp/yr of pool value | Arbitrage trades before fees $\cdot$ Contribution to growth, pp/yr of pool value | Arbitrage trades including fees $\cdot$ Contribution to growth, pp/yr of pool value | Harvesting $\cdot$ Contribution to growth, pp/yr of pool value | 
| --- | --- | --- | --- | --- |
| WETH | +18.33 | −18.78 | −0.450 | +3.40 | 
| WBTC | +8.10 | −8.28 | −0.176 | +2.18 | 
| cbBTC | +9.32 | −9.59 | −0.276 | +2.22 | 
| tBTC | +7.49 | −7.82 | −0.330 | +2.16 |


# C. What the simulator can explain {#simulation}

**Recorded activity lets the simulator closely reproduce the live pools.**

- [C1 Replaying recorded activity](./#simulation/live) — [Replay](./#glossary/replay) matches live returns when recorded activity is supplied.
- [C2 What recorded activity adds to the formula](./#simulation/skill) — Recorded activity explains errors left by the simple formula.
- [C3 Small input errors can change whether the pool stalls](./#simulation/noise) — Small input errors can change whether a pool [stalls](./#glossary/stall).
- [C4 How customers respond remains an open problem](./#simulation/limits) — Predicting customer responses remains an open problem.


# C1 Replaying recorded activity {#simulation/live}

**[Replaying](./#glossary/replay) recorded activity closely matches the live pools’ returns.**

A replay repeats recorded operations in a simulation. Every replay here receives the market prices that actually occurred.

An [LP](./#glossary/lp) owns a share of the pool. [LP/xyk](./#glossary/lp-xyk) measures share growth above a reference, after [donation](./#glossary/donation) charges. The reference pool charges no trading fees. Both pools face the same market prices.

Rates use [percentage points](./#glossary/percentage-point) per year, or pp/yr. The [rate conventions](./#settings) explain the logarithmic calculation.

**Measure:** Error in LP/xyk, in percentage points per year.

**Compared:** Real flow replay, using recorded trade amounts, with the observed live pool.

**Same for both:** Observed period and market prices.

**Higher means:** A larger overstatement of live growth.

A negative error means the replay grew more slowly. Close agreement: with recorded trade amounts, errors range from −0.32 to 0.24 pp/yr over 128 days.

The largest error is 0.32 pp/yr. That is about a fifth of the post’s claimed +1.65 pp/yr gain. Live LP/xyk ranges from −2.76 to +4.48% per year in this history.

The economic replay lets the pool’s state change after each operation. These runs use floating-point arithmetic, which approximates numbers with limited precision.

Smaller policy differences come from paired tests: both settings receive the same prices and activity. Each test has its own uncertainty estimate.

### Which activity the simulation receives

[Arbitrage](./#glossary/arbitrage) means trading price differences between markets for profit. The YB holder owns pool shares with borrowed money. A [ping](./#glossary/ping) supplies an update opportunity without a user transfer.

| Simulation | Inputs | Activity it does not predict | 
| --- | --- | --- |
| Real flow replayed | Recorded times and amounts for identified user activity. Simulated traders exploit price differences. | Operations from [unlabelled contracts](./#glossary/unlabelled-contracts). Users’ responses to changed quotes. | 
| Real flow replayed, including unlabelled contracts | The same inputs, plus operations from unlabelled contracts | User responses to different quotes | 
| Pings with a simulated [YB position](./#glossary/yb-position) | Recorded user-operation times. Simulated arbitrage and YB-holder activity continue. | Actual deposits, withdrawals and customer order sizes | 
| Arbitrage only | Simulated arbitrage and the YB holder. Updates are free and hourly, or absent. | Actual user activity and its times | 

Some replays include unlabelled contracts, whose trading purpose is unknown.

### Copying operation times alone

A ping supplies an update opportunity at a recorded operation time. Pings omit the user’s asset transfer. Simulated arbitrageurs and the debt-financed YB holder can still trade.

**Measure:** LP/xyk difference, in percentage points per year.

**Compared:** Pings with live returns after removing user activity’s direct contribution.

**Same for both:** Observed period.

**Higher means:** A higher result from pings than from the adjusted live result.

The ping differences are −0.12 pp/yr on [WETH](./#glossary/weth) and −2.93 pp/yr on [cbBTC](./#glossary/cbbtc). Negative figures mean the ping result is lower. Each figure subtracts the adjusted live result from the ping result.

WETH is a token representing Ethereum’s [ETH](./#glossary/eth). The Bitcoin pools use tokens representing Bitcoin on Ethereum.

| Pool | Replay minus live LP/xyk, pp/yr | Average replay capital, million crvUSD | Pings minus live LP/xyk after removing direct user effects, pp/yr | Average ping capital, million crvUSD | 
| --- | --- | --- | --- | --- |
| WETH | −0.27 | 32.97 | −0.12 | 2.30 | 
| [WBTC](./#glossary/wbtc) | −0.32 | 51.40 | +0.04 | 28.28 | 
| cbBTC | 0.24 | 80.90 | −2.93 | 77.12 | 
| [tBTC](./#glossary/tbtc) | 0.15 | 35.58 | −0.58 | 29.64 | 

Capital is valued in [crvUSD](./#glossary/crvusd), the token used for borrowing. The simulated YB holder receives no actual [LT](./#glossary/lt) deposits. LT is the token for capital managed by YieldBasis.

The simulated pool’s capital can therefore differ from the live pool’s. The same trade then represents a different share of reserves. Removing the direct return from user activity leaves this difference between pool states. Ping errors also vary across months.

**More detail: how each source of return is treated**

| Source of return | Real flow replayed | Pings | Arbitrage only | 
| --- | --- | --- | --- |
| Arbitrage and its fees | Simulated | Simulated | Simulated | 
| User asset transfers | Replayed | Absent | Absent | 
| User-operation times | Observed | Observed | Absent | 
| [Financing](./#glossary/financing) and removal of donated shares | Recorded donations. Share removals follow the simulated state. | Simulated position | Simulated position | 
| Price-centre moves and asset holdings | Follow each resulting state | Follow each resulting state | Follow each resulting state | 

A [re-peg](./#glossary/re-peg) moves the price around which trading is concentrated. Removing donated shares leaves their assets for the remaining shareholders. Each simulation follows the holdings and price-centre moves produced by its own state.

### Checking the arithmetic exactly

**Measure:** Number of operations with exactly matching states.

**Compared:** The simulated resulting state with the state recorded after the operation.

**Same for both:** Recorded operation and recorded starting state.

**Higher means:** More operations agree exactly.

- Exact agreement for 29,316 WETH operations.
- Exact agreement for 31,973 Bitcoin-pool operations.

This test uses integers and reproduces the recorded states exactly. It checks each operation from its recorded starting state. The economic replay instead lets earlier simulated operations determine later states.

These calculations keep recorded customer activity fixed. Predicting [customers’ responses](./#simulation/limits) to different quotes requires a separate model.

[← previous](./#harvesting/parameters)[next $\to$](./#simulation/skill)


# C2 What recorded activity adds to the formula {#simulation/skill}

**Recorded user activity removes most of the error left by the simple formula.**

A [replay](./#glossary/replay) copies recorded user activity into the simulation. A [ping](./#glossary/ping) copies only an operation time. Both methods receive the market prices that actually occurred.

An [LP](./#glossary/lp) owns a share of the pool. [LP/xyk](./#glossary/lp-xyk) measures share growth above a reference, after [donation](./#glossary/donation) charges. The reference pool charges no trading fees. Both pools face the same market prices.

Rates use [percentage points](./#glossary/percentage-point) per year, or pp/yr. The [rate conventions](./#settings) explain the logarithmic calculation.

[Squared error](./#glossary/squared-error) squares each prediction error before averaging.

**Measure:** Share of the formula’s remaining squared error removed (no unit).

**Compared:** Each simulator with the simple formula.

**Same for both:** [WETH](./#glossary/weth) starting states, periods and known market prices.

**Higher means:** More of the formula’s remaining error removed.

WETH is a token representing Ethereum’s [ETH](./#glossary/eth). The comparison uses identical starting states at each time horizon.

At 7 days, replay removes 88.0–95.8% of the formula’s remaining squared error. Replay also removes most of the remaining error at 30 days. Pings add no improvement over the formula at that longer horizon.

Recorded activity removes most of the formula’s remaining error. Pings add no improvement over the formula at 30 days. Colours distinguish 7-day and 30-day results, rather than sources of return.

The formula uses [QV](./#glossary/qv), which sums squared log-price changes, divided by 8. Each comparison uses the same WETH starting states and known market prices.

### How to read the score

The [skill](./#glossary/skill) score measures the share of a reference prediction’s error removed.

Skill = 1 $-$ (model error $\div$ reference error). A perfect prediction scores 1. No improvement scores 0. Negative scores mean a worse prediction than the reference.

Every method receives the prices that actually occurred. These tests explain returns given those prices. They do not test forecasts of future market prices.

**More detail: an example of the error calculation**

Compare a weather forecast with “tomorrow will be like today.” Square each temperature error, then average the squared errors. Compare the averages to see how much error the detailed forecast removes.

### What the simple formula already explains

The simplest reference predicts zero LP/xyk. The formula uses price moves and has no fitted parameters. Its QV term adds squared logarithmic price moves. The formula divides QV by 8.

**Measure:** Share of the zero prediction’s squared error removed (no unit).

**Compared:** The formula with a prediction of zero LP/xyk.

**Same for both:** The stated WETH sample and observed prices.

**Higher means:** More error removed compared with predicting zero.

On WETH windows starting near equal asset values, the formula removes 64.6% of error at 7 days. It removes 87.1% at 30 days. That already explains most of the outcome once prices are known. The formula alone cannot distinguish small policy gains.

**More detail: scores against zero use different samples**

| Method | Score at 7 days | Score at 30 days | 
| --- | --- | --- |
| QV/8 formula | 0.646 | 0.871 | 
| Pings with a simulated [YB position](./#glossary/yb-position) | 0.841 | 0.879 | 
| Real flow replayed | 0.938 | 0.977 | 
| Real flow replayed, including [unlabelled contracts](./#glossary/unlabelled-contracts) | 0.986 | 0.989 | 

| Method | Starting states at 7 days | Starting states at 30 days | 
| --- | --- | --- |
| Formula | 115 | 92 | 
| Simulators | 122 | 99 | 

The samples differ between the formula and simulators in this table. Use the main chart to measure what simulation adds on identical starting states.

### The Bitcoin pools need their starting asset mix

The Bitcoin pools start away from equal asset values. Adding their starting asset mix accounts for gains or losses when prices move in one direction.

The added term removes 75.6% of zero-prediction squared error at 7 days. It removes 21.9% at 30 days. QV divided by 8 alone gives no improvement for those pools.

Bitcoin simulators were not scored against this formula. [Arbitrage](./#glossary/arbitrage)-only simulations were outside the WETH scoring test above.

**More detail: the Bitcoin formula**

The formula uses the starting risky-asset weight, written w, and the change in logarithmic market price. Its harvesting term also uses squared logarithmic price moves, QV.

$(w_0-\frac12)\Delta\ln P$ + $\frac12 w_0(1-w_0)\mathrm{QV}$

The comparison beyond the formula uses the same starting dates for every method at each horizon.

[← previous](./#simulation/live)[next $\to$](./#simulation/noise)

**More detail: scores against zero on different samples**

These scores compare each method with predicting zero LP/xyk. The formula and simulators use different samples. Use the main chart to compare their added value on identical starting states.

**Chart data $\cdot$ What recorded activity adds beyond the formula**

Share of remaining squared error removed
| Simulation or comparison | 7 days $\cdot$ Share of remaining squared error removed | 30 days $\cdot$ Share of remaining squared error removed | 
| --- | --- | --- |
| Real flow, including unlabelled contracts | 0.958 | 0.902 | 
| Real flow replayed | 0.880 | 0.897 | 
| Pings with a simulated YB position | 0.609 | −0.003 | 

**Chart data $\cdot$ Error removed compared with predicting zero LP/xyk**

Share of zero-prediction squared error removed
| Simulation or comparison | 7 days $\cdot$ Share of zero-prediction squared error removed | 30 days $\cdot$ Share of zero-prediction squared error removed | 
| --- | --- | --- |
| QV/8 formula | 0.646 | 0.871 | 
| Pings with a simulated YB position | 0.841 | 0.879 | 
| Real flow replayed | 0.938 | 0.977 | 
| Real flow replayed, including unlabelled contracts | 0.986 | 0.989 |


# C3 Small input errors can change whether the pool stalls {#simulation/noise}

**Small input differences can change whether a pool [stalls](./#glossary/stall).**

A stall is a price gap above 5% that lasts at least 24 hours. The [price-gap rule](./#settings) defines the threshold and duration.

An [LP](./#glossary/lp) owns a share of the pool. [LP/xyk](./#glossary/lp-xyk) measures share growth above a reference, after [donation](./#glossary/donation) charges. The reference pool charges no trading fees. Both pools face the same market prices.

Rates use [percentage points](./#glossary/percentage-point) per year, or pp/yr. The [rate conventions](./#settings) explain the logarithmic calculation.

**Measure:** Reruns with a stall classification differing from the most common classification, as a percentage.

**Compared:** Each policy’s input-error reruns with its own most common result.

**Same for both:** [WBTC](./#glossary/wbtc) market history.

**Higher means:** Greater sensitivity to small input errors.

WBTC is a token representing Bitcoin. With small input errors, 33–39% of proposal reruns differ from its most common stall classification. All reruns with current settings agree.

> **Common misunderstanding:** “One simulation run gives a definite answer.”
>
> **What is true.**
>
> Small, plausible errors in the inputs can change whether the proposal stalls on the same WBTC history. The classification under current settings stays fixed. One run can therefore mislead.

### A changed recovery can change the return difference

[cbBTC](./#glossary/cbbtc) is another token representing Bitcoin. Its comparison covers 1 August 2026 to 1 October 2026. Every rerun receives the same market-price history.

- When the current pool recovers, proposal-minus-current LP/xyk averages 1.52 pp/yr.
- When the current pool remains stalled, the average is 9.11 pp/yr.

These groups describe recovery of the current pool. The proposal’s gain stays positive in both groups. Its size changes greatly.

### The smaller WETH gain can change sign

[WETH](./#glossary/weth) represents Ethereum’s [ETH](./#glossary/eth). The recorded-activity test covers 1 August 2026 to 1 September 2026.

The mean proposal-minus-current LP/xyk difference is +0.22 pp/yr. Negative differences occur in 10 of 64 input-error reruns.

The mean gain is small compared with the post’s claim. Some input-error reruns give losses. Each dot repeats the same WETH history with plausible input errors and recorded user activity.

The window runs from 1 August 2026 to 1 September 2026. The horizontal axis shows proposal-minus-current LP/xyk in percentage points per year. Vertical spacing has no measured meaning.

### How a small error changes later decisions

A separate cbBTC reconstruction traces the mechanism. On 29 May, a trade missed its trigger by 0.5 [basis points](./#glossary/basis-point) under one token-valuation convention. A basis point is a hundredth of a percentage point.

That miss changed whether the pool moved [price_scale](./#glossary/price_scale), its centre price, back towards the market. The difference affected later price-centre moves for the following month. A threshold can turn a small input error into a lasting difference in holdings.

**More detail: inputs and stall warnings**

Each rerun keeps the market history fixed. The rerun changes token valuations, externally reported prices or transaction timing. Whole-day error segments preserve errors that persist through a day. The test generates the Bitcoin price [reports](./#glossary/report).

Holdings, price-centre moves and [financing](./#glossary/financing) each contribute to the total LP/xyk difference. Financing supplies capital through the YB holder’s interest-funded donations.

Only about 3 distinct Bitcoin market events are available. Counting the same market move for each Bitcoin token would overstate the independent evidence.

> **Common misunderstanding:** “Three Bitcoin pools give three independent tests.”
>
> **What is true.**
>
> The three Bitcoin pools face the same Bitcoin price moves. Counting each pool separately overstates the evidence. The study window holds only about 3 distinct Bitcoin market events.

A warning’s precision is the share of issued warnings that correctly identify a stall. Compare warnings at the same precision.

Recent accounting buffers and the cost of an affordable move give no better warning than the previous week’s stall status.

Input-error reruns keep the price sequence fixed. [Rebuilt histories](./#resampling/why) test different sequences of the observed moves.

[← previous](./#simulation/skill)[next $\to$](./#simulation/limits)

**Chart data $\cdot$ Small input errors can change the sign of the WETH gain**

Proposal minus current LP/xyk, percentage points per year
| LP/xyk difference, percentage points per year | Pair kept in this analysis? | 
| --- | --- |
| +0.077 | Yes | 
| +0.701 | Yes | 
| +0.427 | Yes | 
| +0.059 | Yes | 
| +0.392 | Yes | 
| +0.368 | Yes | 
| +0.218 | Yes | 
| +0.046 | Yes | 
| +0.261 | Yes | 
| +0.341 | Yes | 
| +0.099 | Yes | 
| +0.506 | Yes | 
| +0.138 | Yes | 
| +0.148 | Yes | 
| +0.587 | Yes | 
| +0.248 | Yes | 
| +0.031 | Yes | 
| +0.060 | Yes | 
| −0.230 | Yes | 
| +0.713 | Yes | 
| +0.429 | Yes | 
| +0.310 | Yes | 
| +0.163 | Yes | 
| +0.126 | Yes | 
| +0.189 | Yes | 
| +0.304 | Yes | 
| +0.483 | Yes | 
| +0.024 | Yes | 
| −0.289 | Yes | 
| +0.252 | Yes | 
| +0.380 | Yes | 
| +0.079 | Yes | 
| +0.077 | Yes | 
| −0.025 | Yes | 
| +0.473 | Yes | 
| +0.578 | Yes | 
| −0.312 | Yes | 
| +0.249 | Yes | 
| −0.402 | Yes | 
| −0.058 | Yes | 
| +0.255 | Yes | 
| +0.819 | Yes | 
| +0.244 | Yes | 
| +0.304 | Yes | 
| +0.550 | Yes | 
| +0.224 | Yes | 
| −0.292 | Yes | 
| −0.126 | Yes | 
| +0.253 | Yes | 
| −0.319 | Yes | 
| +0.462 | Yes | 
| +0.041 | Yes | 
| +0.126 | Yes | 
| +0.301 | Yes | 
| +0.226 | Yes | 
| +0.306 | Yes | 
| +0.194 | Yes | 
| +0.354 | Yes | 
| −0.094 | Yes | 
| +0.191 | Yes | 
| +0.269 | Yes | 
| +0.507 | Yes | 
| +0.311 | Yes | 
| +0.601 | Yes |


# C4 How customers respond remains an open problem {#simulation/limits}

**These simulations do not predict how customers respond to different quotes.**

A [replay](./#glossary/replay) copies recorded activity into a simulation. A fixed-activity replay asks what the pool earns if users trade the same amounts at the same times.

Customers can choose another trading venue. Customers can also change order amounts, change trading times or stop trading. Capital held through [LT](./#glossary/lt), YieldBasis’s liquidity token, can enter or leave.

Predicting those responses remains an open problem across automated market-maker simulation. An automated market maker trades through programmed pricing rules. Traders have many motives. This study has not established a reliable response model.

> **Common misunderstanding:** “The simulator shows how customers would react to the new fees.”
>
> **What is true.**
>
> These simulations copy recorded customer trades, or leave customers out. They do not predict how customers respond to different quotes. Modelling that response remains an open problem across the field.

### Specified choices are different from predicted choices

The [customer-response test](./#proposal/demand) imposes rejection of quotes above a cost limit. A separate scenario removes all tested customer flow from the proposal. The resulting returns describe those supplied choices of activity.

A pool’s state determines quotes for a fixed order size. That state also determines trading depth: how much can trade for a small price change.

Estimating missing volume requires a model of customer choices under alternative quotes. Estimating customer retention and benefits to traders requires the same comparison.

**Measure:** Customer dollar volume per day, expressed as a ratio.

**Compared:** [WBTC](./#glossary/wbtc) [stall](./#glossary/stall) days with days without a stall.

**Same for both:** The live WBTC sample.

**Higher means:** More recorded daily trading on stall days.

WBTC is a token representing Bitcoin. On stall days, recorded customer dollar volume per day was 2.53 times the volume on days without stalls.

The market also moved more on stall days. The ratio therefore combines the stall with different market conditions.

> **Common misunderstanding:** “Higher volume on stall days shows that stalls attract customers.”
>
> **What is true.**
>
> Customer volume did rise on stall days. The market also moved more on those days. This comparison cannot separate the stall from the busier market.

A convincing model would reproduce customer behaviour on observations excluded from fitting. The checks would cover trading venues, order sizes, trading times and changes in supplied capital.

[← previous](./#simulation/noise)[next $\to$](./#resampling/why)


# D. Testing different sequences of market moves {#resampling}

**Rebuilt histories show how results depend on the sequence of market moves.**

- [D1 Why one price history is not enough](./#resampling/why) — Reordering stretches of observed prices gives a range of policy outcomes.


# D1 Why one price history is not enough {#resampling/why}

**Changing the order of observed market moves changes the proposal’s results.**

The search selects among 1.6 million settings using one price history. A setting can perform well because it fits that particular sequence.

An [LP](./#glossary/lp) owns a share of the pool. [LP/xyk](./#glossary/lp-xyk) measures share growth above a reference, after [donation](./#glossary/donation) charges. The reference pool charges no trading fees. Both pools face the same market prices.

Rates use [percentage points](./#glossary/percentage-point) per year, or pp/yr. The [rate conventions](./#settings) explain the logarithmic calculation.

**Measure:** Proposal-minus-current LP/xyk, in percentage points per year.

**Compared:** The proposal with deployed current settings.

**Same for both:** Each rebuilt [WETH](./#glossary/weth) price history.

**Higher means:** A larger advantage for the proposal.

WETH represents Ethereum’s [ETH](./#glossary/eth). Rebuilding the price history tests how results depend on the sequence of observed moves. The proposal’s median advantage is positive. Some rebuilt histories give losses.

### How a history is rebuilt

A [block bootstrap](./#glossary/bootstrap) draws consecutive stretches of observed moves again. Moves within each stretch stay together. Stretches can repeat, disappear or continue past the source endpoint to its beginning. Their order over longer periods changes.

Each letter below represents one stretch of the original history. The rebuilt history repeats B and E. It leaves out D and F.

**Original stretches**

ABCDEF

**Rebuilt history**

BBEAEC

The main comparison uses 100 rebuilt histories. Each lasts 556 days. The fixed summary draws stretches lasting 180 days.

Length of each copied stretch: 180 days, 90 days, 30 days or 1 day.

Prices are divided by each history’s starting price. Thin lines show selected examples. The marked reference follows the original price history. All rebuilt histories draw stretches from that original history.

The shaded band runs from percentile 2.5 to percentile 97.5 at each weekly observation. The band describes the spread of rebuilt prices at that observation.

The horizontal axis shows proposal-minus-current LP/xyk on retained pairs of rebuilt histories. The box covers the middle half of outcomes. Its line marks the median. Whiskers extend to the smallest and largest outcomes.

The diamond marks the original-history outcome.

Rebuilt histories: 100. Retained pairs: 100. Excluded pairs: 0.

A pair is excluded if either holder’s wealth after debt reaches zero or becomes negative during the path.

### Results across rebuilt histories

The median LP/xyk advantage is +1.90 pp/yr, similar to the post’s claimed gain. The middle 95% of outcomes runs from −7.89 to +7.12 pp/yr. The advantage is positive in 84 of 100 histories.

The outcome range describes differences between histories. It is not an uncertainty interval for the mean.

> **Common misunderstanding:** “The range of outcomes across rebuilt histories is the uncertainty of the average.”
>
> **What is true.**
>
> The range shows how much results differ from one rebuilt history to another. It is not a [confidence interval](./#glossary/confidence-interval) for the average result.

The fixed summary uses 180-day stretches. The archive excludes a pair if either YB holder’s wealth after debt becomes zero or negative during the path. That exclusion also applies to pool-return summaries. The tables show retained and excluded pairs.

### The internal accounting measure answers another question

[Virtual price](./#glossary/virtual-price) is the pool’s internal accounting index. [Recognised return](./#glossary/recognised-gain) measures its growth after the donation charge.

**Measure:** Proposal-minus-current recognised return, in percentage points per year.

**Compared:** The proposal with deployed current settings.

**Same for both:** The same rebuilt WETH histories.

**Higher means:** A larger advantage in internal accounting growth after the donation charge.

| Recognised-return statistic | Result | 
| --- | --- |
| Length of copied stretches, days | 180 | 
| Median difference, pp/yr | +1.93 | 
| Middle 95% of outcomes, pp/yr | −2.32 to +3.40 | 
| Histories with a positive difference | 92 | 

**More detail: how the measures differ**

Recognised return replaces [M](./#glossary/m), the [market-value](./#glossary/market-value) score inside LP/xyk, with virtual-price growth. It keeps the same donation charge and the same measurement period. The outcome range describes variation across histories.

### Rebuilding does not remove the original selection

The settings were chosen using the original history. Rebuilding that history does not undo the choice. [Tests on unused data](./#proposal/selection) evaluate observations excluded from selection.

> **Common misunderstanding:** “Testing on rebuilt histories is a fresh, independent test.”
>
> **What is true.**
>
> Rebuilt histories reuse moves from the original history, the same history used to choose the settings. They show how results depend on the order of moves. They do not undo the choice.

Input-error reruns keep market moves fixed and alter measured inputs. Rebuilt histories change the sequence of observed moves. Both tests draw their market behaviour from the original history.

[← previous](./#simulation/limits)[next $\to$](./#proposal/test)

**Chart data $\cdot$ Prices on rebuilt histories $\cdot$ 180-day blocks**

Price divided by starting price, sampled weekly
| Rebuilt history | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | 
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Path AA | 1.000 | 0.862 | 0.874 | 0.982 | 1.014 | 1.291 | 1.396 | 1.391 | 1.393 | 1.363 | 1.420 | 1.325 | 1.334 | 1.380 | 1.628 | 1.952 | 2.050 | 1.920 | 2.207 | 2.443 | 2.660 | 2.400 | 2.371 | 2.594 | 2.459 | 2.219 | 2.163 | 2.137 | 2.338 | 2.217 | 2.001 | 2.239 | 1.900 | 1.901 | 1.952 | 1.909 | 1.705 | 1.544 | 1.372 | 1.504 | 1.499 | 1.530 | 1.478 | 1.453 | 1.551 | 1.532 | 1.635 | 1.467 | 1.343 | 1.024 | 1.016 | 0.977 | 0.959 | 0.822 | 0.663 | 0.610 | 0.574 | 0.572 | 0.566 | 0.566 | 0.636 | 0.600 | 0.579 | 0.616 | 0.640 | 0.661 | 0.692 | 0.678 | 0.692 | 0.622 | 0.613 | 0.586 | 0.493 | 0.504 | 0.498 | 0.459 | 0.521 | 0.527 | 0.528 | 0.562 | 
| Path AB | 1.000 | 1.007 | 1.419 | 1.359 | 1.390 | 1.388 | 1.387 | 1.390 | 1.261 | 1.338 | 1.382 | 1.616 | 1.973 | 2.055 | 1.864 | 2.340 | 2.429 | 2.624 | 2.402 | 2.347 | 2.563 | 2.461 | 2.207 | 2.464 | 2.058 | 2.136 | 2.084 | 2.114 | 2.150 | 2.210 | 2.098 | 1.988 | 2.049 | 2.096 | 2.485 | 3.102 | 3.132 | 3.068 | 3.482 | 3.556 | 3.608 | 3.557 | 3.550 | 3.729 | 3.462 | 3.475 | 3.862 | 3.496 | 3.281 | 3.397 | 2.971 | 2.942 | 2.587 | 2.444 | 2.781 | 2.779 | 2.806 | 4.044 | 3.953 | 4.155 | 4.041 | 4.295 | 3.913 | 3.747 | 3.983 | 4.290 | 5.224 | 5.622 | 5.904 | 5.707 | 7.359 | 6.719 | 6.983 | 6.896 | 6.739 | 7.113 | 6.435 | 6.737 | 6.718 | 6.858 | 
| Path AC | 1.000 | 1.010 | 1.455 | 1.422 | 1.495 | 1.454 | 1.545 | 1.408 | 1.348 | 1.433 | 1.544 | 1.880 | 2.023 | 2.124 | 2.054 | 2.648 | 2.418 | 2.513 | 2.481 | 2.425 | 2.559 | 2.315 | 2.424 | 2.523 | 2.222 | 2.122 | 2.411 | 2.447 | 2.140 | 2.401 | 2.469 | 2.855 | 3.608 | 3.719 | 3.359 | 4.083 | 4.296 | 4.592 | 4.219 | 4.136 | 4.423 | 4.270 | 3.979 | 4.336 | 3.989 | 3.825 | 3.994 | 3.752 | 3.442 | 2.973 | 2.692 | 2.873 | 2.887 | 3.015 | 2.789 | 2.776 | 2.979 | 2.763 | 2.594 | 2.665 | 2.202 | 2.289 | 2.092 | 1.982 | 2.007 | 2.222 | 1.984 | 1.986 | 1.992 | 2.208 | 2.228 | 1.969 | 2.027 | 1.496 | 1.355 | 1.334 | 1.240 | 1.328 | 1.389 | 1.352 | 
| Path AD | 1.000 | 0.893 | 0.831 | 0.785 | 0.893 | 0.893 | 0.901 | 1.299 | 1.270 | 1.334 | 1.298 | 1.379 | 1.256 | 1.204 | 1.279 | 1.378 | 1.678 | 1.806 | 1.896 | 1.833 | 2.363 | 2.158 | 2.243 | 2.215 | 2.164 | 2.284 | 2.230 | 2.255 | 3.092 | 3.132 | 3.176 | 3.231 | 3.321 | 3.152 | 2.988 | 3.079 | 3.150 | 3.734 | 4.661 | 4.707 | 4.610 | 5.232 | 5.344 | 5.422 | 5.346 | 5.335 | 5.605 | 5.202 | 5.222 | 5.803 | 5.254 | 4.930 | 4.580 | 4.575 | 4.087 | 3.801 | 3.591 | 4.087 | 4.084 | 4.123 | 5.942 | 5.808 | 6.105 | 5.937 | 6.310 | 5.749 | 5.506 | 5.852 | 6.304 | 7.676 | 8.261 | 8.675 | 8.386 | 10.813 | 9.873 | 10.261 | 10.133 | 9.902 | 11.000 | 11.005 | 
| Path AE | 1.000 | 1.264 | 1.303 | 1.177 | 1.430 | 1.505 | 1.608 | 1.478 | 1.449 | 1.549 | 1.496 | 1.394 | 1.519 | 1.397 | 1.340 | 1.399 | 1.314 | 1.206 | 1.042 | 0.943 | 1.006 | 1.030 | 1.031 | 1.010 | 0.993 | 1.058 | 1.011 | 0.929 | 0.744 | 0.667 | 0.633 | 0.589 | 0.643 | 0.632 | 0.746 | 0.682 | 0.642 | 0.668 | 0.751 | 0.734 | 0.730 | 0.744 | 0.742 | 0.675 | 0.670 | 0.636 | 0.536 | 0.569 | 0.548 | 0.511 | 0.571 | 0.563 | 0.594 | 0.668 | 0.630 | 0.609 | 0.647 | 0.672 | 0.694 | 0.727 | 0.712 | 0.727 | 0.654 | 0.644 | 0.616 | 0.518 | 0.529 | 0.523 | 0.482 | 0.548 | 0.554 | 0.574 | 0.600 | 0.578 | 0.586 | 0.575 | 0.755 | 0.741 | 0.734 | 0.725 | 
| Path AF | 1.000 | 1.000 | 1.054 | 1.099 | 0.936 | 0.974 | 0.982 | 1.047 | 1.109 | 0.986 | 0.995 | 0.710 | 0.642 | 0.646 | 0.680 | 0.703 | 0.678 | 0.728 | 0.717 | 0.707 | 0.724 | 0.780 | 0.785 | 0.745 | 0.777 | 0.747 | 0.796 | 0.796 | 0.803 | 1.158 | 1.131 | 1.189 | 1.157 | 1.229 | 1.120 | 1.073 | 1.140 | 1.228 | 1.495 | 1.609 | 1.690 | 1.634 | 2.107 | 1.923 | 1.999 | 1.974 | 1.929 | 2.036 | 1.842 | 1.929 | 2.007 | 1.768 | 1.852 | 1.572 | 1.573 | 1.615 | 1.579 | 1.410 | 1.278 | 1.135 | 1.244 | 1.240 | 1.266 | 1.223 | 1.202 | 1.283 | 1.268 | 1.353 | 1.214 | 1.111 | 0.847 | 0.841 | 0.808 | 0.792 | 0.812 | 0.859 | 0.881 | 0.818 | 0.808 | 0.866 | 
| Path AG | 1.000 | 1.094 | 1.017 | 0.959 | 1.081 | 1.154 | 1.177 | 1.172 | 1.140 | 1.148 | 1.170 | 1.490 | 1.475 | 1.516 | 1.463 | 1.679 | 1.633 | 1.494 | 1.476 | 1.344 | 1.319 | 1.489 | 1.499 | 2.112 | 2.023 | 2.069 | 2.195 | 2.217 | 3.194 | 3.122 | 3.282 | 3.192 | 3.392 | 3.090 | 2.960 | 3.146 | 3.389 | 4.126 | 4.441 | 4.663 | 4.508 | 5.813 | 5.307 | 5.516 | 5.447 | 5.323 | 5.618 | 5.083 | 5.322 | 5.539 | 4.878 | 4.658 | 4.661 | 3.926 | 4.007 | 3.964 | 3.650 | 4.147 | 4.196 | 4.348 | 4.539 | 4.378 | 4.437 | 4.356 | 5.721 | 5.612 | 5.839 | 5.752 | 6.143 | 6.244 | 6.237 | 5.656 | 4.738 | 4.929 | 5.508 | 5.721 | 6.871 | 7.933 | 7.287 | 7.145 | 
| Path AH | 1.000 | 1.067 | 1.092 | 1.093 | 1.071 | 1.053 | 1.122 | 1.115 | 1.172 | 1.005 | 0.810 | 0.746 | 0.702 | 0.699 | 0.692 | 0.691 | 0.777 | 0.733 | 0.708 | 0.753 | 0.782 | 0.808 | 0.846 | 0.829 | 0.846 | 0.760 | 0.983 | 1.063 | 1.059 | 1.061 | 1.038 | 1.081 | 1.008 | 1.015 | 1.051 | 1.240 | 1.486 | 1.561 | 1.462 | 1.680 | 1.860 | 2.025 | 1.827 | 1.805 | 1.975 | 1.873 | 1.690 | 1.891 | 1.605 | 1.606 | 1.649 | 1.613 | 1.952 | 2.033 | 1.844 | 2.315 | 2.402 | 2.596 | 2.376 | 2.322 | 2.535 | 2.434 | 2.183 | 2.438 | 2.036 | 2.113 | 2.148 | 2.105 | 1.848 | 1.721 | 1.505 | 1.624 | 1.651 | 1.692 | 1.618 | 1.602 | 1.699 | 1.677 | 1.714 | 1.739 | 
| Path AI | 1.000 | 1.005 | 0.969 | 0.900 | 0.878 | 0.690 | 0.726 | 0.745 | 0.688 | 0.766 | 0.783 | 0.802 | 0.811 | 0.811 | 0.834 | 0.820 | 1.096 | 1.064 | 1.070 | 1.096 | 1.138 | 1.173 | 1.206 | 1.112 | 0.860 | 0.928 | 0.897 | 0.920 | 0.879 | 0.871 | 0.923 | 0.911 | 0.978 | 0.872 | 0.724 | 0.616 | 0.616 | 0.583 | 0.580 | 0.582 | 0.619 | 0.616 | 0.589 | 0.610 | 0.675 | 0.694 | 0.685 | 0.684 | 0.687 | 0.644 | 0.625 | 0.597 | 0.611 | 0.505 | 0.525 | 0.480 | 0.455 | 0.460 | 0.510 | 0.455 | 0.456 | 0.457 | 0.506 | 0.511 | 0.452 | 0.465 | 0.343 | 0.311 | 0.306 | 0.284 | 0.305 | 0.313 | 0.356 | 0.331 | 0.323 | 0.344 | 0.357 | 0.357 | 0.331 | 0.329 | 
| Path AJ | 1.000 | 1.122 | 1.154 | 1.334 | 1.686 | 1.738 | 1.570 | 1.908 | 2.008 | 2.146 | 1.972 | 1.933 | 2.067 | 1.995 | 1.859 | 2.026 | 1.864 | 1.788 | 1.867 | 1.754 | 1.609 | 1.389 | 1.258 | 1.343 | 1.373 | 1.375 | 1.333 | 1.324 | 1.494 | 1.509 | 2.098 | 2.084 | 2.128 | 2.118 | 2.094 | 2.125 | 1.859 | 2.086 | 2.144 | 2.479 | 3.134 | 3.230 | 2.917 | 3.546 | 3.731 | 3.988 | 3.664 | 3.592 | 3.841 | 3.708 | 3.456 | 3.766 | 3.784 | 3.647 | 3.641 | 3.877 | 4.156 | 4.124 | 3.996 | 4.055 | 4.041 | 3.777 | 3.557 | 3.134 | 2.962 | 3.029 | 2.775 | 3.010 | 3.089 | 3.300 | 3.325 | 3.395 | 3.370 | 3.338 | 4.118 | 4.444 | 4.438 | 4.316 | 3.772 | 3.873 | 
| Path AK | 1.000 | 1.039 | 1.073 | 1.123 | 1.101 | 1.124 | 1.010 | 0.995 | 0.951 | 0.801 | 0.818 | 0.809 | 0.745 | 0.846 | 0.856 | 0.887 | 0.926 | 0.893 | 0.905 | 0.889 | 1.167 | 1.145 | 1.192 | 1.174 | 1.254 | 1.274 | 1.358 | 1.443 | 1.315 | 1.259 | 1.339 | 1.442 | 1.756 | 1.889 | 1.984 | 1.918 | 2.473 | 2.258 | 2.347 | 2.317 | 2.265 | 2.390 | 2.162 | 2.264 | 2.357 | 2.075 | 1.982 | 2.032 | 1.783 | 1.778 | 1.575 | 1.576 | 1.330 | 1.383 | 1.546 | 1.605 | 1.928 | 2.226 | 2.328 | 2.298 | 2.108 | 2.308 | 2.202 | 2.110 | 2.263 | 2.578 | 3.037 | 3.238 | 3.230 | 3.415 | 3.971 | 3.690 | 3.940 | 3.753 | 3.894 | 4.007 | 3.384 | 3.917 | 4.226 | 4.296 | 
| Path AL | 1.000 | 1.001 | 1.004 | 1.113 | 1.123 | 0.992 | 1.022 | 0.754 | 0.683 | 0.672 | 0.625 | 0.669 | 0.688 | 0.782 | 0.728 | 0.711 | 0.756 | 0.784 | 0.786 | 0.773 | 0.797 | 0.768 | 0.713 | 0.700 | 0.628 | 0.553 | 0.582 | 0.630 | 0.693 | 0.699 | 0.691 | 0.690 | 0.680 | 0.814 | 0.906 | 0.865 | 0.892 | 0.874 | 0.971 | 0.971 | 0.876 | 0.766 | 0.774 | 0.769 | 0.868 | 0.876 | 1.218 | 1.210 | 1.236 | 1.230 | 1.216 | 1.234 | 1.208 | 1.071 | 1.071 | 1.128 | 1.176 | 1.003 | 1.043 | 1.052 | 1.121 | 1.187 | 1.055 | 1.065 | 0.760 | 0.687 | 0.692 | 0.728 | 0.753 | 0.726 | 0.780 | 0.768 | 0.757 | 0.775 | 0.835 | 0.840 | 0.797 | 0.832 | 0.809 | 0.922 | 
| Path AM | 1.000 | 0.999 | 0.892 | 0.830 | 0.784 | 0.892 | 0.892 | 0.900 | 1.297 | 1.268 | 1.333 | 1.296 | 1.378 | 1.255 | 1.202 | 1.278 | 1.376 | 1.676 | 1.804 | 1.894 | 1.831 | 2.361 | 2.156 | 2.240 | 2.212 | 2.162 | 2.351 | 2.499 | 2.276 | 2.180 | 2.317 | 2.496 | 3.040 | 3.271 | 3.435 | 3.321 | 4.282 | 3.909 | 4.063 | 4.013 | 3.921 | 4.139 | 3.744 | 3.920 | 4.080 | 3.593 | 3.431 | 3.519 | 3.087 | 3.079 | 2.728 | 2.729 | 2.875 | 2.998 | 2.555 | 2.658 | 2.680 | 2.857 | 3.025 | 2.689 | 2.715 | 1.937 | 1.750 | 1.764 | 1.855 | 1.918 | 1.850 | 1.987 | 1.956 | 1.930 | 1.975 | 2.128 | 2.141 | 2.032 | 2.120 | 2.037 | 1.920 | 1.826 | 1.575 | 1.596 | 
| Path AN | 1.000 | 1.114 | 1.138 | 1.167 | 1.179 | 1.180 | 1.212 | 1.192 | 1.594 | 1.547 | 1.556 | 1.594 | 1.655 | 1.705 | 1.754 | 1.617 | 1.251 | 1.349 | 1.491 | 1.526 | 1.543 | 2.275 | 2.143 | 2.259 | 2.202 | 2.391 | 2.096 | 1.947 | 2.126 | 2.090 | 2.467 | 2.257 | 2.125 | 2.210 | 2.485 | 2.426 | 2.416 | 2.462 | 2.454 | 2.234 | 2.216 | 2.104 | 1.773 | 1.884 | 1.812 | 1.692 | 1.887 | 1.863 | 1.998 | 1.985 | 1.951 | 1.964 | 2.004 | 2.026 | 2.987 | 2.814 | 2.966 | 2.891 | 3.140 | 2.798 | 2.730 | 2.681 | 2.916 | 3.498 | 4.176 | 4.229 | 4.027 | 5.118 | 4.544 | 5.129 | 4.823 | 4.805 | 5.018 | 4.643 | 4.621 | 4.958 | 4.599 | 4.318 | 4.451 | 4.019 | 
| Path AO | 1.000 | 1.050 | 1.015 | 1.309 | 1.195 | 1.242 | 1.227 | 1.199 | 1.265 | 1.145 | 1.198 | 1.247 | 1.099 | 1.049 | 1.076 | 0.944 | 0.941 | 0.834 | 0.834 | 0.879 | 0.916 | 0.781 | 0.812 | 0.819 | 0.873 | 0.925 | 1.044 | 1.113 | 1.111 | 1.175 | 1.366 | 1.269 | 1.355 | 1.291 | 1.339 | 1.378 | 1.164 | 1.347 | 1.312 | 1.170 | 1.159 | 1.143 | 0.996 | 0.971 | 0.851 | 0.906 | 0.941 | 0.973 | 0.850 | 0.872 | 0.902 | 0.933 | 0.994 | 0.924 | 0.871 | 0.982 | 1.048 | 1.070 | 1.065 | 1.036 | 1.043 | 1.063 | 1.354 | 1.340 | 1.377 | 1.329 | 1.526 | 1.484 | 1.358 | 1.342 | 1.221 | 1.198 | 1.353 | 1.362 | 1.919 | 1.839 | 1.880 | 1.878 | 1.949 | 1.982 | 
| Path AP | 1.000 | 0.975 | 0.855 | 0.909 | 0.945 | 0.977 | 0.853 | 0.876 | 0.906 | 0.937 | 1.001 | 0.891 | 0.851 | 0.551 | 0.588 | 0.588 | 0.612 | 0.625 | 0.625 | 0.645 | 0.622 | 0.621 | 0.661 | 0.708 | 0.703 | 0.681 | 0.763 | 0.767 | 0.728 | 0.760 | 0.730 | 0.688 | 0.654 | 0.586 | 0.524 | 0.566 | 0.524 | 0.520 | 0.564 | 0.620 | 0.625 | 0.618 | 0.617 | 0.608 | 0.728 | 0.810 | 0.773 | 0.798 | 0.781 | 0.868 | 0.868 | 0.783 | 0.932 | 0.932 | 0.941 | 1.355 | 1.325 | 1.393 | 1.354 | 1.440 | 1.311 | 1.256 | 1.335 | 1.438 | 1.751 | 1.884 | 1.979 | 1.913 | 2.467 | 2.252 | 2.341 | 2.311 | 2.259 | 2.384 | 2.157 | 2.258 | 2.350 | 2.070 | 2.114 | 2.098 | 
| Path AQ | 1.000 | 1.107 | 1.205 | 1.087 | 1.074 | 1.175 | 1.115 | 1.006 | 1.125 | 0.955 | 0.956 | 0.981 | 0.960 | 0.857 | 0.776 | 0.690 | 0.756 | 0.754 | 0.769 | 0.743 | 0.730 | 0.779 | 0.770 | 0.822 | 0.737 | 0.675 | 0.533 | 0.531 | 0.541 | 0.539 | 0.491 | 0.487 | 0.462 | 0.390 | 0.414 | 0.398 | 0.372 | 0.415 | 0.409 | 0.439 | 0.436 | 0.429 | 0.432 | 0.441 | 0.572 | 0.569 | 0.574 | 0.580 | 0.640 | 0.620 | 0.586 | 0.561 | 0.511 | 0.487 | 0.467 | 0.501 | 0.571 | 0.672 | 0.717 | 0.715 | 0.756 | 0.879 | 0.817 | 0.872 | 0.831 | 0.862 | 0.887 | 0.749 | 0.867 | 0.845 | 0.753 | 0.746 | 0.736 | 0.641 | 0.625 | 0.548 | 0.583 | 0.606 | 0.614 | 0.603 | 
| Path AR | 1.000 | 0.957 | 0.949 | 0.954 | 0.920 | 0.854 | 0.833 | 0.655 | 0.689 | 0.707 | 0.653 | 0.727 | 0.743 | 0.761 | 0.769 | 0.770 | 0.791 | 0.778 | 1.040 | 1.010 | 1.015 | 1.040 | 1.080 | 1.113 | 1.145 | 1.056 | 0.972 | 0.972 | 0.919 | 0.915 | 0.917 | 0.976 | 0.971 | 0.929 | 0.962 | 1.064 | 1.095 | 1.081 | 1.079 | 1.084 | 1.016 | 0.987 | 0.942 | 0.731 | 0.783 | 0.811 | 0.733 | 0.830 | 0.833 | 0.868 | 0.873 | 0.859 | 0.920 | 0.991 | 0.949 | 0.941 | 0.945 | 0.912 | 0.847 | 0.826 | 0.649 | 0.683 | 0.701 | 0.647 | 0.721 | 0.736 | 0.755 | 0.763 | 0.763 | 0.784 | 0.771 | 1.031 | 1.001 | 1.006 | 1.031 | 1.070 | 1.103 | 1.135 | 1.138 | 1.113 | 
| Path AS | 1.000 | 0.958 | 0.980 | 0.979 | 0.977 | 0.980 | 0.889 | 0.943 | 0.974 | 1.139 | 1.391 | 1.448 | 1.314 | 1.649 | 1.712 | 1.850 | 1.693 | 1.654 | 1.806 | 1.734 | 1.556 | 1.737 | 1.450 | 1.506 | 1.531 | 1.500 | 1.337 | 1.373 | 1.562 | 1.454 | 1.419 | 1.510 | 1.566 | 1.569 | 1.543 | 1.591 | 1.534 | 1.424 | 1.398 | 1.254 | 1.105 | 1.209 | 1.124 | 1.060 | 1.194 | 1.275 | 1.301 | 1.296 | 1.260 | 1.269 | 1.293 | 1.647 | 1.941 | 1.982 | 2.011 | 1.983 | 1.979 | 2.079 | 1.930 | 1.937 | 2.153 | 1.949 | 1.829 | 1.894 | 1.656 | 1.640 | 1.393 | 1.357 | 1.286 | 1.436 | 1.363 | 1.383 | 1.350 | 1.482 | 1.423 | 1.466 | 1.347 | 1.079 | 1.122 | 1.131 | 
| Path AT | 1.000 | 0.942 | 0.979 | 1.101 | 1.075 | 1.071 | 1.091 | 1.087 | 0.990 | 0.982 | 0.932 | 0.785 | 0.835 | 0.803 | 0.750 | 0.836 | 0.826 | 0.885 | 0.879 | 0.865 | 0.870 | 0.889 | 1.153 | 1.147 | 1.157 | 1.169 | 1.293 | 1.348 | 1.149 | 1.196 | 1.205 | 1.285 | 1.361 | 1.210 | 1.221 | 0.871 | 0.787 | 0.793 | 0.835 | 0.863 | 0.832 | 0.894 | 0.880 | 0.868 | 0.888 | 0.957 | 0.963 | 0.914 | 0.954 | 0.916 | 0.864 | 0.821 | 0.805 | 0.905 | 0.884 | 0.880 | 0.896 | 0.893 | 0.813 | 0.807 | 0.766 | 0.646 | 0.686 | 0.660 | 0.616 | 0.687 | 0.678 | 0.727 | 0.723 | 0.711 | 0.715 | 0.731 | 0.948 | 0.942 | 0.951 | 0.961 | 1.060 | 1.027 | 0.981 | 0.635 | 
| Path AU | 1.000 | 0.974 | 0.923 | 1.031 | 0.978 | 0.993 | 0.969 | 1.064 | 1.021 | 1.052 | 0.967 | 0.774 | 0.694 | 0.659 | 0.612 | 0.669 | 0.657 | 0.776 | 0.710 | 0.668 | 0.695 | 0.782 | 0.763 | 0.760 | 0.774 | 0.772 | 0.847 | 0.903 | 0.901 | 0.952 | 1.107 | 1.029 | 1.099 | 1.047 | 1.086 | 1.117 | 0.944 | 1.092 | 1.064 | 0.949 | 0.939 | 0.927 | 0.807 | 0.787 | 0.690 | 0.734 | 0.763 | 0.788 | 0.689 | 0.707 | 0.732 | 0.757 | 0.732 | 0.728 | 0.722 | 0.721 | 0.810 | 0.764 | 0.738 | 0.785 | 0.815 | 0.842 | 0.881 | 0.864 | 0.882 | 0.793 | 0.781 | 0.747 | 0.629 | 0.642 | 0.635 | 0.585 | 0.664 | 0.672 | 0.696 | 0.727 | 0.701 | 0.711 | 0.717 | 0.764 | 
| Path AV | 1.000 | 1.022 | 1.325 | 1.317 | 1.329 | 1.343 | 1.482 | 1.435 | 1.357 | 1.300 | 1.121 | 1.137 | 1.277 | 1.318 | 1.678 | 1.815 | 1.808 | 1.811 | 1.772 | 1.846 | 1.722 | 1.734 | 1.795 | 2.117 | 2.538 | 2.666 | 2.523 | 2.542 | 2.674 | 2.765 | 2.667 | 2.864 | 2.819 | 2.782 | 2.846 | 3.067 | 3.086 | 2.928 | 3.055 | 2.936 | 2.768 | 2.632 | 2.356 | 2.107 | 2.275 | 2.108 | 2.092 | 2.266 | 2.493 | 2.514 | 2.483 | 2.481 | 2.355 | 2.190 | 2.069 | 2.355 | 2.353 | 2.376 | 3.424 | 3.347 | 3.518 | 3.421 | 3.636 | 3.313 | 3.173 | 3.372 | 3.632 | 4.423 | 4.760 | 4.998 | 4.832 | 6.231 | 5.689 | 5.912 | 5.839 | 5.706 | 6.022 | 5.448 | 5.629 | 4.918 | 
| Path AW | 1.000 | 0.940 | 0.937 | 0.978 | 0.905 | 0.901 | 0.967 | 0.897 | 0.842 | 0.865 | 0.715 | 0.743 | 0.679 | 0.643 | 0.651 | 0.721 | 0.644 | 0.644 | 0.646 | 0.717 | 0.723 | 0.639 | 0.658 | 0.485 | 0.440 | 0.433 | 0.479 | 0.490 | 0.502 | 0.508 | 0.508 | 0.522 | 0.513 | 0.686 | 0.666 | 0.670 | 0.686 | 0.712 | 0.734 | 0.755 | 0.696 | 0.539 | 0.581 | 0.642 | 0.657 | 0.664 | 0.980 | 0.923 | 0.973 | 0.948 | 1.030 | 0.917 | 0.938 | 1.217 | 1.210 | 1.221 | 1.234 | 1.361 | 1.319 | 1.247 | 1.194 | 1.030 | 1.044 | 1.173 | 1.211 | 1.541 | 1.668 | 1.661 | 1.664 | 1.628 | 1.695 | 1.582 | 1.593 | 1.649 | 1.944 | 2.331 | 2.449 | 2.293 | 2.436 | 2.530 | 
| Path AX | 1.000 | 1.063 | 0.968 | 0.927 | 0.986 | 1.062 | 1.293 | 1.391 | 1.461 | 1.413 | 1.821 | 1.663 | 1.728 | 1.707 | 1.668 | 1.760 | 1.593 | 1.667 | 1.736 | 1.528 | 1.459 | 1.497 | 1.313 | 1.310 | 1.160 | 1.161 | 1.155 | 1.119 | 1.135 | 1.132 | 1.058 | 0.996 | 0.878 | 0.829 | 0.848 | 0.777 | 0.843 | 0.865 | 0.924 | 0.931 | 0.951 | 0.944 | 0.935 | 1.153 | 1.244 | 1.243 | 1.208 | 1.213 | 1.332 | 1.383 | 1.211 | 1.032 | 1.058 | 1.046 | 1.062 | 0.929 | 1.042 | 1.071 | 1.239 | 1.566 | 1.614 | 1.458 | 1.772 | 1.864 | 1.993 | 1.831 | 1.795 | 1.919 | 1.853 | 1.727 | 1.882 | 1.731 | 1.660 | 1.734 | 1.629 | 1.494 | 1.290 | 1.168 | 1.152 | 1.179 | 
| Path AY | 1.000 | 1.031 | 0.994 | 0.922 | 0.906 | 0.812 | 0.716 | 0.783 | 0.728 | 0.687 | 0.774 | 0.826 | 0.843 | 0.840 | 0.817 | 0.822 | 0.838 | 1.067 | 1.056 | 1.085 | 1.048 | 1.203 | 1.170 | 1.070 | 1.057 | 0.963 | 0.929 | 0.768 | 0.798 | 0.730 | 0.691 | 0.700 | 0.775 | 0.692 | 0.692 | 0.695 | 0.770 | 0.777 | 0.687 | 0.707 | 0.522 | 0.472 | 0.465 | 0.432 | 0.463 | 0.476 | 0.541 | 0.504 | 0.492 | 0.523 | 0.542 | 0.543 | 0.513 | 0.509 | 0.483 | 0.407 | 0.433 | 0.416 | 0.389 | 0.434 | 0.428 | 0.459 | 0.456 | 0.448 | 0.451 | 0.461 | 0.598 | 0.595 | 0.600 | 0.606 | 0.669 | 0.648 | 0.613 | 0.587 | 0.506 | 0.513 | 0.576 | 0.595 | 0.592 | 0.582 | 
| Path AZ | 1.000 | 1.095 | 1.044 | 1.001 | 1.073 | 1.223 | 1.440 | 1.536 | 1.532 | 1.620 | 1.883 | 1.750 | 1.869 | 1.780 | 1.847 | 1.900 | 1.605 | 1.858 | 1.810 | 1.613 | 1.598 | 1.576 | 1.373 | 1.339 | 1.174 | 1.249 | 1.158 | 0.899 | 0.963 | 0.997 | 0.901 | 1.020 | 1.024 | 1.067 | 1.074 | 1.057 | 1.098 | 1.078 | 1.388 | 1.408 | 1.421 | 1.447 | 1.508 | 1.544 | 1.543 | 1.378 | 1.282 | 1.211 | 1.378 | 1.377 | 1.390 | 2.003 | 1.954 | 1.976 | 2.709 | 2.744 | 2.783 | 2.831 | 2.909 | 2.762 | 2.618 | 2.698 | 2.760 | 3.272 | 4.084 | 4.124 | 4.040 | 4.585 | 4.682 | 4.751 | 4.684 | 4.675 | 4.911 | 4.559 | 4.576 | 5.085 | 4.604 | 4.320 | 4.349 | 6.127 | 
| Path BA | 1.000 | 1.037 | 1.039 | 1.022 | 1.054 | 1.016 | 0.943 | 0.926 | 0.830 | 0.732 | 0.800 | 0.744 | 0.702 | 0.791 | 0.845 | 0.862 | 0.858 | 0.835 | 0.840 | 0.856 | 1.091 | 1.080 | 1.109 | 1.071 | 1.229 | 1.196 | 1.205 | 1.163 | 1.335 | 1.298 | 1.188 | 1.174 | 1.069 | 1.048 | 1.183 | 1.192 | 1.679 | 1.609 | 1.644 | 1.643 | 1.641 | 1.645 | 1.492 | 1.583 | 1.635 | 1.913 | 2.334 | 2.431 | 2.206 | 2.769 | 2.874 | 3.105 | 3.135 | 3.024 | 3.247 | 3.196 | 3.154 | 3.227 | 3.478 | 3.498 | 3.320 | 3.464 | 3.329 | 3.138 | 2.984 | 2.672 | 2.390 | 2.580 | 2.390 | 2.372 | 2.569 | 2.826 | 2.850 | 2.816 | 2.813 | 2.770 | 3.320 | 3.694 | 3.588 | 3.607 | 
| Path BB | 1.000 | 1.052 | 1.125 | 1.033 | 1.013 | 1.083 | 1.046 | 0.975 | 1.062 | 0.977 | 0.937 | 0.978 | 0.919 | 0.843 | 0.728 | 0.659 | 0.704 | 0.720 | 0.721 | 0.706 | 0.694 | 0.740 | 0.735 | 0.773 | 0.663 | 0.534 | 0.428 | 0.444 | 0.457 | 0.386 | 0.447 | 0.435 | 0.388 | 0.384 | 0.379 | 0.330 | 0.322 | 0.282 | 0.300 | 0.312 | 0.322 | 0.282 | 0.289 | 0.299 | 0.309 | 0.331 | 0.294 | 0.281 | 0.182 | 0.194 | 0.194 | 0.202 | 0.177 | 0.155 | 0.174 | 0.179 | 0.206 | 0.261 | 0.269 | 0.243 | 0.295 | 0.311 | 0.332 | 0.305 | 0.299 | 0.320 | 0.309 | 0.288 | 0.314 | 0.288 | 0.277 | 0.289 | 0.271 | 0.249 | 0.215 | 0.195 | 0.208 | 0.213 | 0.209 | 0.217 | 
| Path BC | 1.000 | 1.081 | 0.989 | 0.966 | 1.055 | 1.013 | 0.909 | 1.015 | 0.847 | 0.879 | 0.894 | 0.876 | 0.769 | 0.716 | 0.626 | 0.676 | 0.687 | 0.704 | 0.673 | 0.667 | 0.707 | 0.698 | 0.749 | 0.668 | 0.554 | 0.472 | 0.455 | 0.471 | 0.492 | 0.474 | 0.481 | 0.472 | 0.620 | 0.608 | 0.632 | 0.623 | 0.665 | 0.676 | 0.676 | 0.613 | 0.513 | 0.534 | 0.597 | 0.620 | 0.744 | 0.859 | 0.898 | 0.887 | 0.814 | 0.891 | 0.850 | 0.815 | 0.864 | 0.891 | 0.859 | 0.858 | 0.913 | 0.979 | 0.972 | 0.941 | 0.955 | 0.952 | 0.890 | 0.838 | 0.738 | 0.698 | 0.713 | 0.654 | 0.709 | 0.728 | 0.777 | 0.783 | 0.800 | 0.794 | 0.786 | 0.970 | 1.047 | 1.045 | 0.947 | 0.932 | 
| Path BD | 1.000 | 0.881 | 0.964 | 0.896 | 0.845 | 0.953 | 1.017 | 1.038 | 1.034 | 1.005 | 1.012 | 1.031 | 1.313 | 1.300 | 1.336 | 1.290 | 1.481 | 1.440 | 1.317 | 1.302 | 1.185 | 1.163 | 1.312 | 1.321 | 1.862 | 1.784 | 1.976 | 1.756 | 1.773 | 1.265 | 1.143 | 1.152 | 1.212 | 1.253 | 1.208 | 1.298 | 1.277 | 1.260 | 1.290 | 1.390 | 1.398 | 1.327 | 1.385 | 1.330 | 1.254 | 1.192 | 1.068 | 0.955 | 1.031 | 0.955 | 0.948 | 1.027 | 1.285 | 1.210 | 1.276 | 1.244 | 1.351 | 1.204 | 1.174 | 1.153 | 1.254 | 1.505 | 1.796 | 1.819 | 1.732 | 2.201 | 1.954 | 2.206 | 2.075 | 2.067 | 2.159 | 1.997 | 1.988 | 2.133 | 1.978 | 1.857 | 1.908 | 1.576 | 1.681 | 1.715 | 
| Path BE | 1.000 | 1.135 | 1.159 | 1.176 | 1.159 | 1.157 | 1.216 | 1.129 | 1.133 | 1.259 | 1.140 | 1.069 | 1.107 | 0.969 | 0.959 | 0.815 | 0.794 | 0.752 | 0.840 | 0.797 | 0.809 | 0.789 | 0.867 | 0.832 | 0.857 | 0.787 | 0.730 | 0.642 | 0.613 | 0.629 | 0.552 | 0.550 | 0.488 | 0.488 | 0.514 | 0.536 | 0.457 | 0.475 | 0.479 | 0.511 | 0.541 | 0.481 | 0.485 | 0.346 | 0.313 | 0.315 | 0.332 | 0.343 | 0.331 | 0.355 | 0.350 | 0.345 | 0.429 | 0.465 | 0.463 | 0.464 | 0.453 | 0.472 | 0.441 | 0.444 | 0.459 | 0.542 | 0.649 | 0.682 | 0.639 | 0.734 | 0.813 | 0.885 | 0.798 | 0.789 | 0.863 | 0.818 | 0.738 | 0.826 | 0.701 | 0.702 | 0.720 | 0.705 | 0.716 | 0.715 | 
| Path BF | 1.000 | 0.995 | 1.068 | 0.991 | 0.930 | 0.956 | 0.789 | 0.821 | 0.750 | 0.711 | 0.720 | 0.797 | 0.711 | 0.712 | 0.714 | 0.792 | 0.799 | 0.706 | 0.727 | 0.536 | 0.486 | 0.478 | 0.445 | 0.476 | 0.489 | 0.556 | 0.510 | 0.538 | 0.524 | 0.570 | 0.508 | 0.495 | 0.486 | 0.529 | 0.635 | 0.758 | 0.767 | 0.730 | 0.928 | 0.824 | 0.930 | 0.875 | 0.872 | 0.910 | 0.842 | 0.838 | 0.899 | 0.834 | 0.783 | 0.805 | 0.665 | 0.691 | 0.715 | 0.753 | 0.785 | 0.669 | 0.696 | 0.702 | 0.748 | 0.792 | 0.704 | 0.711 | 0.507 | 0.459 | 0.462 | 0.486 | 0.502 | 0.485 | 0.520 | 0.512 | 0.505 | 0.517 | 0.557 | 0.561 | 0.532 | 0.555 | 0.533 | 0.503 | 0.567 | 0.573 | 
| Path BG | 1.000 | 1.066 | 1.067 | 1.110 | 1.135 | 1.135 | 1.170 | 1.128 | 1.126 | 1.199 | 1.285 | 1.276 | 1.236 | 1.254 | 1.250 | 1.168 | 1.100 | 0.969 | 0.916 | 0.937 | 0.858 | 0.931 | 0.955 | 1.021 | 1.028 | 1.050 | 1.036 | 1.077 | 1.211 | 1.183 | 1.178 | 1.200 | 1.196 | 1.089 | 1.080 | 1.026 | 0.864 | 0.918 | 0.883 | 0.825 | 0.920 | 0.908 | 0.974 | 0.968 | 0.951 | 0.958 | 0.978 | 1.269 | 1.262 | 1.273 | 1.286 | 1.419 | 1.360 | 1.286 | 1.280 | 1.283 | 1.366 | 1.359 | 1.300 | 1.346 | 1.489 | 1.532 | 1.511 | 1.510 | 1.516 | 1.421 | 1.380 | 1.318 | 1.023 | 1.095 | 1.135 | 1.026 | 1.160 | 1.165 | 1.214 | 1.222 | 1.202 | 1.249 | 1.244 | 1.299 | 
| Path BH | 1.000 | 0.976 | 0.958 | 1.042 | 1.250 | 1.492 | 1.512 | 1.439 | 1.829 | 1.624 | 1.833 | 1.724 | 1.717 | 1.793 | 1.659 | 1.651 | 1.772 | 1.643 | 1.543 | 1.585 | 1.310 | 1.362 | 1.244 | 1.179 | 1.194 | 1.322 | 1.321 | 1.338 | 1.357 | 1.380 | 1.419 | 1.347 | 1.276 | 1.315 | 1.346 | 1.595 | 1.991 | 2.011 | 1.969 | 2.235 | 2.283 | 2.316 | 2.284 | 2.279 | 2.394 | 2.222 | 2.231 | 2.479 | 2.245 | 2.106 | 2.181 | 1.907 | 1.771 | 1.992 | 1.878 | 1.815 | 1.929 | 2.004 | 2.069 | 2.166 | 2.123 | 2.168 | 1.948 | 1.920 | 1.835 | 1.546 | 1.578 | 1.561 | 1.437 | 1.633 | 1.652 | 1.712 | 1.787 | 1.724 | 1.747 | 1.715 | 2.252 | 2.210 | 2.166 | 2.221 | 
| Path BI | 1.000 | 0.915 | 0.861 | 0.895 | 1.007 | 0.983 | 0.979 | 0.998 | 0.994 | 0.905 | 0.898 | 0.853 | 0.718 | 0.763 | 0.735 | 0.685 | 0.765 | 0.755 | 0.809 | 0.804 | 0.791 | 0.796 | 0.813 | 1.055 | 1.049 | 1.058 | 1.073 | 1.054 | 1.357 | 1.376 | 1.389 | 1.414 | 1.474 | 1.510 | 1.508 | 1.347 | 1.253 | 1.184 | 1.347 | 1.346 | 1.359 | 1.959 | 1.915 | 2.013 | 1.957 | 2.080 | 1.895 | 1.815 | 1.929 | 2.078 | 2.530 | 2.723 | 2.647 | 2.535 | 2.186 | 2.216 | 2.490 | 2.570 | 3.272 | 3.540 | 3.525 | 3.532 | 3.455 | 3.599 | 3.357 | 3.381 | 3.499 | 4.127 | 4.949 | 5.197 | 4.867 | 5.594 | 6.194 | 6.742 | 6.083 | 6.010 | 6.574 | 6.235 | 6.309 | 6.987 | 
| Path BJ | 1.000 | 1.023 | 1.212 | 1.514 | 1.528 | 1.497 | 1.699 | 1.735 | 1.761 | 1.736 | 1.733 | 1.820 | 1.690 | 1.696 | 1.885 | 1.706 | 1.601 | 1.658 | 1.450 | 1.435 | 1.220 | 1.188 | 1.126 | 1.257 | 1.193 | 1.211 | 1.264 | 1.214 | 1.089 | 1.216 | 1.015 | 1.054 | 1.071 | 1.049 | 0.921 | 0.858 | 0.750 | 0.810 | 0.823 | 0.844 | 0.807 | 0.799 | 0.847 | 0.836 | 0.897 | 0.800 | 0.664 | 0.565 | 0.565 | 0.535 | 0.532 | 0.533 | 0.548 | 0.571 | 0.585 | 0.584 | 0.522 | 0.485 | 0.458 | 0.522 | 0.521 | 0.526 | 0.758 | 0.741 | 0.779 | 0.758 | 0.805 | 0.734 | 0.703 | 0.747 | 0.805 | 0.980 | 1.054 | 1.107 | 1.071 | 1.380 | 1.260 | 1.310 | 1.450 | 1.578 | 
| Path BK | 1.000 | 0.998 | 1.048 | 0.973 | 0.977 | 1.086 | 0.983 | 0.922 | 0.955 | 0.835 | 0.827 | 0.703 | 0.684 | 0.649 | 0.724 | 0.687 | 0.698 | 0.681 | 0.748 | 0.718 | 0.739 | 0.679 | 0.544 | 0.488 | 0.463 | 0.430 | 0.445 | 0.375 | 0.399 | 0.384 | 0.358 | 0.399 | 0.394 | 0.423 | 0.420 | 0.413 | 0.416 | 0.425 | 0.551 | 0.548 | 0.553 | 0.558 | 0.616 | 0.597 | 0.564 | 0.540 | 0.466 | 0.473 | 0.531 | 0.548 | 0.698 | 0.755 | 0.731 | 0.839 | 0.816 | 0.747 | 0.738 | 0.671 | 0.659 | 0.744 | 0.749 | 1.055 | 1.011 | 1.033 | 1.032 | 1.031 | 1.034 | 0.938 | 0.995 | 1.028 | 1.202 | 1.467 | 1.528 | 1.386 | 1.740 | 1.806 | 1.951 | 1.786 | 1.950 | 1.873 | 
| Path BL | 1.000 | 1.038 | 0.909 | 0.774 | 0.810 | 0.788 | 0.897 | 0.908 | 1.244 | 1.261 | 1.278 | 1.300 | 1.336 | 1.269 | 1.203 | 1.239 | 1.268 | 1.503 | 1.876 | 1.894 | 1.855 | 2.106 | 2.151 | 2.182 | 2.151 | 2.147 | 2.366 | 2.292 | 2.326 | 2.318 | 2.166 | 2.040 | 1.798 | 1.699 | 1.737 | 1.592 | 1.726 | 1.772 | 1.893 | 1.907 | 1.947 | 1.933 | 1.915 | 2.362 | 2.549 | 2.546 | 2.475 | 2.484 | 2.729 | 2.832 | 2.480 | 2.113 | 2.145 | 2.043 | 2.120 | 2.181 | 1.842 | 2.132 | 2.077 | 1.852 | 1.834 | 1.809 | 1.576 | 1.536 | 1.347 | 1.434 | 1.490 | 1.539 | 1.345 | 1.381 | 1.428 | 1.477 | 1.578 | 1.404 | 1.342 | 0.869 | 0.926 | 0.927 | 0.910 | 1.196 | 
| Path BM | 1.000 | 0.987 | 1.010 | 1.088 | 1.095 | 1.039 | 1.084 | 1.041 | 0.982 | 0.933 | 0.836 | 0.748 | 0.807 | 0.748 | 0.742 | 0.804 | 0.884 | 0.892 | 0.881 | 0.880 | 0.867 | 1.039 | 1.156 | 1.103 | 1.138 | 1.115 | 1.141 | 1.214 | 1.261 | 1.303 | 1.139 | 1.169 | 1.209 | 1.251 | 1.336 | 1.189 | 1.136 | 0.735 | 0.784 | 0.785 | 0.816 | 0.834 | 0.835 | 0.861 | 0.829 | 0.828 | 0.882 | 0.945 | 0.938 | 0.909 | 0.922 | 0.919 | 0.842 | 0.839 | 0.876 | 0.811 | 0.807 | 0.866 | 0.803 | 0.754 | 0.775 | 0.640 | 0.665 | 0.608 | 0.576 | 0.583 | 0.646 | 0.577 | 0.577 | 0.579 | 0.642 | 0.647 | 0.572 | 0.589 | 0.435 | 0.394 | 0.388 | 0.360 | 0.355 | 0.369 | 
| Path BN | 1.000 | 1.027 | 1.004 | 0.897 | 0.812 | 0.722 | 0.791 | 0.789 | 0.805 | 0.778 | 0.764 | 0.816 | 0.806 | 0.860 | 0.772 | 0.707 | 0.538 | 0.535 | 0.514 | 0.504 | 0.516 | 0.546 | 0.560 | 0.520 | 0.536 | 0.586 | 0.585 | 0.511 | 0.574 | 0.590 | 0.682 | 0.862 | 0.888 | 0.802 | 0.975 | 1.026 | 1.097 | 1.008 | 0.988 | 1.056 | 1.020 | 0.950 | 1.036 | 0.953 | 0.914 | 0.954 | 0.896 | 0.822 | 0.710 | 0.643 | 0.686 | 0.702 | 0.651 | 0.635 | 0.557 | 0.593 | 0.616 | 0.636 | 0.556 | 0.571 | 0.590 | 0.611 | 0.652 | 0.580 | 0.555 | 0.359 | 0.383 | 0.383 | 0.399 | 0.407 | 0.407 | 0.420 | 0.405 | 0.404 | 0.430 | 0.461 | 0.458 | 0.444 | 0.483 | 0.579 | 
| Path BO | 1.000 | 0.998 | 1.055 | 1.227 | 1.140 | 1.217 | 1.159 | 1.203 | 1.238 | 1.045 | 1.210 | 1.178 | 1.051 | 1.040 | 1.026 | 0.894 | 0.872 | 0.765 | 0.813 | 0.845 | 0.873 | 0.763 | 0.783 | 0.810 | 0.838 | 0.895 | 0.869 | 0.877 | 0.886 | 0.978 | 0.947 | 0.895 | 0.858 | 0.740 | 0.750 | 0.843 | 0.870 | 1.107 | 1.198 | 1.193 | 1.195 | 1.169 | 1.218 | 1.136 | 1.144 | 1.184 | 1.397 | 1.675 | 1.759 | 1.647 | 1.893 | 2.096 | 2.135 | 2.139 | 2.093 | 2.180 | 2.034 | 2.048 | 2.120 | 2.500 | 2.998 | 3.148 | 2.948 | 3.388 | 3.752 | 4.084 | 3.685 | 3.640 | 3.982 | 3.776 | 3.408 | 3.814 | 3.236 | 3.238 | 3.325 | 3.252 | 2.904 | 2.630 | 2.466 | 2.394 | 
| Path BP | 1.000 | 1.020 | 1.016 | 0.988 | 0.995 | 1.014 | 1.291 | 1.278 | 1.313 | 1.268 | 1.456 | 1.415 | 1.295 | 1.280 | 1.165 | 1.143 | 1.290 | 1.299 | 1.830 | 1.754 | 1.793 | 1.791 | 1.789 | 1.793 | 1.627 | 1.726 | 1.929 | 2.072 | 2.039 | 2.012 | 2.059 | 2.219 | 2.232 | 2.118 | 2.210 | 2.123 | 2.002 | 1.904 | 1.705 | 1.525 | 1.646 | 1.525 | 1.513 | 1.639 | 1.803 | 1.819 | 1.796 | 1.795 | 1.767 | 2.118 | 2.357 | 2.249 | 2.349 | 2.417 | 2.228 | 1.723 | 1.858 | 2.054 | 2.103 | 2.125 | 3.134 | 2.953 | 3.112 | 3.033 | 3.294 | 2.936 | 2.864 | 2.813 | 3.059 | 3.670 | 4.382 | 4.438 | 4.225 | 5.369 | 4.767 | 5.381 | 5.061 | 5.041 | 5.062 | 4.745 | 
| Path BQ | 1.000 | 1.020 | 1.016 | 0.988 | 0.995 | 1.014 | 1.291 | 1.278 | 1.313 | 1.268 | 1.456 | 1.415 | 1.295 | 1.280 | 1.165 | 1.143 | 1.290 | 1.299 | 1.830 | 1.754 | 1.793 | 1.791 | 1.789 | 1.793 | 1.627 | 1.726 | 1.801 | 1.795 | 1.874 | 1.734 | 1.726 | 1.852 | 1.718 | 1.613 | 1.657 | 1.369 | 1.423 | 1.301 | 1.232 | 1.248 | 1.381 | 1.233 | 1.234 | 1.238 | 1.373 | 1.385 | 1.224 | 1.260 | 0.930 | 0.842 | 0.829 | 0.771 | 0.896 | 0.898 | 0.883 | 0.911 | 0.878 | 0.815 | 0.800 | 0.718 | 0.633 | 0.692 | 0.643 | 0.607 | 0.683 | 0.730 | 0.745 | 0.742 | 0.722 | 0.726 | 0.740 | 0.943 | 0.933 | 0.959 | 0.925 | 1.062 | 1.033 | 0.946 | 0.963 | 1.004 | 
| Path BR | 1.000 | 1.074 | 1.057 | 1.043 | 1.067 | 1.150 | 1.157 | 1.098 | 1.146 | 1.101 | 1.038 | 0.987 | 0.884 | 0.790 | 0.853 | 0.790 | 0.784 | 0.850 | 0.935 | 0.943 | 0.931 | 0.930 | 0.916 | 1.098 | 1.222 | 1.166 | 1.224 | 1.379 | 1.473 | 1.503 | 1.497 | 1.456 | 1.466 | 1.493 | 1.902 | 1.883 | 1.935 | 1.867 | 2.144 | 2.085 | 1.908 | 1.885 | 1.716 | 1.684 | 1.901 | 1.914 | 2.696 | 2.583 | 2.641 | 2.639 | 2.635 | 2.641 | 2.519 | 2.499 | 2.707 | 2.978 | 3.003 | 2.967 | 2.964 | 2.919 | 3.498 | 3.892 | 3.714 | 3.832 | 3.755 | 4.168 | 4.170 | 3.762 | 3.290 | 3.325 | 3.304 | 3.728 | 3.764 | 5.233 | 5.198 | 5.309 | 5.285 | 5.223 | 5.390 | 6.861 | 
| Path BS | 1.000 | 0.929 | 1.014 | 0.997 | 1.177 | 1.077 | 1.014 | 1.054 | 1.186 | 1.158 | 1.153 | 1.175 | 1.171 | 1.066 | 1.057 | 1.004 | 0.846 | 0.899 | 0.865 | 0.807 | 0.900 | 0.889 | 0.953 | 0.947 | 0.931 | 0.937 | 0.930 | 0.946 | 0.969 | 0.927 | 0.918 | 0.973 | 0.961 | 1.030 | 0.919 | 0.763 | 0.649 | 0.649 | 0.614 | 0.611 | 0.613 | 0.652 | 0.649 | 0.621 | 0.643 | 0.711 | 0.731 | 0.722 | 0.721 | 0.724 | 0.679 | 0.659 | 0.652 | 0.611 | 0.593 | 0.567 | 0.440 | 0.471 | 0.488 | 0.441 | 0.499 | 0.501 | 0.522 | 0.525 | 0.517 | 0.537 | 0.527 | 0.679 | 0.689 | 0.695 | 0.708 | 0.738 | 0.755 | 0.755 | 0.674 | 0.627 | 0.592 | 0.674 | 0.640 | 0.606 | 
| Path BT | 1.000 | 1.194 | 1.209 | 1.151 | 1.463 | 1.299 | 1.466 | 1.379 | 1.374 | 1.435 | 1.327 | 1.321 | 1.417 | 1.315 | 1.234 | 1.268 | 1.048 | 1.089 | 0.996 | 0.943 | 0.955 | 1.057 | 0.944 | 0.945 | 0.948 | 1.051 | 0.952 | 1.036 | 0.935 | 0.923 | 1.010 | 0.958 | 0.864 | 0.967 | 0.821 | 0.821 | 0.844 | 0.825 | 0.737 | 0.667 | 0.593 | 0.650 | 0.648 | 0.661 | 0.639 | 0.628 | 0.670 | 0.662 | 0.707 | 0.634 | 0.580 | 0.442 | 0.400 | 0.406 | 0.396 | 0.435 | 0.417 | 0.430 | 0.395 | 0.317 | 0.284 | 0.270 | 0.250 | 0.273 | 0.269 | 0.317 | 0.290 | 0.273 | 0.284 | 0.320 | 0.312 | 0.311 | 0.317 | 0.316 | 0.287 | 0.285 | 0.271 | 0.228 | 0.237 | 0.233 | 
| Path BU | 1.000 | 0.957 | 0.949 | 0.954 | 0.920 | 0.854 | 0.833 | 0.655 | 0.689 | 0.707 | 0.653 | 0.727 | 0.743 | 0.761 | 0.769 | 0.770 | 0.791 | 0.778 | 1.040 | 1.010 | 1.015 | 1.040 | 1.080 | 1.113 | 1.145 | 1.056 | 0.886 | 0.971 | 0.968 | 0.988 | 0.955 | 0.938 | 1.001 | 0.990 | 1.056 | 0.947 | 0.867 | 0.661 | 0.656 | 0.631 | 0.618 | 0.634 | 0.670 | 0.688 | 0.638 | 0.658 | 0.719 | 0.775 | 0.742 | 0.736 | 0.739 | 0.713 | 0.724 | 0.780 | 0.950 | 1.022 | 1.074 | 1.038 | 1.338 | 1.222 | 1.270 | 1.254 | 1.226 | 1.294 | 1.170 | 1.225 | 1.275 | 1.123 | 1.072 | 1.100 | 0.965 | 0.962 | 0.853 | 0.853 | 0.898 | 0.937 | 0.798 | 0.831 | 0.796 | 0.686 | 
| Path BV | 1.000 | 1.170 | 1.427 | 1.487 | 1.349 | 1.693 | 1.757 | 1.899 | 1.738 | 1.698 | 1.854 | 1.780 | 1.597 | 1.783 | 1.489 | 1.546 | 1.571 | 1.539 | 1.352 | 1.259 | 1.101 | 1.188 | 1.207 | 1.238 | 1.183 | 1.172 | 1.260 | 1.431 | 1.461 | 1.482 | 1.462 | 1.459 | 1.532 | 1.422 | 1.428 | 1.587 | 1.437 | 1.348 | 1.396 | 1.221 | 1.209 | 1.027 | 1.000 | 0.948 | 1.058 | 1.004 | 1.019 | 0.995 | 1.092 | 1.049 | 1.080 | 0.993 | 1.197 | 1.062 | 1.199 | 1.128 | 1.123 | 1.173 | 1.085 | 1.081 | 1.159 | 1.075 | 1.010 | 1.037 | 0.857 | 0.891 | 0.814 | 0.771 | 0.781 | 0.865 | 0.772 | 0.773 | 0.775 | 0.859 | 0.867 | 0.766 | 0.789 | 0.582 | 0.656 | 0.700 | 
| Path BW | 1.000 | 1.001 | 1.004 | 1.113 | 1.123 | 0.992 | 1.022 | 0.754 | 0.683 | 0.672 | 0.625 | 0.669 | 0.688 | 0.782 | 0.728 | 0.711 | 0.756 | 0.784 | 0.786 | 0.773 | 0.797 | 0.768 | 0.713 | 0.700 | 0.628 | 0.553 | 0.576 | 0.524 | 0.520 | 0.494 | 0.416 | 0.442 | 0.425 | 0.397 | 0.443 | 0.437 | 0.469 | 0.466 | 0.458 | 0.461 | 0.471 | 0.611 | 0.607 | 0.613 | 0.619 | 0.683 | 0.661 | 0.626 | 0.599 | 0.517 | 0.524 | 0.589 | 0.660 | 0.614 | 0.600 | 0.638 | 0.662 | 0.663 | 0.652 | 0.673 | 0.648 | 0.602 | 0.591 | 0.530 | 0.467 | 0.511 | 0.475 | 0.448 | 0.505 | 0.539 | 0.550 | 0.548 | 0.533 | 0.536 | 0.546 | 0.696 | 0.689 | 0.708 | 0.749 | 0.870 | 
| Path BX | 1.000 | 0.966 | 1.027 | 1.067 | 1.102 | 1.154 | 1.131 | 1.155 | 1.038 | 1.022 | 0.977 | 0.823 | 0.840 | 0.831 | 0.765 | 0.869 | 0.880 | 0.912 | 0.952 | 0.918 | 0.930 | 0.913 | 1.199 | 1.177 | 1.224 | 1.206 | 1.208 | 1.432 | 1.788 | 1.805 | 1.768 | 2.006 | 2.049 | 2.079 | 2.050 | 2.046 | 2.149 | 1.995 | 2.003 | 2.225 | 2.015 | 1.891 | 1.958 | 1.712 | 1.695 | 1.440 | 1.403 | 1.330 | 1.484 | 1.409 | 1.430 | 1.396 | 1.505 | 1.539 | 1.410 | 1.530 | 1.570 | 1.677 | 1.690 | 1.726 | 1.713 | 1.697 | 2.093 | 2.259 | 2.256 | 2.193 | 2.201 | 2.418 | 2.509 | 2.197 | 1.873 | 1.958 | 1.905 | 2.170 | 2.195 | 3.009 | 3.048 | 3.091 | 3.029 | 3.093 | 
| Path BY | 1.000 | 0.982 | 1.289 | 1.265 | 1.316 | 1.296 | 1.385 | 1.407 | 1.406 | 1.275 | 1.068 | 1.111 | 1.242 | 1.290 | 1.549 | 1.788 | 1.869 | 1.846 | 1.694 | 1.854 | 1.769 | 1.695 | 1.818 | 2.070 | 2.439 | 2.601 | 2.421 | 2.444 | 1.744 | 1.576 | 1.588 | 1.670 | 1.727 | 1.666 | 1.789 | 1.761 | 1.738 | 1.778 | 1.916 | 1.927 | 1.829 | 1.908 | 1.833 | 1.729 | 1.644 | 1.472 | 1.316 | 1.421 | 1.317 | 1.307 | 1.415 | 1.557 | 1.500 | 1.566 | 1.449 | 1.442 | 1.548 | 1.435 | 1.348 | 1.385 | 1.144 | 1.189 | 1.087 | 1.030 | 1.043 | 1.155 | 1.031 | 1.032 | 1.035 | 1.147 | 1.157 | 1.023 | 1.053 | 0.777 | 0.704 | 0.693 | 0.644 | 0.690 | 0.658 | 0.631 | 
| Path BZ | 1.000 | 1.139 | 1.152 | 1.580 | 1.601 | 1.623 | 1.651 | 1.697 | 1.611 | 1.527 | 1.573 | 1.609 | 1.908 | 2.382 | 2.405 | 2.356 | 2.674 | 2.731 | 2.771 | 2.731 | 2.726 | 2.864 | 2.658 | 2.668 | 2.965 | 2.685 | 2.065 | 2.173 | 2.231 | 2.058 | 2.292 | 2.343 | 2.402 | 2.427 | 2.429 | 2.496 | 2.454 | 3.281 | 3.185 | 3.202 | 3.281 | 3.406 | 3.510 | 3.611 | 3.329 | 2.575 | 2.777 | 3.070 | 3.142 | 3.176 | 4.684 | 4.412 | 5.606 | 6.473 | 6.768 | 6.683 | 6.131 | 6.712 | 6.403 | 6.136 | 6.581 | 7.496 | 8.831 | 9.415 | 9.393 | 9.932 | 11.548 | 10.732 | 11.458 | 10.915 | 11.325 | 11.652 | 9.840 | 11.390 | 11.094 | 9.892 | 9.796 | 9.664 | 9.287 | 9.102 | 
| Path CA | 1.000 | 1.011 | 1.011 | 1.039 | 1.022 | 1.366 | 1.326 | 1.333 | 1.366 | 1.418 | 1.461 | 1.504 | 1.386 | 1.072 | 1.156 | 1.278 | 1.308 | 1.322 | 1.950 | 1.837 | 1.936 | 1.887 | 2.050 | 1.827 | 1.782 | 1.750 | 1.831 | 1.841 | 1.886 | 1.958 | 2.017 | 2.076 | 1.914 | 1.480 | 1.596 | 1.764 | 1.806 | 1.825 | 2.692 | 2.536 | 2.673 | 2.605 | 2.829 | 2.522 | 2.460 | 2.416 | 2.627 | 3.152 | 3.764 | 3.811 | 3.629 | 4.612 | 4.521 | 4.720 | 4.552 | 4.613 | 4.530 | 5.948 | 5.836 | 6.071 | 5.981 | 6.387 | 6.492 | 6.485 | 5.881 | 4.927 | 5.125 | 5.727 | 5.949 | 7.144 | 8.249 | 8.624 | 8.516 | 7.813 | 8.553 | 8.159 | 7.819 | 8.386 | 8.373 | 7.918 | 
| Path CB | 1.000 | 1.015 | 1.011 | 0.945 | 0.890 | 0.784 | 0.741 | 0.758 | 0.695 | 0.753 | 0.773 | 0.826 | 0.832 | 0.850 | 0.844 | 0.836 | 1.031 | 1.112 | 1.111 | 1.080 | 1.084 | 1.191 | 1.236 | 1.082 | 0.922 | 0.964 | 0.962 | 0.913 | 0.849 | 0.927 | 0.911 | 1.076 | 0.984 | 0.926 | 0.963 | 1.083 | 1.058 | 1.053 | 1.073 | 1.070 | 0.974 | 0.966 | 0.917 | 0.773 | 0.821 | 0.790 | 0.737 | 0.823 | 0.812 | 0.871 | 0.865 | 0.851 | 0.945 | 0.942 | 0.961 | 0.928 | 0.912 | 0.974 | 0.962 | 1.027 | 0.921 | 0.844 | 0.643 | 0.638 | 0.614 | 0.601 | 0.617 | 0.652 | 0.669 | 0.621 | 0.640 | 0.700 | 0.754 | 0.721 | 0.715 | 0.719 | 0.693 | 0.644 | 0.658 | 0.674 | 
| Path CC | 1.000 | 1.234 | 1.331 | 1.329 | 1.293 | 1.298 | 1.425 | 1.479 | 1.295 | 1.104 | 1.154 | 1.123 | 1.279 | 1.294 | 1.773 | 1.797 | 1.822 | 1.853 | 1.905 | 1.808 | 1.714 | 1.766 | 1.807 | 2.142 | 2.674 | 2.700 | 2.646 | 3.003 | 3.067 | 3.112 | 3.068 | 3.062 | 3.217 | 2.986 | 2.997 | 3.331 | 3.015 | 2.829 | 2.930 | 2.562 | 2.537 | 2.155 | 2.100 | 1.990 | 2.221 | 2.108 | 2.140 | 2.089 | 2.293 | 2.201 | 2.268 | 2.084 | 2.049 | 2.197 | 1.960 | 1.627 | 1.385 | 1.385 | 1.310 | 1.304 | 1.307 | 1.391 | 1.384 | 1.324 | 1.371 | 1.517 | 1.560 | 1.540 | 1.538 | 1.544 | 1.447 | 1.405 | 1.342 | 1.042 | 1.116 | 1.156 | 1.045 | 1.182 | 1.139 | 1.057 | 
| Path CD | 1.000 | 0.993 | 0.954 | 0.935 | 0.959 | 1.014 | 1.040 | 0.966 | 0.995 | 1.088 | 1.172 | 1.122 | 1.113 | 1.118 | 1.078 | 1.001 | 0.976 | 0.767 | 0.808 | 0.829 | 0.765 | 0.852 | 0.871 | 0.893 | 0.902 | 0.903 | 0.794 | 0.792 | 0.702 | 0.702 | 0.740 | 0.771 | 0.657 | 0.684 | 0.689 | 0.735 | 0.778 | 0.692 | 0.699 | 0.498 | 0.450 | 0.454 | 0.477 | 0.493 | 0.476 | 0.511 | 0.503 | 0.497 | 0.508 | 0.547 | 0.551 | 0.523 | 0.523 | 0.558 | 0.500 | 0.458 | 0.349 | 0.347 | 0.333 | 0.327 | 0.335 | 0.354 | 0.363 | 0.337 | 0.348 | 0.380 | 0.409 | 0.392 | 0.389 | 0.391 | 0.377 | 0.350 | 0.341 | 0.268 | 0.282 | 0.290 | 0.267 | 0.298 | 0.333 | 0.345 | 
| Path CE | 1.000 | 1.023 | 1.103 | 1.109 | 1.053 | 1.098 | 1.055 | 0.995 | 0.946 | 0.847 | 0.758 | 0.818 | 0.758 | 0.752 | 0.815 | 0.896 | 0.904 | 0.893 | 0.892 | 0.878 | 1.052 | 1.171 | 1.117 | 1.153 | 1.130 | 1.254 | 1.285 | 1.342 | 1.260 | 1.156 | 0.999 | 0.904 | 0.965 | 0.987 | 0.989 | 0.969 | 0.952 | 1.015 | 1.008 | 1.060 | 0.909 | 0.733 | 0.674 | 0.635 | 0.632 | 0.626 | 0.625 | 0.703 | 0.663 | 0.640 | 0.681 | 0.707 | 0.736 | 0.764 | 0.786 | 0.664 | 0.768 | 0.748 | 0.667 | 0.661 | 0.652 | 0.568 | 0.554 | 0.486 | 0.517 | 0.537 | 0.555 | 0.485 | 0.497 | 0.515 | 0.532 | 0.569 | 0.506 | 0.484 | 0.313 | 0.334 | 0.334 | 0.347 | 0.311 | 0.296 | 
| Path CF | 1.000 | 1.001 | 0.981 | 0.964 | 1.028 | 1.021 | 1.073 | 0.921 | 0.742 | 0.683 | 0.643 | 0.640 | 0.634 | 0.633 | 0.712 | 0.671 | 0.649 | 0.690 | 0.716 | 0.740 | 0.774 | 0.759 | 0.775 | 0.696 | 0.686 | 0.656 | 0.538 | 0.552 | 0.540 | 0.482 | 0.437 | 0.388 | 0.425 | 0.424 | 0.433 | 0.418 | 0.411 | 0.439 | 0.433 | 0.463 | 0.415 | 0.380 | 0.289 | 0.287 | 0.276 | 0.271 | 0.278 | 0.294 | 0.301 | 0.280 | 0.288 | 0.315 | 0.313 | 0.322 | 0.297 | 0.230 | 0.247 | 0.274 | 0.280 | 0.283 | 0.417 | 0.393 | 0.414 | 0.404 | 0.439 | 0.391 | 0.382 | 0.375 | 0.407 | 0.489 | 0.584 | 0.591 | 0.563 | 0.715 | 0.635 | 0.717 | 0.674 | 0.671 | 0.668 | 0.681 | 
| Path CG | 1.000 | 0.995 | 0.952 | 0.985 | 1.090 | 1.121 | 1.107 | 1.105 | 1.110 | 1.040 | 1.010 | 0.965 | 0.749 | 0.802 | 0.831 | 0.751 | 0.850 | 0.853 | 0.889 | 0.894 | 0.880 | 0.914 | 0.898 | 1.156 | 1.173 | 1.183 | 1.195 | 1.273 | 1.365 | 1.354 | 1.312 | 1.331 | 1.327 | 1.240 | 1.168 | 1.029 | 0.972 | 0.994 | 0.911 | 0.988 | 1.014 | 1.084 | 1.091 | 1.115 | 1.107 | 1.096 | 1.352 | 1.459 | 1.457 | 1.417 | 1.422 | 1.562 | 1.444 | 1.756 | 1.847 | 1.975 | 1.814 | 1.779 | 1.902 | 1.836 | 1.711 | 1.865 | 1.715 | 1.645 | 1.718 | 1.614 | 1.480 | 1.279 | 1.157 | 1.236 | 1.264 | 1.266 | 1.240 | 1.219 | 1.299 | 1.290 | 1.357 | 1.164 | 1.121 | 1.119 | 
| Path CH | 1.000 | 0.949 | 0.900 | 0.927 | 0.949 | 1.124 | 1.404 | 1.417 | 1.388 | 1.576 | 1.609 | 1.633 | 1.610 | 1.607 | 1.688 | 1.567 | 1.573 | 1.748 | 1.582 | 1.485 | 1.537 | 1.345 | 1.331 | 1.131 | 1.102 | 1.044 | 1.139 | 1.149 | 1.161 | 1.281 | 1.241 | 1.173 | 1.124 | 0.969 | 0.983 | 1.104 | 1.140 | 1.451 | 1.569 | 1.563 | 1.566 | 1.532 | 1.596 | 1.489 | 1.499 | 1.552 | 1.830 | 2.194 | 2.304 | 2.158 | 2.480 | 2.746 | 2.717 | 2.801 | 2.700 | 2.506 | 2.461 | 2.207 | 1.946 | 2.128 | 1.978 | 1.865 | 2.102 | 2.245 | 2.290 | 2.281 | 2.219 | 2.234 | 2.276 | 2.899 | 2.870 | 2.949 | 2.846 | 3.268 | 3.178 | 2.908 | 2.873 | 2.615 | 2.818 | 2.835 | 
| Path CI | 1.000 | 1.036 | 0.936 | 1.059 | 1.063 | 1.108 | 1.115 | 1.097 | 1.140 | 1.120 | 1.441 | 1.462 | 1.475 | 1.502 | 1.566 | 1.604 | 1.602 | 1.431 | 1.331 | 1.257 | 1.431 | 1.430 | 1.444 | 2.081 | 2.034 | 2.138 | 2.269 | 2.357 | 2.830 | 3.268 | 3.416 | 3.373 | 3.095 | 3.388 | 3.232 | 3.097 | 3.322 | 3.784 | 4.457 | 4.752 | 4.741 | 5.013 | 5.829 | 5.417 | 5.783 | 5.510 | 5.716 | 5.881 | 4.967 | 5.749 | 5.600 | 4.993 | 4.455 | 4.883 | 4.868 | 4.969 | 4.800 | 4.716 | 5.035 | 4.975 | 5.310 | 4.762 | 4.361 | 3.324 | 3.300 | 3.171 | 3.109 | 3.187 | 3.370 | 3.457 | 3.210 | 3.308 | 3.616 | 3.897 | 3.729 | 3.698 | 3.716 | 3.583 | 3.775 | 3.936 | 
| Path CJ | 1.000 | 1.255 | 1.303 | 1.408 | 1.289 | 1.259 | 1.375 | 1.320 | 1.184 | 1.322 | 1.104 | 1.146 | 1.165 | 1.141 | 1.002 | 0.933 | 0.816 | 0.881 | 0.895 | 0.918 | 0.877 | 0.869 | 0.921 | 0.909 | 0.975 | 0.870 | 0.883 | 0.744 | 0.791 | 0.761 | 0.710 | 0.792 | 0.782 | 0.839 | 0.833 | 0.819 | 0.825 | 0.842 | 1.093 | 1.086 | 1.096 | 1.107 | 1.222 | 1.184 | 1.119 | 1.072 | 0.924 | 0.937 | 1.053 | 1.087 | 1.384 | 1.497 | 1.472 | 1.435 | 1.558 | 1.388 | 1.354 | 1.330 | 1.447 | 1.736 | 2.072 | 2.099 | 1.998 | 2.539 | 2.254 | 2.545 | 2.393 | 2.384 | 2.490 | 2.304 | 2.293 | 2.460 | 2.282 | 2.142 | 2.201 | 1.818 | 1.891 | 1.728 | 1.724 | 1.823 | 
| Path CK | 1.000 | 0.907 | 0.760 | 0.790 | 0.883 | 0.917 | 1.102 | 1.272 | 1.330 | 1.313 | 1.205 | 1.319 | 1.258 | 1.206 | 1.293 | 1.473 | 1.735 | 1.850 | 1.846 | 1.952 | 2.269 | 2.109 | 2.252 | 2.145 | 2.225 | 2.290 | 2.233 | 2.325 | 2.110 | 2.648 | 2.749 | 2.970 | 2.719 | 2.656 | 2.901 | 2.785 | 2.498 | 2.789 | 2.329 | 2.417 | 2.458 | 2.408 | 2.114 | 1.969 | 1.722 | 1.858 | 1.888 | 1.936 | 1.851 | 1.833 | 1.944 | 1.919 | 2.086 | 2.128 | 2.120 | 2.062 | 2.076 | 2.115 | 2.693 | 2.667 | 2.740 | 2.644 | 3.036 | 2.953 | 2.702 | 2.669 | 2.430 | 2.384 | 2.691 | 2.710 | 3.818 | 3.658 | 3.740 | 3.736 | 3.731 | 3.740 | 3.393 | 3.600 | 3.441 | 2.227 | 
| Path CL | 1.000 | 1.014 | 1.139 | 1.176 | 1.497 | 1.619 | 1.613 | 1.616 | 1.580 | 1.646 | 1.536 | 1.546 | 1.601 | 1.888 | 2.264 | 2.377 | 2.226 | 2.559 | 2.833 | 3.084 | 2.783 | 2.749 | 3.007 | 2.852 | 2.574 | 2.880 | 2.826 | 2.835 | 3.143 | 3.170 | 2.803 | 2.885 | 2.129 | 1.928 | 1.899 | 1.765 | 1.890 | 1.941 | 2.209 | 2.055 | 2.007 | 2.135 | 2.214 | 2.218 | 2.182 | 2.250 | 2.169 | 2.013 | 1.977 | 1.773 | 1.563 | 1.709 | 1.596 | 1.569 | 1.580 | 1.614 | 2.093 | 2.081 | 2.100 | 2.122 | 2.341 | 2.267 | 2.144 | 2.054 | 1.771 | 1.796 | 2.017 | 2.082 | 2.651 | 2.868 | 2.856 | 2.861 | 2.799 | 2.915 | 2.720 | 2.739 | 2.835 | 3.344 | 2.984 | 2.477 | 
| Path CM | 1.000 | 0.904 | 0.910 | 0.958 | 0.990 | 0.955 | 1.026 | 1.010 | 0.996 | 1.019 | 1.099 | 1.105 | 1.049 | 1.094 | 1.051 | 0.991 | 0.943 | 0.844 | 0.755 | 0.815 | 0.755 | 0.749 | 0.812 | 0.893 | 0.900 | 0.889 | 0.811 | 0.836 | 0.913 | 0.984 | 0.942 | 0.934 | 0.939 | 0.905 | 0.841 | 0.820 | 0.644 | 0.678 | 0.696 | 0.642 | 0.715 | 0.731 | 0.750 | 0.757 | 0.758 | 0.779 | 0.766 | 1.024 | 0.994 | 0.999 | 1.024 | 1.063 | 1.163 | 1.194 | 1.275 | 1.285 | 1.312 | 1.302 | 1.290 | 1.591 | 1.717 | 1.715 | 1.668 | 1.674 | 1.839 | 1.908 | 1.671 | 1.424 | 1.489 | 1.448 | 1.650 | 1.669 | 2.288 | 2.318 | 2.350 | 2.390 | 2.457 | 2.332 | 2.199 | 2.091 | 
| Path CN | 1.000 | 1.022 | 0.937 | 1.016 | 1.043 | 1.114 | 1.123 | 1.146 | 1.138 | 1.127 | 1.390 | 1.500 | 1.498 | 1.457 | 1.462 | 1.606 | 1.667 | 1.460 | 1.244 | 1.301 | 1.265 | 1.442 | 1.458 | 1.999 | 2.025 | 2.053 | 2.111 | 2.176 | 2.097 | 2.094 | 2.229 | 2.390 | 2.372 | 2.298 | 2.332 | 2.324 | 2.172 | 2.046 | 1.802 | 1.703 | 1.742 | 1.596 | 1.731 | 1.776 | 1.898 | 1.912 | 1.953 | 1.938 | 1.920 | 2.368 | 2.556 | 2.552 | 2.417 | 2.699 | 2.253 | 2.339 | 2.378 | 2.330 | 2.046 | 1.905 | 1.666 | 1.798 | 1.827 | 1.873 | 1.791 | 1.774 | 1.881 | 1.856 | 1.991 | 1.776 | 1.475 | 1.255 | 1.255 | 1.187 | 1.181 | 1.185 | 1.261 | 1.254 | 1.312 | 1.276 | 
| Path CO | 1.000 | 1.028 | 0.976 | 0.925 | 0.953 | 0.975 | 1.156 | 1.443 | 1.457 | 1.427 | 1.620 | 1.654 | 1.678 | 1.655 | 1.652 | 1.735 | 1.610 | 1.617 | 1.796 | 1.627 | 1.526 | 1.580 | 1.382 | 1.368 | 1.163 | 1.133 | 1.029 | 1.128 | 1.125 | 1.148 | 1.109 | 1.090 | 1.163 | 1.149 | 1.227 | 1.100 | 1.008 | 0.768 | 0.762 | 0.733 | 0.718 | 0.737 | 0.779 | 0.799 | 0.742 | 0.764 | 0.836 | 0.900 | 0.862 | 0.854 | 0.859 | 0.828 | 0.768 | 0.806 | 0.749 | 0.751 | 0.835 | 0.756 | 0.709 | 0.735 | 0.642 | 0.636 | 0.540 | 0.526 | 0.499 | 0.557 | 0.529 | 0.536 | 0.524 | 0.575 | 0.552 | 0.569 | 0.522 | 0.418 | 0.375 | 0.356 | 0.331 | 0.361 | 0.400 | 0.357 | 
| Path CP | 1.000 | 0.985 | 1.180 | 1.313 | 1.253 | 1.293 | 1.267 | 1.406 | 1.407 | 1.269 | 1.110 | 1.122 | 1.115 | 1.258 | 1.270 | 1.766 | 1.754 | 1.791 | 1.783 | 1.762 | 1.789 | 1.564 | 1.756 | 1.805 | 2.087 | 2.638 | 2.734 | 2.688 | 3.174 | 2.902 | 2.733 | 2.842 | 3.196 | 3.121 | 3.107 | 3.166 | 3.156 | 2.873 | 2.850 | 2.707 | 2.280 | 2.422 | 2.331 | 2.176 | 2.427 | 2.396 | 2.569 | 2.553 | 2.509 | 2.526 | 2.581 | 3.348 | 3.327 | 4.105 | 4.429 | 4.423 | 4.301 | 4.317 | 4.742 | 4.921 | 4.309 | 3.672 | 3.840 | 3.735 | 4.256 | 4.304 | 5.901 | 5.978 | 6.062 | 6.165 | 6.337 | 6.016 | 5.703 | 5.877 | 6.011 | 7.126 | 8.896 | 8.983 | 9.381 | 8.679 | 
| Path CQ | 1.000 | 1.064 | 1.105 | 1.142 | 0.998 | 1.025 | 1.060 | 1.096 | 1.171 | 1.042 | 0.996 | 0.645 | 0.687 | 0.688 | 0.715 | 0.731 | 0.732 | 0.754 | 0.727 | 0.726 | 0.773 | 0.829 | 0.822 | 0.796 | 0.808 | 0.806 | 0.794 | 0.750 | 0.853 | 0.853 | 0.861 | 1.241 | 1.213 | 1.275 | 1.240 | 1.317 | 1.200 | 1.150 | 1.222 | 1.316 | 1.603 | 1.725 | 1.811 | 1.751 | 2.258 | 2.061 | 2.142 | 2.116 | 2.067 | 2.182 | 1.974 | 2.067 | 2.314 | 2.408 | 2.121 | 2.025 | 2.077 | 1.822 | 1.817 | 1.610 | 1.611 | 1.697 | 1.769 | 1.508 | 1.569 | 1.581 | 1.686 | 1.785 | 1.587 | 1.602 | 1.143 | 1.033 | 1.041 | 1.095 | 1.132 | 1.092 | 1.173 | 1.154 | 1.027 | 0.982 | 
| Path CR | 1.000 | 1.129 | 1.137 | 1.601 | 1.534 | 1.569 | 1.567 | 1.565 | 1.569 | 1.423 | 1.510 | 1.560 | 1.824 | 2.227 | 2.319 | 2.104 | 2.641 | 2.741 | 2.962 | 2.711 | 2.649 | 2.893 | 2.777 | 2.491 | 2.781 | 2.322 | 2.419 | 2.169 | 1.912 | 2.091 | 1.944 | 1.833 | 2.066 | 2.206 | 2.251 | 2.242 | 2.181 | 2.196 | 2.237 | 2.849 | 2.821 | 2.898 | 2.797 | 3.212 | 3.123 | 2.858 | 2.823 | 2.570 | 2.522 | 2.846 | 2.866 | 4.038 | 4.224 | 3.694 | 3.657 | 3.108 | 3.027 | 2.869 | 3.203 | 3.039 | 3.085 | 3.012 | 3.306 | 3.174 | 3.270 | 3.004 | 2.406 | 2.158 | 2.049 | 1.903 | 2.078 | 2.043 | 2.412 | 2.206 | 2.077 | 2.160 | 2.429 | 2.372 | 2.090 | 2.286 | 
| Path CS | 1.000 | 1.022 | 0.937 | 1.016 | 1.043 | 1.114 | 1.123 | 1.146 | 1.138 | 1.127 | 1.390 | 1.500 | 1.498 | 1.457 | 1.462 | 1.606 | 1.667 | 1.460 | 1.244 | 1.301 | 1.265 | 1.442 | 1.458 | 1.999 | 2.025 | 2.053 | 2.078 | 2.165 | 2.179 | 2.145 | 2.228 | 2.188 | 2.816 | 2.857 | 2.883 | 2.936 | 3.060 | 3.134 | 3.131 | 2.797 | 2.601 | 2.457 | 2.797 | 2.795 | 2.822 | 4.066 | 3.975 | 4.178 | 4.063 | 4.319 | 3.934 | 3.768 | 3.742 | 3.508 | 3.406 | 3.253 | 2.525 | 2.704 | 2.801 | 2.532 | 2.864 | 2.876 | 2.996 | 3.016 | 2.968 | 3.083 | 3.028 | 3.897 | 3.953 | 3.990 | 4.063 | 4.235 | 4.337 | 4.333 | 3.871 | 3.600 | 3.401 | 3.870 | 4.406 | 4.403 | 
| Path CT | 1.000 | 1.287 | 1.305 | 1.317 | 1.342 | 1.398 | 1.432 | 1.431 | 1.278 | 1.189 | 1.123 | 1.278 | 1.277 | 1.290 | 1.858 | 1.816 | 1.909 | 1.857 | 1.973 | 1.798 | 1.722 | 1.830 | 1.971 | 2.400 | 2.583 | 2.713 | 2.002 | 1.843 | 1.734 | 1.726 | 1.710 | 1.708 | 1.921 | 1.811 | 1.750 | 1.861 | 1.933 | 1.996 | 2.089 | 2.048 | 2.091 | 1.879 | 1.851 | 1.770 | 1.491 | 1.522 | 1.505 | 1.386 | 1.575 | 1.593 | 1.651 | 1.724 | 1.407 | 1.422 | 1.413 | 1.594 | 1.610 | 2.237 | 2.223 | 2.270 | 2.259 | 2.233 | 2.267 | 1.982 | 2.225 | 2.287 | 2.645 | 3.343 | 3.446 | 3.111 | 3.782 | 3.980 | 4.253 | 3.908 | 3.832 | 4.097 | 3.955 | 3.686 | 3.662 | 3.740 | 
| Path CU | 1.000 | 1.063 | 1.104 | 1.140 | 1.194 | 1.170 | 1.195 | 1.074 | 1.058 | 1.011 | 0.852 | 0.870 | 0.860 | 0.792 | 0.900 | 0.910 | 0.943 | 0.985 | 0.950 | 0.963 | 0.945 | 1.241 | 1.218 | 1.267 | 1.248 | 1.333 | 1.373 | 1.307 | 1.661 | 1.475 | 1.665 | 1.566 | 1.560 | 1.629 | 1.507 | 1.500 | 1.610 | 1.493 | 1.402 | 1.440 | 1.190 | 1.237 | 1.130 | 1.071 | 1.084 | 1.201 | 1.072 | 1.073 | 1.076 | 1.193 | 1.204 | 1.064 | 0.988 | 0.971 | 0.871 | 0.767 | 0.839 | 0.780 | 0.736 | 0.829 | 0.885 | 0.903 | 0.900 | 0.875 | 0.881 | 0.898 | 1.143 | 1.132 | 1.163 | 1.123 | 1.289 | 1.253 | 1.147 | 1.133 | 1.032 | 1.012 | 1.142 | 1.150 | 1.066 | 1.058 | 
| Path CV | 1.000 | 1.035 | 0.906 | 0.897 | 0.762 | 0.742 | 0.703 | 0.785 | 0.745 | 0.756 | 0.738 | 0.810 | 0.778 | 0.802 | 0.736 | 0.590 | 0.529 | 0.502 | 0.467 | 0.509 | 0.501 | 0.591 | 0.541 | 0.509 | 0.529 | 0.596 | 0.559 | 0.643 | 0.712 | 0.774 | 0.699 | 0.690 | 0.755 | 0.716 | 0.646 | 0.723 | 0.614 | 0.614 | 0.631 | 0.617 | 0.551 | 0.499 | 0.443 | 0.486 | 0.484 | 0.494 | 0.477 | 0.469 | 0.501 | 0.495 | 0.528 | 0.474 | 0.535 | 0.488 | 0.507 | 0.501 | 0.490 | 0.517 | 0.468 | 0.489 | 0.510 | 0.449 | 0.428 | 0.439 | 0.386 | 0.385 | 0.341 | 0.341 | 0.359 | 0.374 | 0.319 | 0.332 | 0.335 | 0.357 | 0.378 | 0.336 | 0.339 | 0.242 | 0.244 | 0.256 | 
| Path CW | 1.000 | 0.956 | 0.619 | 0.660 | 0.660 | 0.687 | 0.702 | 0.702 | 0.724 | 0.698 | 0.697 | 0.742 | 0.795 | 0.789 | 0.765 | 0.776 | 0.773 | 0.723 | 0.681 | 0.600 | 0.567 | 0.580 | 0.531 | 0.576 | 0.591 | 0.631 | 0.685 | 0.664 | 0.628 | 0.601 | 0.518 | 0.526 | 0.591 | 0.610 | 0.776 | 0.840 | 0.836 | 0.838 | 0.819 | 0.854 | 0.796 | 0.802 | 0.830 | 0.979 | 1.174 | 1.233 | 1.154 | 1.327 | 1.469 | 1.599 | 1.443 | 1.425 | 1.428 | 1.610 | 1.719 | 1.754 | 1.747 | 1.699 | 1.711 | 1.743 | 2.220 | 2.198 | 2.258 | 2.179 | 2.502 | 2.433 | 2.227 | 2.200 | 2.002 | 1.965 | 2.218 | 2.233 | 3.146 | 3.014 | 3.082 | 3.079 | 3.075 | 3.082 | 4.342 | 4.160 | 
| Path CX | 1.000 | 0.903 | 1.098 | 1.155 | 1.234 | 1.134 | 1.112 | 1.189 | 1.148 | 1.070 | 1.166 | 1.072 | 1.028 | 1.074 | 1.009 | 0.925 | 0.799 | 0.724 | 0.772 | 0.790 | 0.791 | 0.775 | 0.762 | 0.812 | 0.807 | 0.848 | 0.842 | 0.767 | 0.735 | 0.781 | 0.842 | 1.025 | 1.103 | 1.158 | 1.119 | 1.443 | 1.318 | 1.370 | 1.353 | 1.322 | 1.395 | 1.262 | 1.321 | 1.375 | 1.211 | 1.157 | 1.186 | 1.041 | 1.038 | 0.919 | 0.920 | 0.969 | 0.920 | 0.822 | 0.764 | 0.722 | 0.822 | 0.821 | 0.829 | 1.195 | 1.168 | 1.228 | 1.194 | 1.269 | 1.156 | 1.107 | 1.177 | 1.268 | 1.544 | 1.661 | 1.745 | 1.687 | 2.175 | 1.986 | 2.064 | 2.038 | 1.992 | 2.102 | 2.073 | 2.121 | 
| Path CY | 1.000 | 1.030 | 0.760 | 0.688 | 0.677 | 0.630 | 0.674 | 0.693 | 0.788 | 0.733 | 0.716 | 0.762 | 0.790 | 0.792 | 0.779 | 0.803 | 0.774 | 0.718 | 0.705 | 0.633 | 0.558 | 0.610 | 0.567 | 0.535 | 0.603 | 0.643 | 0.620 | 0.575 | 0.561 | 0.441 | 0.464 | 0.477 | 0.440 | 0.490 | 0.500 | 0.513 | 0.518 | 0.519 | 0.533 | 0.524 | 0.701 | 0.680 | 0.684 | 0.701 | 0.728 | 0.750 | 0.771 | 0.711 | 0.550 | 0.593 | 0.656 | 0.671 | 0.696 | 0.955 | 0.967 | 0.981 | 0.998 | 1.025 | 0.973 | 0.923 | 0.951 | 0.973 | 1.153 | 1.439 | 1.453 | 1.423 | 1.616 | 1.650 | 1.674 | 1.651 | 1.647 | 1.731 | 1.606 | 1.613 | 1.792 | 1.622 | 1.522 | 1.576 | 1.643 | 1.683 | 
| Path CZ | 1.000 | 1.042 | 0.972 | 0.979 | 1.013 | 1.195 | 1.433 | 1.504 | 1.409 | 1.619 | 1.793 | 1.952 | 1.761 | 1.740 | 1.903 | 1.805 | 1.629 | 1.823 | 1.547 | 1.547 | 1.589 | 1.554 | 1.388 | 1.257 | 1.117 | 1.224 | 1.194 | 1.299 | 1.558 | 1.860 | 1.884 | 1.794 | 2.280 | 2.024 | 2.285 | 2.149 | 2.140 | 2.235 | 2.068 | 2.058 | 2.209 | 2.049 | 1.923 | 1.976 | 1.632 | 1.697 | 1.551 | 1.470 | 1.488 | 1.648 | 1.471 | 1.472 | 1.388 | 1.552 | 1.611 | 1.935 | 2.235 | 2.336 | 2.307 | 2.116 | 2.317 | 2.210 | 2.118 | 2.272 | 2.587 | 3.048 | 3.250 | 3.242 | 3.428 | 3.986 | 3.704 | 3.955 | 3.768 | 3.909 | 4.022 | 3.397 | 3.932 | 3.830 | 3.594 | 3.721 | 
| Path DA | 1.000 | 0.921 | 1.046 | 1.058 | 1.097 | 1.145 | 1.105 | 1.119 | 1.099 | 1.443 | 1.416 | 1.473 | 1.451 | 1.550 | 1.575 | 1.573 | 1.427 | 1.195 | 1.244 | 1.390 | 1.443 | 1.733 | 2.001 | 2.093 | 2.066 | 1.896 | 2.017 | 2.031 | 2.102 | 2.479 | 2.973 | 3.122 | 2.924 | 3.361 | 3.721 | 4.050 | 3.655 | 3.610 | 3.950 | 3.745 | 3.380 | 3.783 | 3.210 | 3.211 | 3.298 | 3.225 | 2.880 | 2.609 | 2.318 | 2.541 | 2.533 | 2.586 | 2.425 | 2.442 | 2.528 | 2.981 | 3.575 | 3.754 | 3.516 | 4.041 | 4.474 | 4.870 | 4.394 | 4.341 | 4.749 | 4.504 | 4.064 | 4.548 | 3.860 | 3.862 | 3.966 | 3.878 | 3.463 | 3.137 | 2.788 | 3.055 | 3.046 | 3.109 | 2.995 | 2.991 | 
| Path DB | 1.000 | 0.842 | 0.895 | 0.861 | 0.804 | 0.897 | 0.885 | 0.949 | 0.943 | 0.927 | 0.933 | 0.954 | 1.237 | 1.230 | 1.241 | 1.254 | 1.383 | 1.340 | 1.267 | 1.214 | 1.047 | 1.061 | 1.192 | 1.230 | 1.566 | 1.695 | 1.770 | 1.758 | 1.984 | 2.004 | 2.786 | 2.767 | 2.826 | 2.813 | 2.780 | 2.822 | 2.468 | 2.770 | 2.847 | 3.292 | 4.162 | 4.290 | 3.874 | 4.709 | 4.954 | 5.295 | 4.865 | 4.770 | 5.101 | 4.924 | 4.589 | 5.001 | 5.269 | 4.700 | 3.902 | 3.322 | 3.321 | 3.141 | 3.127 | 3.135 | 3.336 | 3.318 | 3.175 | 3.288 | 3.637 | 3.741 | 3.692 | 3.688 | 3.703 | 3.471 | 3.370 | 3.219 | 2.498 | 2.676 | 2.771 | 2.505 | 2.834 | 2.845 | 2.957 | 3.055 | 
| Path DC | 1.000 | 0.917 | 0.792 | 0.717 | 0.766 | 0.783 | 0.784 | 0.768 | 0.755 | 0.805 | 0.799 | 0.841 | 0.721 | 0.581 | 0.535 | 0.503 | 0.501 | 0.496 | 0.496 | 0.558 | 0.526 | 0.508 | 0.540 | 0.561 | 0.579 | 0.607 | 0.566 | 0.507 | 0.447 | 0.489 | 0.455 | 0.429 | 0.483 | 0.516 | 0.526 | 0.524 | 0.510 | 0.514 | 0.523 | 0.666 | 0.660 | 0.678 | 0.654 | 0.751 | 0.731 | 0.668 | 0.660 | 0.601 | 0.590 | 0.666 | 0.670 | 0.945 | 1.295 | 1.241 | 1.268 | 1.267 | 1.266 | 1.269 | 1.151 | 1.221 | 1.261 | 1.475 | 1.801 | 1.875 | 1.701 | 2.136 | 2.217 | 2.395 | 2.192 | 2.142 | 2.339 | 2.246 | 2.014 | 2.249 | 1.878 | 1.950 | 1.982 | 1.942 | 1.992 | 2.129 | 
| Path DD | 1.000 | 0.959 | 1.002 | 0.941 | 0.863 | 0.745 | 0.675 | 0.720 | 0.737 | 0.738 | 0.723 | 0.711 | 0.757 | 0.752 | 0.791 | 0.678 | 0.547 | 0.503 | 0.474 | 0.471 | 0.467 | 0.467 | 0.525 | 0.495 | 0.478 | 0.508 | 0.499 | 0.556 | 0.569 | 0.583 | 0.589 | 0.589 | 0.606 | 0.596 | 0.796 | 0.773 | 0.777 | 0.796 | 0.827 | 0.852 | 0.876 | 0.808 | 0.625 | 0.674 | 0.745 | 0.762 | 0.771 | 1.137 | 1.071 | 1.129 | 1.100 | 1.194 | 1.112 | 1.031 | 0.968 | 0.995 | 0.822 | 0.854 | 0.781 | 0.740 | 0.749 | 0.829 | 0.741 | 0.741 | 0.743 | 0.824 | 0.831 | 0.735 | 0.757 | 0.558 | 0.506 | 0.498 | 0.463 | 0.496 | 0.509 | 0.579 | 0.539 | 0.526 | 0.542 | 0.498 | 
| Path DE | 1.000 | 1.129 | 1.139 | 1.584 | 1.573 | 1.607 | 1.600 | 1.581 | 1.605 | 1.403 | 1.575 | 1.619 | 1.872 | 2.367 | 2.439 | 2.203 | 2.678 | 2.817 | 3.011 | 2.767 | 2.713 | 2.901 | 2.800 | 2.610 | 2.844 | 2.616 | 2.547 | 2.164 | 2.108 | 1.998 | 2.230 | 2.117 | 2.148 | 2.097 | 2.302 | 2.210 | 2.277 | 2.092 | 1.675 | 1.503 | 1.427 | 1.325 | 1.447 | 1.423 | 1.680 | 1.536 | 1.447 | 1.504 | 1.692 | 1.652 | 1.645 | 1.676 | 1.567 | 1.630 | 1.832 | 1.789 | 1.782 | 1.815 | 1.810 | 1.647 | 1.634 | 1.552 | 1.307 | 1.389 | 1.337 | 1.248 | 1.392 | 1.374 | 1.473 | 1.464 | 1.439 | 1.449 | 1.480 | 1.920 | 1.908 | 1.926 | 1.946 | 2.147 | 2.098 | 2.291 | 
| Path DF | 1.000 | 1.000 | 1.031 | 0.994 | 0.992 | 1.057 | 1.133 | 1.124 | 1.089 | 1.105 | 1.101 | 1.029 | 0.970 | 0.854 | 0.807 | 0.826 | 0.756 | 0.820 | 0.842 | 0.900 | 0.906 | 0.925 | 0.919 | 0.910 | 1.123 | 1.211 | 1.106 | 1.136 | 1.111 | 0.992 | 0.898 | 0.798 | 0.875 | 0.872 | 0.890 | 0.860 | 0.845 | 0.902 | 0.891 | 0.952 | 0.853 | 0.781 | 0.596 | 0.591 | 0.568 | 0.557 | 0.571 | 0.604 | 0.620 | 0.575 | 0.593 | 0.648 | 0.626 | 0.632 | 0.644 | 0.671 | 0.687 | 0.686 | 0.613 | 0.570 | 0.539 | 0.613 | 0.613 | 0.619 | 0.892 | 0.872 | 0.916 | 0.891 | 0.947 | 0.863 | 0.826 | 0.878 | 0.946 | 1.152 | 1.240 | 1.302 | 1.258 | 1.623 | 1.424 | 1.515 | 
| Path DG | 1.000 | 0.943 | 1.063 | 1.135 | 1.158 | 1.153 | 1.121 | 1.129 | 1.150 | 1.465 | 1.451 | 1.491 | 1.439 | 1.652 | 1.606 | 1.470 | 1.452 | 1.322 | 1.297 | 1.464 | 1.474 | 2.077 | 1.990 | 2.034 | 2.033 | 2.030 | 2.228 | 2.341 | 2.173 | 2.181 | 2.424 | 2.194 | 2.059 | 2.132 | 1.865 | 1.846 | 1.568 | 1.528 | 1.448 | 1.616 | 1.534 | 1.557 | 1.520 | 1.669 | 1.602 | 1.650 | 1.516 | 1.214 | 1.089 | 1.034 | 0.960 | 1.049 | 0.998 | 0.851 | 0.889 | 0.865 | 0.986 | 0.997 | 1.367 | 1.385 | 1.404 | 1.428 | 1.468 | 1.394 | 1.321 | 1.362 | 1.393 | 1.651 | 2.061 | 2.081 | 2.038 | 2.313 | 2.363 | 2.397 | 2.364 | 2.359 | 2.478 | 2.300 | 2.086 | 2.619 | 
| Path DH | 1.000 | 0.905 | 0.850 | 0.880 | 0.769 | 0.762 | 0.647 | 0.630 | 0.598 | 0.667 | 0.633 | 0.642 | 0.627 | 0.689 | 0.661 | 0.681 | 0.626 | 0.501 | 0.449 | 0.427 | 0.396 | 0.433 | 0.425 | 0.502 | 0.459 | 0.433 | 0.422 | 0.397 | 0.396 | 0.413 | 0.382 | 0.380 | 0.408 | 0.379 | 0.355 | 0.365 | 0.302 | 0.314 | 0.287 | 0.272 | 0.275 | 0.304 | 0.272 | 0.272 | 0.273 | 0.302 | 0.305 | 0.270 | 0.278 | 0.205 | 0.186 | 0.183 | 0.184 | 0.196 | 0.211 | 0.209 | 0.203 | 0.205 | 0.205 | 0.191 | 0.180 | 0.159 | 0.150 | 0.153 | 0.141 | 0.152 | 0.157 | 0.167 | 0.169 | 0.172 | 0.171 | 0.169 | 0.209 | 0.225 | 0.225 | 0.219 | 0.220 | 0.241 | 0.289 | 0.322 | 
| Path DI | 1.000 | 0.945 | 0.966 | 0.885 | 0.960 | 0.986 | 1.053 | 1.061 | 1.083 | 1.075 | 1.065 | 1.314 | 1.418 | 1.416 | 1.377 | 1.382 | 1.518 | 1.575 | 1.379 | 1.176 | 1.229 | 1.196 | 1.362 | 1.378 | 1.889 | 1.914 | 1.918 | 1.889 | 2.018 | 2.051 | 2.049 | 1.858 | 1.556 | 1.619 | 1.809 | 1.879 | 2.257 | 2.606 | 2.724 | 2.690 | 2.468 | 2.702 | 2.578 | 2.470 | 2.649 | 3.017 | 3.555 | 3.790 | 3.781 | 3.998 | 4.649 | 4.320 | 5.394 | 5.162 | 5.119 | 5.145 | 4.961 | 4.607 | 4.492 | 3.531 | 3.716 | 3.816 | 3.521 | 3.921 | 4.007 | 4.107 | 4.151 | 4.154 | 4.269 | 4.197 | 5.611 | 5.447 | 5.477 | 5.612 | 5.825 | 6.002 | 6.176 | 5.694 | 5.753 | 5.756 | 
| Path DJ | 1.000 | 1.010 | 1.115 | 1.080 | 1.021 | 0.978 | 0.843 | 0.855 | 0.961 | 0.992 | 1.262 | 1.366 | 1.360 | 1.363 | 1.333 | 1.388 | 1.295 | 1.304 | 1.350 | 1.592 | 1.909 | 2.005 | 1.878 | 2.158 | 2.390 | 2.601 | 2.457 | 2.513 | 2.516 | 2.465 | 2.423 | 2.583 | 2.565 | 2.697 | 2.313 | 1.864 | 1.716 | 1.615 | 1.608 | 1.593 | 1.591 | 1.789 | 1.687 | 1.630 | 1.733 | 1.800 | 1.859 | 1.946 | 1.907 | 1.947 | 1.750 | 1.724 | 1.705 | 1.770 | 1.824 | 1.877 | 1.730 | 1.338 | 1.443 | 1.595 | 1.633 | 1.650 | 2.434 | 2.292 | 2.417 | 2.355 | 2.558 | 2.280 | 2.224 | 2.184 | 2.375 | 2.850 | 3.402 | 3.446 | 3.280 | 4.169 | 3.701 | 4.178 | 4.806 | 5.321 | 
| Path DK | 1.000 | 1.051 | 0.902 | 0.727 | 0.669 | 0.630 | 0.627 | 0.621 | 0.620 | 0.697 | 0.658 | 0.635 | 0.676 | 0.702 | 0.725 | 0.759 | 0.744 | 0.759 | 0.682 | 0.672 | 0.643 | 0.541 | 0.552 | 0.546 | 0.503 | 0.572 | 0.478 | 0.499 | 0.486 | 0.553 | 0.560 | 0.767 | 0.777 | 0.788 | 0.802 | 0.824 | 0.782 | 0.742 | 0.764 | 0.782 | 0.927 | 1.157 | 1.168 | 1.144 | 1.299 | 1.326 | 1.346 | 1.327 | 1.324 | 1.391 | 1.291 | 1.296 | 1.368 | 1.331 | 1.340 | 1.365 | 1.739 | 1.721 | 1.769 | 1.707 | 1.960 | 1.906 | 1.744 | 1.723 | 1.569 | 1.539 | 1.737 | 1.749 | 2.465 | 2.361 | 2.414 | 2.412 | 2.409 | 2.414 | 2.190 | 2.324 | 2.401 | 2.808 | 2.537 | 2.557 | 
| Path DL | 1.000 | 1.030 | 0.760 | 0.688 | 0.677 | 0.630 | 0.674 | 0.693 | 0.788 | 0.733 | 0.716 | 0.762 | 0.790 | 0.792 | 0.779 | 0.803 | 0.774 | 0.718 | 0.705 | 0.633 | 0.558 | 0.610 | 0.567 | 0.535 | 0.603 | 0.643 | 0.640 | 0.630 | 0.622 | 0.636 | 0.685 | 0.689 | 0.654 | 0.683 | 0.656 | 0.618 | 0.588 | 0.526 | 0.471 | 0.508 | 0.471 | 0.467 | 0.506 | 0.557 | 0.562 | 0.555 | 0.554 | 0.546 | 0.654 | 0.728 | 0.695 | 0.717 | 0.681 | 0.681 | 0.709 | 0.725 | 0.725 | 0.747 | 0.720 | 0.719 | 0.766 | 0.821 | 0.815 | 0.789 | 0.801 | 0.798 | 0.746 | 0.703 | 0.619 | 0.585 | 0.598 | 0.548 | 0.595 | 0.610 | 0.652 | 0.657 | 0.671 | 0.666 | 0.672 | 0.934 | 
| Path DM | 1.000 | 0.980 | 1.005 | 1.063 | 1.090 | 1.012 | 1.043 | 1.140 | 1.229 | 1.176 | 1.166 | 1.172 | 1.130 | 1.049 | 1.023 | 0.804 | 0.846 | 0.869 | 0.802 | 0.893 | 0.913 | 0.935 | 0.945 | 0.946 | 0.972 | 0.956 | 0.936 | 1.022 | 0.981 | 0.880 | 0.982 | 0.820 | 0.852 | 0.866 | 0.848 | 0.745 | 0.694 | 0.607 | 0.654 | 0.665 | 0.682 | 0.652 | 0.646 | 0.685 | 0.676 | 0.725 | 0.647 | 0.537 | 0.457 | 0.457 | 0.432 | 0.430 | 0.442 | 0.405 | 0.400 | 0.364 | 0.357 | 0.403 | 0.406 | 0.572 | 0.548 | 0.560 | 0.560 | 0.559 | 0.560 | 0.508 | 0.539 | 0.557 | 0.651 | 0.795 | 0.828 | 0.751 | 0.943 | 0.979 | 1.058 | 0.968 | 0.946 | 1.033 | 0.926 | 0.817 | 
| Path DN | 1.000 | 0.897 | 1.002 | 0.836 | 0.868 | 0.882 | 0.865 | 0.759 | 0.707 | 0.618 | 0.667 | 0.678 | 0.695 | 0.665 | 0.658 | 0.698 | 0.689 | 0.739 | 0.659 | 0.547 | 0.466 | 0.466 | 0.440 | 0.439 | 0.440 | 0.468 | 0.534 | 0.562 | 0.601 | 0.552 | 0.541 | 0.579 | 0.559 | 0.521 | 0.567 | 0.522 | 0.501 | 0.523 | 0.491 | 0.450 | 0.389 | 0.352 | 0.376 | 0.385 | 0.385 | 0.377 | 0.371 | 0.395 | 0.393 | 0.413 | 0.354 | 0.285 | 0.295 | 0.294 | 0.281 | 0.291 | 0.322 | 0.331 | 0.327 | 0.327 | 0.328 | 0.307 | 0.298 | 0.285 | 0.221 | 0.237 | 0.245 | 0.222 | 0.251 | 0.252 | 0.263 | 0.264 | 0.260 | 0.270 | 0.265 | 0.342 | 0.346 | 0.350 | 0.341 | 0.335 | 
| Path DO | 1.000 | 0.976 | 0.958 | 1.042 | 1.250 | 1.492 | 1.512 | 1.439 | 1.829 | 1.624 | 1.833 | 1.724 | 1.717 | 1.793 | 1.659 | 1.651 | 1.772 | 1.643 | 1.543 | 1.585 | 1.310 | 1.362 | 1.244 | 1.179 | 1.194 | 1.322 | 1.324 | 1.407 | 1.354 | 1.264 | 1.410 | 1.392 | 1.492 | 1.482 | 1.457 | 1.467 | 1.499 | 1.944 | 1.933 | 1.951 | 1.971 | 2.175 | 2.106 | 1.992 | 1.908 | 1.645 | 1.668 | 1.874 | 1.934 | 2.462 | 2.664 | 2.653 | 3.044 | 3.848 | 3.966 | 3.581 | 4.353 | 4.580 | 4.896 | 4.498 | 4.410 | 4.716 | 4.552 | 4.242 | 4.623 | 4.253 | 4.079 | 4.259 | 4.001 | 3.670 | 3.170 | 2.870 | 3.064 | 3.134 | 3.138 | 3.075 | 3.022 | 3.221 | 3.804 | 3.480 | 
| Path DP | 1.000 | 0.981 | 1.107 | 1.115 | 1.571 | 1.505 | 1.539 | 1.538 | 1.536 | 1.539 | 1.396 | 1.481 | 1.530 | 1.790 | 2.185 | 2.275 | 2.064 | 2.591 | 2.689 | 2.906 | 2.660 | 2.599 | 2.838 | 2.725 | 2.444 | 2.729 | 2.966 | 2.622 | 2.699 | 1.992 | 1.804 | 1.776 | 1.651 | 1.768 | 1.816 | 2.067 | 1.923 | 1.877 | 1.998 | 2.071 | 2.075 | 2.042 | 2.105 | 2.029 | 1.883 | 1.849 | 1.659 | 1.462 | 1.599 | 1.487 | 1.402 | 1.580 | 1.569 | 1.532 | 1.630 | 1.690 | 1.694 | 1.666 | 1.718 | 1.655 | 1.537 | 1.509 | 1.353 | 1.193 | 1.305 | 1.213 | 1.144 | 1.289 | 1.377 | 1.405 | 1.399 | 1.361 | 1.370 | 1.396 | 1.778 | 1.760 | 1.808 | 1.745 | 1.488 | 1.556 | 
| Path DQ | 1.000 | 1.023 | 1.103 | 1.109 | 1.053 | 1.098 | 1.055 | 0.995 | 0.946 | 0.847 | 0.758 | 0.818 | 0.758 | 0.752 | 0.815 | 0.896 | 0.904 | 0.893 | 0.892 | 0.878 | 1.052 | 1.171 | 1.117 | 1.153 | 1.130 | 1.254 | 1.378 | 1.329 | 1.427 | 1.405 | 1.386 | 1.418 | 1.528 | 1.538 | 1.459 | 1.522 | 1.463 | 1.379 | 1.311 | 1.174 | 1.050 | 1.134 | 1.051 | 1.042 | 1.129 | 1.242 | 1.253 | 1.238 | 1.236 | 1.218 | 1.459 | 1.623 | 1.572 | 1.741 | 1.554 | 1.556 | 1.560 | 1.730 | 1.745 | 1.542 | 1.588 | 1.172 | 1.061 | 1.045 | 0.972 | 1.040 | 1.069 | 1.216 | 1.131 | 1.105 | 1.175 | 1.218 | 1.221 | 1.201 | 1.239 | 1.194 | 1.108 | 1.088 | 1.117 | 1.031 | 
| Path DR | 1.000 | 0.999 | 0.998 | 1.000 | 0.907 | 0.963 | 0.995 | 1.163 | 1.419 | 1.478 | 1.341 | 1.684 | 1.748 | 1.888 | 1.728 | 1.689 | 1.844 | 1.771 | 1.588 | 1.773 | 1.481 | 1.537 | 1.562 | 1.531 | 1.344 | 1.252 | 1.212 | 1.154 | 1.466 | 1.302 | 1.470 | 1.382 | 1.377 | 1.438 | 1.330 | 1.324 | 1.421 | 1.318 | 1.237 | 1.271 | 1.050 | 1.092 | 0.998 | 0.945 | 0.957 | 1.060 | 0.946 | 0.947 | 0.950 | 1.053 | 1.062 | 0.939 | 1.075 | 1.157 | 1.215 | 1.175 | 1.515 | 1.383 | 1.437 | 1.419 | 1.387 | 1.464 | 1.324 | 1.387 | 1.443 | 1.271 | 1.214 | 1.245 | 1.092 | 1.089 | 0.965 | 0.965 | 1.017 | 1.060 | 0.904 | 0.940 | 0.948 | 1.010 | 1.081 | 0.993 | 
| Path DS | 1.000 | 1.409 | 1.350 | 1.380 | 1.379 | 1.377 | 1.380 | 1.252 | 1.328 | 1.372 | 1.605 | 1.959 | 2.040 | 1.851 | 2.324 | 2.412 | 2.606 | 2.385 | 2.331 | 2.545 | 2.444 | 2.192 | 2.447 | 2.043 | 2.121 | 2.156 | 2.347 | 2.148 | 2.099 | 2.292 | 2.200 | 1.973 | 2.204 | 1.840 | 1.910 | 1.942 | 1.902 | 1.671 | 1.556 | 1.360 | 1.468 | 1.492 | 1.530 | 1.462 | 1.448 | 1.536 | 1.516 | 1.626 | 1.450 | 1.204 | 1.025 | 1.025 | 1.028 | 1.063 | 0.928 | 0.953 | 0.986 | 1.020 | 1.089 | 0.969 | 0.926 | 0.600 | 0.639 | 0.640 | 0.666 | 0.680 | 0.681 | 0.702 | 0.676 | 0.675 | 0.719 | 0.771 | 0.765 | 0.741 | 0.752 | 0.750 | 0.700 | 0.660 | 0.711 | 0.865 | 
| Path DT | 1.000 | 1.117 | 1.161 | 1.394 | 1.609 | 1.683 | 1.662 | 1.524 | 1.669 | 1.592 | 1.526 | 1.636 | 1.864 | 2.196 | 2.341 | 2.335 | 2.469 | 2.871 | 2.668 | 2.849 | 2.714 | 2.816 | 2.897 | 2.446 | 2.832 | 2.758 | 2.916 | 2.985 | 3.017 | 4.449 | 4.191 | 4.418 | 4.306 | 4.676 | 4.167 | 4.065 | 3.993 | 4.342 | 5.210 | 6.220 | 6.298 | 5.997 | 7.621 | 6.766 | 7.638 | 7.183 | 7.156 | 7.473 | 6.913 | 6.882 | 7.384 | 6.848 | 6.335 | 6.014 | 5.587 | 6.102 | 5.998 | 7.082 | 6.477 | 6.099 | 6.342 | 7.131 | 6.964 | 6.933 | 7.064 | 7.042 | 6.411 | 6.359 | 6.040 | 5.088 | 5.406 | 5.201 | 4.855 | 5.416 | 5.347 | 5.733 | 5.696 | 5.599 | 6.123 | 6.598 | 
| Path DU | 1.000 | 1.092 | 1.048 | 0.940 | 1.050 | 0.877 | 0.910 | 0.925 | 0.906 | 0.796 | 0.741 | 0.648 | 0.700 | 0.711 | 0.729 | 0.697 | 0.690 | 0.732 | 0.722 | 0.775 | 0.691 | 0.574 | 0.488 | 0.488 | 0.462 | 0.460 | 0.503 | 0.507 | 0.513 | 0.566 | 0.548 | 0.518 | 0.496 | 0.428 | 0.434 | 0.487 | 0.503 | 0.640 | 0.693 | 0.690 | 0.691 | 0.676 | 0.705 | 0.657 | 0.662 | 0.685 | 0.808 | 0.969 | 1.018 | 0.953 | 1.095 | 1.213 | 1.139 | 1.106 | 1.056 | 0.820 | 0.878 | 0.909 | 0.822 | 0.930 | 0.934 | 0.973 | 0.979 | 0.964 | 1.001 | 0.983 | 1.265 | 1.283 | 1.295 | 1.319 | 1.375 | 1.408 | 1.407 | 1.257 | 1.169 | 1.104 | 1.256 | 1.256 | 1.199 | 1.229 | 
| Path DV | 1.000 | 0.999 | 0.971 | 0.975 | 1.071 | 1.111 | 0.973 | 0.829 | 0.867 | 0.843 | 0.961 | 0.972 | 1.332 | 1.350 | 1.369 | 1.392 | 1.431 | 1.358 | 1.287 | 1.327 | 1.357 | 1.609 | 2.008 | 2.028 | 1.986 | 2.254 | 2.179 | 1.921 | 2.101 | 1.953 | 1.842 | 2.075 | 2.217 | 2.261 | 2.252 | 2.191 | 2.206 | 2.247 | 2.862 | 2.834 | 2.912 | 2.810 | 3.226 | 3.138 | 2.871 | 2.836 | 2.582 | 2.534 | 2.860 | 2.880 | 4.057 | 3.887 | 4.244 | 4.554 | 4.224 | 3.966 | 4.074 | 3.366 | 3.499 | 3.198 | 3.030 | 3.068 | 3.397 | 3.033 | 3.036 | 3.045 | 3.376 | 3.405 | 3.010 | 3.099 | 2.287 | 2.071 | 2.039 | 1.896 | 2.030 | 2.085 | 2.373 | 2.208 | 2.207 | 2.229 | 
| Lower percentile | 1.000 | 0.887 | 0.760 | 0.702 | 0.677 | 0.657 | 0.674 | 0.655 | 0.683 | 0.672 | 0.638 | 0.643 | 0.658 | 0.638 | 0.619 | 0.623 | 0.542 | 0.503 | 0.484 | 0.506 | 0.476 | 0.472 | 0.465 | 0.487 | 0.461 | 0.446 | 0.450 | 0.457 | 0.452 | 0.426 | 0.426 | 0.413 | 0.416 | 0.393 | 0.417 | 0.405 | 0.390 | 0.419 | 0.421 | 0.444 | 0.401 | 0.365 | 0.331 | 0.322 | 0.311 | 0.323 | 0.318 | 0.317 | 0.315 | 0.316 | 0.317 | 0.299 | 0.304 | 0.307 | 0.289 | 0.259 | 0.283 | 0.301 | 0.302 | 0.299 | 0.311 | 0.309 | 0.314 | 0.295 | 0.283 | 0.319 | 0.299 | 0.280 | 0.294 | 0.286 | 0.290 | 0.299 | 0.293 | 0.269 | 0.273 | 0.287 | 0.269 | 0.241 | 0.265 | 0.275 | 
| Median | 1.000 | 1.010 | 1.013 | 1.026 | 1.053 | 1.080 | 1.103 | 1.102 | 1.135 | 1.102 | 1.116 | 1.122 | 1.147 | 1.106 | 1.077 | 1.003 | 1.039 | 1.066 | 1.041 | 1.010 | 1.052 | 1.167 | 1.181 | 1.153 | 1.159 | 1.178 | 1.195 | 1.188 | 1.261 | 1.261 | 1.197 | 1.220 | 1.212 | 1.245 | 1.224 | 1.269 | 1.227 | 1.281 | 1.312 | 1.263 | 1.202 | 1.221 | 1.220 | 1.168 | 1.228 | 1.242 | 1.267 | 1.265 | 1.289 | 1.250 | 1.289 | 1.346 | 1.345 | 1.308 | 1.310 | 1.360 | 1.376 | 1.372 | 1.351 | 1.429 | 1.447 | 1.470 | 1.426 | 1.439 | 1.448 | 1.475 | 1.508 | 1.512 | 1.481 | 1.504 | 1.443 | 1.458 | 1.504 | 1.443 | 1.623 | 1.548 | 1.439 | 1.576 | 1.469 | 1.567 | 
| Upper percentile | 1.000 | 1.260 | 1.386 | 1.548 | 1.588 | 1.654 | 1.656 | 1.717 | 1.797 | 1.673 | 1.844 | 1.908 | 1.999 | 2.212 | 2.333 | 2.367 | 2.624 | 2.736 | 2.804 | 2.810 | 2.713 | 2.841 | 2.820 | 2.640 | 2.808 | 2.721 | 2.783 | 2.765 | 3.119 | 3.152 | 3.232 | 3.212 | 3.358 | 3.375 | 3.399 | 3.708 | 3.832 | 4.023 | 4.449 | 4.686 | 4.562 | 5.128 | 5.326 | 5.420 | 5.399 | 5.330 | 5.612 | 5.146 | 5.165 | 5.649 | 5.076 | 4.963 | 5.335 | 5.030 | 5.000 | 5.061 | 4.884 | 5.363 | 5.455 | 5.551 | 5.962 | 6.112 | 6.308 | 6.225 | 6.107 | 5.684 | 5.871 | 5.918 | 6.104 | 6.716 | 7.826 | 7.719 | 7.720 | 7.377 | 7.691 | 7.669 | 8.385 | 8.700 | 8.852 | 8.317 | 
| Original history | 1.000 | 0.876 | 0.746 | 0.780 | 0.759 | 0.865 | 0.875 | 1.199 | 1.215 | 1.232 | 1.253 | 1.288 | 1.222 | 1.159 | 1.194 | 1.222 | 1.448 | 1.808 | 1.825 | 1.788 | 2.029 | 2.072 | 2.103 | 2.073 | 2.069 | 2.174 | 2.018 | 2.025 | 2.251 | 2.038 | 1.912 | 1.980 | 1.732 | 1.714 | 1.457 | 1.419 | 1.345 | 1.501 | 1.425 | 1.446 | 1.412 | 1.550 | 1.488 | 1.533 | 1.408 | 1.128 | 1.011 | 0.960 | 0.892 | 0.974 | 0.958 | 1.131 | 1.034 | 0.974 | 1.012 | 1.139 | 1.112 | 1.107 | 1.128 | 1.124 | 1.024 | 1.015 | 0.964 | 0.812 | 0.863 | 0.830 | 0.775 | 0.865 | 0.854 | 0.915 | 0.909 | 0.894 | 0.900 | 0.919 | 1.193 | 1.186 | 1.196 | 1.209 | 1.334 | 1.292 | 

**Chart data $\cdot$ Pool-return differences across rebuilt histories $\cdot$ 180-day blocks**

Summary of pool-return differences
| Statistic | LP/xyk difference, percentage points per year | 
| --- | --- |
| Minimum | −33.37 | 
| Lower [quartile](./#glossary/quartile) | +1.52 | 
| Median | +1.90 | 
| Upper quartile | +2.81 | 
| Maximum | +16.27 | 
| Original history | +1.65 | 

Proposal minus current LP/xyk, percentage points per year
| LP/xyk difference, percentage points per year | Pair kept in this analysis? | 
| --- | --- |
| +1.12 | Yes | 
| −33.37 | Yes | 
| −3.40 | Yes | 
| +1.86 | Yes | 
| +2.03 | Yes | 
| −2.01 | Yes | 
| +0.27 | Yes | 
| −10.08 | Yes | 
| +1.79 | Yes | 
| +2.93 | Yes | 
| +7.77 | Yes | 
| +1.65 | Yes | 
| +1.77 | Yes | 
| +2.79 | Yes | 
| +2.06 | Yes | 
| −11.16 | Yes | 
| +3.13 | Yes | 
| +1.78 | Yes | 
| +1.58 | Yes | 
| +1.97 | Yes | 
| +1.90 | Yes | 
| +4.62 | Yes | 
| +4.50 | Yes | 
| +3.08 | Yes | 
| +1.70 | Yes | 
| +16.27 | Yes | 
| +3.11 | Yes | 
| +2.54 | Yes | 
| +1.81 | Yes | 
| +0.23 | Yes | 
| −5.46 | Yes | 
| +2.21 | Yes | 
| +1.89 | Yes | 
| +2.73 | Yes | 
| +8.21 | Yes | 
| +2.57 | Yes | 
| +1.60 | Yes | 
| +1.70 | Yes | 
| +1.93 | Yes | 
| +2.15 | Yes | 
| +3.58 | Yes | 
| +1.61 | Yes | 
| +1.72 | Yes | 
| +3.10 | Yes | 
| +1.90 | Yes | 
| +1.82 | Yes | 
| +2.14 | Yes | 
| +3.10 | Yes | 
| +1.68 | Yes | 
| +2.33 | Yes | 
| +1.96 | Yes | 
| −2.20 | Yes | 
| +0.25 | Yes | 
| +1.63 | Yes | 
| +2.18 | Yes | 
| +1.40 | Yes | 
| +1.97 | Yes | 
| +5.82 | Yes | 
| +2.09 | Yes | 
| +3.03 | Yes | 
| +0.70 | Yes | 
| +2.46 | Yes | 
| +3.39 | Yes | 
| −2.00 | Yes | 
| +1.86 | Yes | 
| +1.79 | Yes | 
| +2.73 | Yes | 
| −2.54 | Yes | 
| −0.04 | Yes | 
| −3.19 | Yes | 
| +1.52 | Yes | 
| +1.78 | Yes | 
| +1.78 | Yes | 
| +1.99 | Yes | 
| +1.29 | Yes | 
| +2.71 | Yes | 
| +2.72 | Yes | 
| +2.86 | Yes | 
| +2.55 | Yes | 
| +3.28 | Yes | 
| +5.12 | Yes | 
| +1.63 | Yes | 
| +1.86 | Yes | 
| +6.07 | Yes | 
| +6.40 | Yes | 
| −2.10 | Yes | 
| −0.84 | Yes | 
| +3.10 | Yes | 
| −0.02 | Yes | 
| +2.95 | Yes | 
| +3.47 | Yes | 
| +1.95 | Yes | 
| +3.40 | Yes | 
| +1.49 | Yes | 
| +1.94 | Yes | 
| +2.94 | Yes | 
| −1.35 | Yes | 
| −1.82 | Yes | 
| +1.78 | Yes | 
| +0.35 | Yes | 

**Chart data $\cdot$ Prices on rebuilt histories $\cdot$ 90-day blocks**

Price divided by starting price, sampled weekly
| Rebuilt history | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | 
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Path AA | 1.000 | 0.862 | 0.874 | 0.982 | 1.014 | 1.291 | 1.396 | 1.391 | 1.393 | 1.363 | 1.420 | 1.325 | 1.334 | 1.388 | 1.322 | 1.372 | 1.411 | 1.192 | 1.380 | 1.344 | 1.198 | 1.187 | 1.171 | 1.020 | 0.994 | 0.872 | 0.900 | 0.807 | 0.739 | 0.564 | 0.559 | 0.538 | 0.527 | 0.540 | 0.571 | 0.586 | 0.544 | 0.561 | 0.613 | 0.700 | 0.675 | 0.725 | 0.714 | 0.704 | 0.721 | 0.777 | 0.781 | 0.741 | 0.774 | 0.743 | 0.701 | 0.666 | 0.785 | 0.717 | 0.745 | 0.736 | 0.719 | 0.759 | 0.687 | 0.719 | 0.748 | 0.659 | 0.629 | 0.645 | 0.566 | 0.504 | 0.613 | 0.645 | 0.690 | 0.634 | 0.621 | 0.664 | 0.641 | 0.598 | 0.651 | 0.599 | 0.575 | 0.600 | 0.557 | 0.523 | 
| Path AB | 1.000 | 1.007 | 1.419 | 1.359 | 1.390 | 1.388 | 1.387 | 1.390 | 1.261 | 1.338 | 1.382 | 1.616 | 1.973 | 2.006 | 2.049 | 2.039 | 2.016 | 2.046 | 1.789 | 2.008 | 2.064 | 2.387 | 3.017 | 3.110 | 2.808 | 3.413 | 3.121 | 3.263 | 3.174 | 3.617 | 3.658 | 5.015 | 5.081 | 5.152 | 5.240 | 5.386 | 5.113 | 4.847 | 4.995 | 5.148 | 5.701 | 5.090 | 5.095 | 5.110 | 5.665 | 5.715 | 5.052 | 5.201 | 3.838 | 3.475 | 3.422 | 3.182 | 3.743 | 3.830 | 4.127 | 4.152 | 3.940 | 4.111 | 3.950 | 3.724 | 3.541 | 3.171 | 2.836 | 3.062 | 2.837 | 2.520 | 2.447 | 2.337 | 1.814 | 1.943 | 2.012 | 1.819 | 2.058 | 2.066 | 2.153 | 2.167 | 2.132 | 2.215 | 2.246 | 2.267 | 
| Path AC | 1.000 | 1.010 | 1.455 | 1.422 | 1.495 | 1.454 | 1.545 | 1.408 | 1.348 | 1.433 | 1.544 | 1.880 | 2.023 | 2.215 | 2.221 | 2.015 | 2.137 | 2.208 | 2.583 | 3.152 | 3.283 | 2.978 | 3.739 | 3.880 | 4.193 | 3.838 | 3.914 | 4.185 | 4.040 | 3.765 | 4.103 | 3.774 | 3.620 | 3.780 | 3.551 | 3.257 | 2.813 | 2.547 | 2.719 | 2.926 | 2.966 | 3.332 | 3.440 | 4.379 | 4.737 | 4.717 | 4.726 | 4.623 | 4.816 | 4.493 | 4.524 | 4.683 | 5.721 | 5.959 | 5.406 | 6.786 | 7.043 | 7.611 | 6.966 | 6.806 | 7.433 | 7.136 | 6.400 | 7.147 | 5.968 | 6.051 | 5.733 | 5.804 | 6.428 | 5.739 | 5.744 | 5.761 | 6.387 | 6.443 | 5.695 | 5.864 | 4.327 | 3.918 | 4.184 | 3.985 | 
| Path AD | 1.000 | 0.893 | 0.831 | 0.785 | 0.893 | 0.893 | 0.901 | 1.299 | 1.270 | 1.334 | 1.298 | 1.379 | 1.256 | 1.204 | 1.216 | 1.690 | 1.679 | 1.715 | 1.707 | 1.687 | 1.712 | 1.498 | 1.681 | 1.728 | 1.998 | 2.525 | 2.413 | 2.504 | 2.193 | 1.869 | 1.954 | 1.901 | 2.166 | 2.190 | 3.003 | 3.042 | 3.085 | 3.138 | 3.225 | 3.480 | 3.538 | 3.534 | 3.205 | 2.685 | 2.793 | 3.121 | 3.242 | 3.893 | 4.495 | 4.700 | 4.641 | 4.257 | 4.493 | 4.340 | 4.265 | 4.552 | 4.498 | 4.801 | 4.306 | 3.943 | 3.005 | 2.984 | 2.868 | 2.811 | 2.882 | 2.794 | 2.506 | 2.209 | 2.416 | 2.246 | 2.118 | 2.387 | 2.549 | 2.601 | 2.590 | 2.519 | 2.537 | 2.584 | 2.354 | 2.255 | 
| Path AE | 1.000 | 1.264 | 1.303 | 1.177 | 1.430 | 1.505 | 1.608 | 1.478 | 1.449 | 1.549 | 1.496 | 1.394 | 1.519 | 1.283 | 1.101 | 0.887 | 0.817 | 0.768 | 0.765 | 0.758 | 0.757 | 0.851 | 0.803 | 0.776 | 0.825 | 0.857 | 0.916 | 0.969 | 0.994 | 0.922 | 0.951 | 1.039 | 1.120 | 1.072 | 1.063 | 1.068 | 1.030 | 0.956 | 0.933 | 0.950 | 0.983 | 0.860 | 0.851 | 0.723 | 0.705 | 0.668 | 0.746 | 0.708 | 0.718 | 0.701 | 0.769 | 0.739 | 0.775 | 0.814 | 0.756 | 0.758 | 0.843 | 0.763 | 0.716 | 0.741 | 0.648 | 0.642 | 0.545 | 0.531 | 0.504 | 0.581 | 0.554 | 0.572 | 0.560 | 0.622 | 0.622 | 0.561 | 0.491 | 0.496 | 0.493 | 0.556 | 0.561 | 0.781 | 0.765 | 0.849 | 
| Path AF | 1.000 | 1.000 | 1.054 | 1.099 | 0.936 | 0.974 | 0.982 | 1.047 | 1.109 | 0.986 | 0.995 | 0.710 | 0.642 | 0.731 | 0.748 | 0.756 | 1.115 | 1.050 | 1.107 | 1.079 | 1.171 | 1.044 | 1.018 | 1.000 | 1.088 | 1.305 | 1.569 | 1.633 | 1.438 | 1.373 | 1.408 | 1.236 | 1.232 | 1.092 | 1.092 | 1.151 | 1.200 | 1.022 | 1.064 | 1.079 | 1.142 | 1.015 | 1.025 | 0.731 | 0.661 | 0.666 | 0.700 | 0.724 | 0.699 | 0.750 | 0.738 | 0.729 | 0.708 | 0.719 | 0.738 | 0.705 | 0.698 | 0.740 | 0.731 | 0.784 | 0.699 | 0.581 | 0.494 | 0.494 | 0.467 | 0.469 | 0.597 | 0.646 | 0.643 | 0.644 | 0.630 | 0.656 | 0.613 | 0.617 | 0.638 | 0.753 | 0.903 | 0.948 | 1.030 | 0.918 | 
| Path AG | 1.000 | 1.094 | 1.017 | 0.959 | 1.081 | 1.154 | 1.177 | 1.172 | 1.140 | 1.148 | 1.170 | 1.490 | 1.475 | 1.539 | 1.556 | 2.294 | 2.161 | 2.278 | 2.220 | 2.411 | 2.149 | 2.096 | 2.059 | 2.239 | 2.687 | 3.207 | 3.111 | 2.446 | 2.574 | 2.643 | 2.438 | 2.716 | 2.775 | 2.845 | 2.875 | 2.877 | 2.957 | 2.907 | 3.886 | 3.617 | 3.446 | 3.575 | 3.679 | 3.107 | 3.596 | 3.503 | 3.123 | 3.093 | 3.051 | 2.658 | 2.591 | 2.273 | 2.358 | 2.541 | 2.431 | 2.411 | 2.423 | 2.337 | 2.170 | 2.116 | 1.663 | 1.750 | 1.797 | 1.658 | 1.847 | 2.137 | 2.248 | 2.403 | 2.208 | 2.165 | 2.315 | 2.235 | 2.082 | 2.269 | 2.087 | 2.002 | 2.091 | 1.964 | 2.028 | 2.372 | 
| Path AH | 1.000 | 1.067 | 1.092 | 1.093 | 1.071 | 1.053 | 1.122 | 1.115 | 1.172 | 1.005 | 0.810 | 0.746 | 0.702 | 0.854 | 0.986 | 1.030 | 1.018 | 0.933 | 1.022 | 0.975 | 0.934 | 1.002 | 1.141 | 1.344 | 1.433 | 1.430 | 1.660 | 1.770 | 1.766 | 1.867 | 2.171 | 2.018 | 2.154 | 2.052 | 2.129 | 2.191 | 1.850 | 2.141 | 2.086 | 2.085 | 2.270 | 2.048 | 2.023 | 2.213 | 2.099 | 1.894 | 2.120 | 1.799 | 1.800 | 1.848 | 1.807 | 1.614 | 1.675 | 1.785 | 1.773 | 1.864 | 1.599 | 1.288 | 1.186 | 1.116 | 1.111 | 1.101 | 1.099 | 1.236 | 1.166 | 1.120 | 1.214 | 1.246 | 1.332 | 1.341 | 1.370 | 1.360 | 1.347 | 1.662 | 1.793 | 1.791 | 1.741 | 1.748 | 1.581 | 1.655 | 
| Path AI | 1.000 | 1.005 | 0.969 | 0.900 | 0.878 | 0.690 | 0.726 | 0.745 | 0.688 | 0.766 | 0.783 | 0.802 | 0.811 | 0.788 | 0.805 | 0.777 | 0.764 | 0.816 | 0.806 | 0.860 | 0.771 | 0.706 | 0.538 | 0.534 | 0.514 | 0.503 | 0.558 | 0.524 | 0.481 | 0.415 | 0.376 | 0.401 | 0.410 | 0.411 | 0.403 | 0.396 | 0.422 | 0.419 | 0.440 | 0.398 | 0.357 | 0.399 | 0.333 | 0.345 | 0.351 | 0.344 | 0.302 | 0.281 | 0.246 | 0.266 | 0.270 | 0.277 | 0.258 | 0.266 | 0.261 | 0.289 | 0.290 | 0.261 | 0.229 | 0.231 | 0.229 | 0.259 | 0.261 | 0.363 | 0.361 | 0.364 | 0.362 | 0.369 | 0.368 | 0.335 | 0.333 | 0.316 | 0.266 | 0.283 | 0.272 | 0.254 | 0.283 | 0.280 | 0.274 | 0.293 | 
| Path AJ | 1.000 | 1.122 | 1.154 | 1.334 | 1.686 | 1.738 | 1.570 | 1.908 | 2.008 | 2.146 | 1.972 | 1.933 | 2.067 | 2.167 | 2.126 | 2.400 | 2.417 | 3.405 | 3.262 | 3.335 | 3.332 | 3.327 | 3.336 | 3.026 | 3.210 | 3.317 | 4.034 | 3.753 | 3.665 | 3.899 | 4.043 | 4.051 | 3.985 | 4.109 | 3.960 | 3.676 | 3.610 | 3.237 | 2.854 | 2.658 | 2.697 | 2.633 | 2.891 | 2.775 | 2.859 | 2.627 | 2.104 | 1.887 | 1.791 | 1.664 | 1.817 | 1.786 | 2.109 | 2.154 | 2.185 | 2.155 | 2.151 | 2.259 | 2.097 | 2.105 | 2.339 | 2.118 | 1.987 | 2.058 | 1.800 | 1.742 | 1.639 | 1.632 | 1.705 | 1.577 | 1.570 | 1.684 | 1.562 | 1.467 | 1.507 | 1.245 | 1.294 | 1.183 | 1.214 | 1.404 | 
| Path AK | 1.000 | 1.039 | 1.073 | 1.123 | 1.101 | 1.124 | 1.010 | 0.995 | 0.951 | 0.801 | 0.818 | 0.809 | 0.745 | 0.851 | 0.924 | 0.824 | 0.804 | 0.789 | 0.858 | 1.030 | 1.230 | 1.245 | 1.185 | 1.507 | 1.338 | 1.510 | 1.170 | 1.262 | 1.395 | 1.428 | 1.443 | 2.128 | 2.005 | 2.114 | 2.060 | 2.237 | 1.994 | 1.945 | 1.910 | 2.177 | 2.293 | 2.391 | 2.038 | 2.120 | 2.137 | 2.279 | 2.413 | 2.145 | 2.165 | 1.545 | 1.396 | 1.407 | 1.431 | 1.463 | 1.465 | 1.436 | 1.411 | 1.504 | 1.494 | 1.571 | 1.347 | 1.086 | 0.999 | 0.941 | 0.936 | 0.875 | 1.261 | 1.232 | 1.295 | 1.260 | 1.339 | 1.220 | 1.168 | 1.242 | 1.337 | 1.629 | 1.753 | 1.841 | 1.710 | 1.826 | 
| Path AL | 1.000 | 1.001 | 1.004 | 1.113 | 1.123 | 0.992 | 1.022 | 0.754 | 0.683 | 0.672 | 0.625 | 0.669 | 0.688 | 0.736 | 0.830 | 0.886 | 0.904 | 0.900 | 0.876 | 0.882 | 0.898 | 1.144 | 1.133 | 1.164 | 1.123 | 1.290 | 1.311 | 1.114 | 1.085 | 1.029 | 1.148 | 1.089 | 1.106 | 1.080 | 1.185 | 1.138 | 1.172 | 1.077 | 0.863 | 0.657 | 0.738 | 0.762 | 0.970 | 1.049 | 1.044 | 1.046 | 1.024 | 1.066 | 0.995 | 1.002 | 1.037 | 1.223 | 1.217 | 1.201 | 1.200 | 1.204 | 1.129 | 1.096 | 1.047 | 0.813 | 0.870 | 0.901 | 0.815 | 0.922 | 0.925 | 0.958 | 1.021 | 1.081 | 0.961 | 0.970 | 0.692 | 0.625 | 0.630 | 0.663 | 0.685 | 0.661 | 0.710 | 0.699 | 0.689 | 0.736 | 
| Path AM | 1.000 | 0.999 | 0.892 | 0.830 | 0.784 | 0.892 | 0.892 | 0.900 | 1.297 | 1.268 | 1.333 | 1.296 | 1.378 | 1.292 | 1.403 | 1.250 | 1.220 | 1.198 | 1.303 | 1.563 | 1.866 | 1.890 | 1.799 | 2.287 | 2.030 | 2.292 | 2.012 | 2.246 | 2.132 | 2.164 | 2.112 | 2.319 | 2.226 | 2.293 | 2.107 | 1.687 | 1.513 | 1.437 | 1.335 | 1.182 | 1.275 | 1.409 | 1.442 | 1.458 | 2.150 | 2.025 | 2.135 | 2.081 | 2.260 | 2.014 | 1.964 | 1.930 | 1.845 | 2.070 | 2.128 | 2.461 | 3.110 | 3.206 | 2.895 | 3.519 | 3.703 | 3.958 | 3.636 | 3.565 | 3.812 | 3.753 | 3.834 | 4.974 | 4.944 | 4.989 | 5.041 | 5.563 | 5.387 | 5.095 | 4.880 | 4.208 | 4.266 | 4.793 | 4.757 | 4.608 | 
| Path AN | 1.000 | 1.114 | 1.138 | 1.167 | 1.179 | 1.180 | 1.212 | 1.192 | 1.594 | 1.547 | 1.556 | 1.594 | 1.655 | 1.632 | 1.625 | 1.610 | 1.608 | 1.808 | 1.705 | 1.647 | 1.751 | 1.819 | 1.879 | 1.967 | 1.928 | 1.968 | 1.920 | 1.938 | 2.695 | 2.677 | 2.734 | 2.721 | 2.690 | 2.730 | 2.387 | 2.679 | 2.755 | 3.185 | 4.026 | 3.837 | 3.828 | 4.048 | 4.707 | 4.374 | 4.670 | 4.449 | 4.615 | 4.749 | 4.011 | 4.642 | 4.522 | 4.031 | 4.074 | 4.766 | 5.816 | 6.057 | 5.495 | 6.898 | 7.160 | 7.737 | 7.082 | 6.919 | 7.556 | 7.254 | 6.506 | 6.813 | 6.929 | 7.122 | 6.761 | 6.409 | 6.605 | 6.756 | 8.008 | 9.998 | 10.096 | 9.888 | 11.223 | 11.461 | 11.581 | 12.779 | 
| Path AO | 1.000 | 1.050 | 1.015 | 1.309 | 1.195 | 1.242 | 1.227 | 1.199 | 1.265 | 1.145 | 1.198 | 1.247 | 1.099 | 1.227 | 1.321 | 1.387 | 1.341 | 1.729 | 1.578 | 1.640 | 1.620 | 1.583 | 1.671 | 1.512 | 1.583 | 1.647 | 1.559 | 1.542 | 1.420 | 1.613 | 1.632 | 1.691 | 1.766 | 1.703 | 1.726 | 1.695 | 2.225 | 2.183 | 2.271 | 2.372 | 2.264 | 2.322 | 2.038 | 2.032 | 1.800 | 1.801 | 1.897 | 1.978 | 1.686 | 1.754 | 1.768 | 1.885 | 1.896 | 2.018 | 2.164 | 2.147 | 2.080 | 2.111 | 2.104 | 1.966 | 1.852 | 1.632 | 1.542 | 1.577 | 1.445 | 1.513 | 1.484 | 1.675 | 1.687 | 2.377 | 2.277 | 2.328 | 2.326 | 2.323 | 2.329 | 2.112 | 2.241 | 2.316 | 2.154 | 2.104 | 
| Path AP | 1.000 | 0.975 | 0.855 | 0.909 | 0.945 | 0.977 | 0.853 | 0.876 | 0.906 | 0.937 | 1.001 | 0.891 | 0.851 | 0.714 | 0.716 | 0.704 | 0.726 | 0.700 | 0.650 | 0.638 | 0.572 | 0.504 | 0.551 | 0.513 | 0.483 | 0.545 | 0.547 | 0.623 | 0.630 | 0.864 | 0.875 | 0.887 | 0.902 | 0.927 | 0.880 | 0.835 | 0.860 | 0.880 | 1.043 | 1.212 | 1.192 | 1.200 | 1.226 | 1.590 | 1.581 | 1.595 | 1.611 | 1.778 | 1.722 | 1.629 | 1.560 | 1.345 | 1.397 | 1.445 | 1.543 | 1.373 | 1.312 | 0.850 | 0.906 | 0.906 | 0.943 | 0.964 | 0.964 | 0.994 | 0.958 | 0.963 | 0.929 | 1.067 | 1.038 | 0.949 | 0.938 | 0.854 | 0.838 | 0.946 | 0.952 | 1.341 | 1.285 | 1.314 | 1.396 | 1.343 | 
| Path AQ | 1.000 | 1.107 | 1.205 | 1.087 | 1.074 | 1.175 | 1.115 | 1.006 | 1.125 | 0.955 | 0.956 | 0.981 | 0.960 | 0.799 | 0.837 | 0.820 | 0.838 | 0.753 | 0.742 | 0.709 | 0.597 | 0.610 | 0.603 | 0.555 | 0.631 | 0.638 | 0.735 | 0.655 | 0.639 | 0.627 | 0.682 | 0.819 | 0.977 | 0.990 | 0.942 | 1.197 | 1.063 | 1.200 | 1.129 | 1.135 | 1.124 | 1.387 | 1.497 | 1.495 | 1.454 | 1.459 | 1.603 | 1.663 | 1.456 | 1.241 | 1.298 | 1.262 | 1.450 | 1.443 | 1.427 | 1.448 | 1.266 | 1.421 | 1.461 | 1.689 | 2.135 | 2.201 | 1.987 | 2.416 | 2.542 | 2.555 | 2.425 | 2.462 | 2.403 | 2.638 | 2.532 | 2.609 | 2.397 | 1.920 | 1.722 | 1.635 | 1.518 | 1.658 | 1.700 | 1.798 | 
| Path AR | 1.000 | 0.957 | 0.949 | 0.954 | 0.920 | 0.854 | 0.833 | 0.655 | 0.689 | 0.707 | 0.653 | 0.727 | 0.743 | 0.761 | 0.756 | 0.727 | 0.712 | 0.730 | 0.772 | 0.792 | 0.735 | 0.758 | 0.829 | 0.893 | 0.854 | 0.847 | 0.902 | 0.972 | 0.978 | 0.928 | 0.968 | 0.930 | 0.877 | 0.834 | 0.747 | 0.668 | 0.721 | 0.668 | 0.663 | 0.773 | 0.753 | 0.818 | 0.729 | 0.711 | 0.699 | 0.760 | 0.911 | 1.088 | 1.102 | 1.049 | 1.333 | 1.184 | 1.222 | 1.306 | 1.261 | 1.175 | 1.281 | 1.178 | 1.130 | 1.180 | 1.108 | 1.016 | 0.878 | 0.795 | 0.849 | 0.869 | 0.866 | 0.884 | 0.854 | 0.839 | 0.896 | 0.885 | 0.945 | 0.847 | 0.776 | 0.592 | 0.587 | 0.564 | 0.582 | 0.571 | 
| Path AS | 1.000 | 0.958 | 0.980 | 0.979 | 0.977 | 0.980 | 0.889 | 0.943 | 0.974 | 1.139 | 1.391 | 1.448 | 1.314 | 1.561 | 1.534 | 1.811 | 1.657 | 1.560 | 1.622 | 1.824 | 1.781 | 1.773 | 1.807 | 1.801 | 1.640 | 1.627 | 1.794 | 1.862 | 2.012 | 1.842 | 1.799 | 1.965 | 1.887 | 1.692 | 1.889 | 1.578 | 1.638 | 1.665 | 1.631 | 1.467 | 1.442 | 1.536 | 1.526 | 1.604 | 1.376 | 1.109 | 1.021 | 0.961 | 0.957 | 0.948 | 0.946 | 1.064 | 1.248 | 1.269 | 1.268 | 1.150 | 0.963 | 1.002 | 1.120 | 1.163 | 1.397 | 1.613 | 1.686 | 1.665 | 1.527 | 1.513 | 1.700 | 1.754 | 2.233 | 2.416 | 2.406 | 2.411 | 2.358 | 2.456 | 2.292 | 2.308 | 2.389 | 2.817 | 3.117 | 3.206 | 
| Path AT | 1.000 | 0.942 | 0.979 | 1.101 | 1.075 | 1.071 | 1.091 | 1.087 | 0.990 | 0.982 | 0.932 | 0.785 | 0.835 | 0.810 | 0.897 | 0.801 | 0.802 | 0.804 | 0.891 | 0.899 | 0.795 | 0.818 | 0.604 | 0.547 | 0.538 | 0.501 | 0.513 | 0.567 | 0.583 | 0.576 | 0.575 | 0.578 | 0.541 | 0.526 | 0.502 | 0.390 | 0.417 | 0.432 | 0.391 | 0.387 | 0.310 | 0.278 | 0.264 | 0.245 | 0.268 | 0.263 | 0.311 | 0.284 | 0.268 | 0.278 | 0.313 | 0.306 | 0.341 | 0.303 | 0.306 | 0.218 | 0.197 | 0.199 | 0.209 | 0.216 | 0.208 | 0.224 | 0.220 | 0.217 | 0.223 | 0.221 | 0.242 | 0.232 | 0.239 | 0.220 | 0.176 | 0.158 | 0.150 | 0.139 | 0.152 | 0.149 | 0.177 | 0.162 | 0.166 | 0.163 | 
| Path AU | 1.000 | 0.974 | 0.923 | 1.031 | 0.978 | 0.993 | 0.969 | 1.064 | 1.021 | 1.052 | 0.967 | 0.774 | 0.694 | 0.770 | 0.829 | 0.870 | 0.841 | 1.085 | 0.991 | 1.030 | 1.017 | 0.994 | 1.049 | 0.949 | 0.993 | 1.034 | 0.961 | 0.924 | 0.906 | 0.929 | 0.982 | 1.007 | 0.935 | 0.964 | 1.054 | 1.135 | 1.086 | 1.077 | 1.083 | 1.099 | 1.172 | 1.164 | 1.224 | 1.049 | 0.846 | 0.778 | 0.733 | 0.729 | 0.723 | 0.722 | 0.811 | 0.765 | 0.798 | 0.707 | 0.707 | 0.745 | 0.777 | 0.662 | 0.689 | 0.695 | 0.741 | 0.784 | 0.697 | 0.704 | 0.502 | 0.416 | 0.423 | 0.421 | 0.394 | 0.371 | 0.327 | 0.309 | 0.316 | 0.289 | 0.314 | 0.322 | 0.344 | 0.346 | 0.341 | 0.456 | 
| Path AV | 1.000 | 1.022 | 1.325 | 1.317 | 1.329 | 1.343 | 1.482 | 1.435 | 1.357 | 1.300 | 1.121 | 1.137 | 1.277 | 1.243 | 1.224 | 1.138 | 1.218 | 1.251 | 1.424 | 1.325 | 1.294 | 1.376 | 1.427 | 1.430 | 1.407 | 1.451 | 1.374 | 1.171 | 1.224 | 1.191 | 1.357 | 1.372 | 1.881 | 1.906 | 1.933 | 1.966 | 2.020 | 1.918 | 1.818 | 1.816 | 1.723 | 1.749 | 1.708 | 1.874 | 1.799 | 1.854 | 1.703 | 1.364 | 1.223 | 1.161 | 1.079 | 1.178 | 1.260 | 1.394 | 1.434 | 1.415 | 1.414 | 1.419 | 1.331 | 1.292 | 1.234 | 0.958 | 1.026 | 1.062 | 0.960 | 0.981 | 1.007 | 0.985 | 0.880 | 0.797 | 0.708 | 0.776 | 0.773 | 0.790 | 0.763 | 0.750 | 0.800 | 0.791 | 0.812 | 0.754 | 
| Path AW | 1.000 | 0.940 | 0.937 | 0.978 | 0.905 | 0.901 | 0.967 | 0.897 | 0.842 | 0.865 | 0.715 | 0.743 | 0.679 | 0.658 | 0.676 | 0.722 | 0.727 | 0.743 | 0.737 | 0.730 | 0.901 | 0.972 | 0.971 | 0.944 | 0.948 | 1.041 | 1.043 | 1.342 | 1.362 | 1.374 | 1.399 | 1.459 | 1.494 | 1.492 | 1.333 | 1.240 | 1.171 | 1.333 | 1.332 | 1.411 | 1.502 | 1.610 | 1.598 | 1.548 | 1.571 | 1.566 | 1.463 | 1.378 | 1.214 | 1.147 | 1.173 | 1.075 | 1.061 | 1.065 | 1.170 | 1.214 | 1.063 | 0.906 | 0.947 | 0.921 | 1.050 | 1.062 | 1.456 | 1.475 | 1.495 | 1.565 | 1.420 | 1.507 | 1.557 | 1.821 | 2.222 | 2.314 | 2.099 | 2.635 | 2.735 | 2.956 | 2.705 | 2.643 | 2.592 | 2.926 | 
| Path AX | 1.000 | 1.063 | 0.968 | 0.927 | 0.986 | 1.062 | 1.293 | 1.391 | 1.461 | 1.413 | 1.821 | 1.663 | 1.728 | 1.697 | 1.610 | 1.680 | 1.615 | 1.522 | 1.447 | 1.296 | 1.159 | 1.251 | 1.160 | 1.151 | 1.246 | 1.371 | 1.273 | 1.246 | 1.298 | 1.211 | 1.219 | 1.262 | 1.488 | 1.784 | 1.874 | 1.755 | 2.017 | 2.233 | 2.431 | 2.013 | 2.141 | 2.223 | 2.296 | 2.404 | 2.356 | 2.406 | 2.162 | 2.130 | 2.036 | 1.715 | 1.751 | 1.732 | 1.722 | 1.781 | 1.903 | 1.693 | 1.618 | 1.047 | 1.117 | 1.117 | 1.163 | 1.188 | 1.189 | 1.226 | 1.181 | 1.030 | 1.092 | 1.129 | 1.320 | 1.611 | 1.678 | 1.522 | 1.911 | 1.983 | 2.143 | 1.961 | 1.916 | 2.093 | 2.178 | 2.433 | 
| Path AY | 1.000 | 1.031 | 0.994 | 0.922 | 0.906 | 0.812 | 0.716 | 0.783 | 0.728 | 0.687 | 0.774 | 0.826 | 0.843 | 0.890 | 0.778 | 0.770 | 0.655 | 0.638 | 0.604 | 0.675 | 0.640 | 0.650 | 0.634 | 0.696 | 0.668 | 0.689 | 0.616 | 0.599 | 0.572 | 0.444 | 0.475 | 0.492 | 0.445 | 0.503 | 0.505 | 0.526 | 0.530 | 0.521 | 0.542 | 0.521 | 0.521 | 0.535 | 0.527 | 0.704 | 0.683 | 0.687 | 0.704 | 0.731 | 0.753 | 0.775 | 0.714 | 0.552 | 0.522 | 0.523 | 0.524 | 0.582 | 0.587 | 0.519 | 0.534 | 0.394 | 0.357 | 0.351 | 0.327 | 0.350 | 0.359 | 0.357 | 0.341 | 0.287 | 0.293 | 0.290 | 0.267 | 0.303 | 0.307 | 0.318 | 0.332 | 0.320 | 0.325 | 0.319 | 0.310 | 0.311 | 
| Path AZ | 1.000 | 1.095 | 1.044 | 1.001 | 1.073 | 1.223 | 1.440 | 1.536 | 1.532 | 1.620 | 1.883 | 1.750 | 1.869 | 1.784 | 1.402 | 1.475 | 1.515 | 1.398 | 1.556 | 1.591 | 1.631 | 1.648 | 1.649 | 1.695 | 1.666 | 2.228 | 2.195 | 2.210 | 3.113 | 2.983 | 3.050 | 3.047 | 3.043 | 3.050 | 2.767 | 2.936 | 3.033 | 3.547 | 4.329 | 4.447 | 4.490 | 6.470 | 6.324 | 6.648 | 6.465 | 6.871 | 6.260 | 5.996 | 6.372 | 6.864 | 8.358 | 8.995 | 9.802 | 9.822 | 9.663 | 9.964 | 9.601 | 8.914 | 8.752 | 7.849 | 6.920 | 7.567 | 7.036 | 6.635 | 7.476 | 6.858 | 7.883 | 8.729 | 9.501 | 8.573 | 8.469 | 9.265 | 8.786 | 7.928 | 8.873 | 7.530 | 7.534 | 7.737 | 6.393 | 6.647 | 
| Path BA | 1.000 | 1.037 | 1.039 | 1.022 | 1.054 | 1.016 | 0.943 | 0.926 | 0.830 | 0.732 | 0.800 | 0.744 | 0.702 | 0.800 | 0.809 | 0.892 | 0.864 | 0.817 | 0.783 | 0.675 | 0.684 | 0.769 | 0.794 | 1.010 | 1.093 | 1.089 | 1.204 | 1.184 | 1.398 | 1.278 | 1.204 | 1.252 | 1.407 | 1.374 | 1.368 | 1.394 | 1.390 | 1.265 | 1.255 | 1.159 | 1.148 | 1.180 | 1.138 | 1.307 | 1.271 | 1.163 | 1.149 | 1.046 | 1.026 | 1.159 | 1.167 | 1.643 | 1.669 | 1.679 | 1.593 | 1.663 | 1.597 | 1.506 | 1.432 | 1.282 | 1.147 | 1.238 | 1.147 | 1.138 | 1.233 | 1.211 | 1.374 | 1.403 | 1.424 | 1.404 | 1.401 | 1.472 | 1.367 | 1.372 | 1.524 | 1.380 | 1.295 | 1.341 | 1.381 | 1.421 | 
| Path BB | 1.000 | 1.052 | 1.125 | 1.033 | 1.013 | 1.083 | 1.046 | 0.975 | 1.062 | 0.977 | 0.937 | 0.978 | 0.919 | 0.834 | 0.815 | 0.860 | 0.778 | 0.814 | 0.848 | 0.746 | 0.713 | 0.731 | 0.641 | 0.640 | 0.567 | 0.567 | 0.513 | 0.479 | 0.482 | 0.499 | 0.589 | 0.706 | 0.741 | 0.694 | 0.798 | 0.883 | 0.962 | 0.868 | 0.857 | 0.874 | 0.872 | 0.848 | 0.851 | 0.935 | 0.971 | 0.850 | 0.724 | 0.757 | 0.737 | 0.839 | 0.849 | 1.164 | 1.247 | 1.228 | 1.472 | 1.638 | 1.563 | 1.613 | 1.580 | 1.754 | 1.755 | 1.583 | 1.384 | 1.399 | 1.390 | 1.461 | 1.426 | 1.420 | 1.447 | 1.442 | 1.313 | 1.303 | 1.237 | 1.042 | 1.107 | 1.065 | 0.994 | 1.109 | 1.457 | 1.429 | 
| Path BC | 1.000 | 1.081 | 0.989 | 0.966 | 1.055 | 1.013 | 0.909 | 1.015 | 0.847 | 0.879 | 0.894 | 0.876 | 0.769 | 0.749 | 0.780 | 0.785 | 0.773 | 0.803 | 0.788 | 1.014 | 1.029 | 1.039 | 1.058 | 1.103 | 1.129 | 1.128 | 1.049 | 1.194 | 1.111 | 1.085 | 1.154 | 1.196 | 1.199 | 1.179 | 1.216 | 1.172 | 1.088 | 1.068 | 0.958 | 0.762 | 0.762 | 0.721 | 0.718 | 0.719 | 0.765 | 0.761 | 0.729 | 0.754 | 0.835 | 0.858 | 0.847 | 0.846 | 0.781 | 0.884 | 0.887 | 0.924 | 0.930 | 0.916 | 0.951 | 0.934 | 1.202 | 1.220 | 1.231 | 1.254 | 1.307 | 1.318 | 1.292 | 1.382 | 1.334 | 1.243 | 1.355 | 1.246 | 1.195 | 1.248 | 1.172 | 1.075 | 0.929 | 0.841 | 0.695 | 0.722 | 
| Path BD | 1.000 | 0.881 | 0.964 | 0.896 | 0.845 | 0.953 | 1.017 | 1.038 | 1.034 | 1.005 | 1.012 | 1.031 | 1.313 | 1.384 | 1.224 | 1.260 | 0.930 | 0.842 | 0.829 | 0.771 | 0.825 | 0.848 | 0.965 | 0.898 | 0.876 | 0.932 | 1.084 | 1.077 | 1.100 | 1.095 | 1.082 | 1.098 | 0.960 | 1.078 | 1.108 | 1.281 | 1.619 | 1.669 | 1.507 | 1.600 | 1.667 | 1.678 | 1.651 | 1.715 | 1.685 | 2.168 | 2.199 | 2.220 | 2.260 | 2.356 | 2.413 | 2.410 | 2.268 | 2.979 | 2.923 | 3.041 | 2.995 | 3.199 | 3.251 | 3.248 | 2.945 | 2.467 | 2.567 | 2.868 | 2.979 | 2.272 | 2.053 | 2.068 | 2.176 | 2.250 | 2.170 | 2.330 | 2.294 | 2.264 | 2.316 | 2.496 | 2.511 | 2.382 | 2.642 | 2.665 | 
| Path BE | 1.000 | 1.135 | 1.159 | 1.176 | 1.159 | 1.157 | 1.216 | 1.129 | 1.133 | 1.259 | 1.140 | 1.069 | 1.107 | 1.026 | 0.951 | 0.893 | 0.918 | 0.758 | 0.788 | 0.720 | 0.682 | 0.691 | 0.765 | 0.683 | 0.684 | 0.686 | 0.722 | 1.041 | 1.018 | 1.070 | 1.040 | 1.105 | 1.007 | 0.965 | 1.025 | 1.104 | 1.345 | 1.447 | 1.520 | 1.375 | 1.427 | 1.250 | 1.065 | 1.113 | 1.083 | 1.234 | 1.248 | 1.711 | 1.734 | 1.758 | 1.788 | 1.838 | 2.266 | 2.360 | 2.141 | 2.688 | 2.789 | 3.014 | 2.759 | 2.695 | 2.943 | 2.826 | 2.535 | 2.830 | 2.363 | 2.632 | 2.743 | 2.810 | 2.807 | 2.507 | 2.332 | 2.203 | 2.507 | 2.505 | 2.530 | 3.645 | 3.563 | 3.745 | 3.822 | 3.780 | 
| Path BF | 1.000 | 0.995 | 1.068 | 0.991 | 0.930 | 0.956 | 0.789 | 0.821 | 0.750 | 0.711 | 0.720 | 0.797 | 0.711 | 0.736 | 0.747 | 0.759 | 0.780 | 0.741 | 0.702 | 0.724 | 0.740 | 0.877 | 1.096 | 1.106 | 1.083 | 1.230 | 1.380 | 1.308 | 1.460 | 1.385 | 1.406 | 1.373 | 1.507 | 1.446 | 1.490 | 1.369 | 1.097 | 0.984 | 0.934 | 1.015 | 1.054 | 1.266 | 1.462 | 1.528 | 1.509 | 1.384 | 1.515 | 1.446 | 1.385 | 1.486 | 1.692 | 1.994 | 2.053 | 1.959 | 2.021 | 1.980 | 2.199 | 2.200 | 1.984 | 1.735 | 1.754 | 1.742 | 1.966 | 1.986 | 2.760 | 2.860 | 2.857 | 3.212 | 3.029 | 2.927 | 3.112 | 3.232 | 3.338 | 3.494 | 3.425 | 3.497 | 3.143 | 3.097 | 2.875 | 2.886 | 
| Path BG | 1.000 | 1.066 | 1.067 | 1.110 | 1.135 | 1.135 | 1.170 | 1.128 | 1.126 | 1.199 | 1.285 | 1.276 | 1.236 | 1.287 | 1.369 | 1.422 | 1.468 | 1.537 | 1.507 | 1.538 | 1.382 | 1.362 | 1.302 | 1.097 | 1.119 | 1.107 | 0.941 | 0.941 | 0.979 | 1.001 | 1.001 | 1.032 | 0.995 | 0.993 | 1.058 | 1.134 | 1.125 | 1.090 | 1.106 | 1.131 | 1.235 | 1.186 | 1.063 | 1.188 | 0.992 | 1.029 | 1.046 | 1.025 | 0.900 | 0.838 | 0.733 | 0.791 | 0.821 | 0.751 | 0.734 | 0.802 | 0.770 | 0.690 | 0.771 | 0.644 | 0.668 | 0.679 | 0.665 | 0.584 | 0.544 | 0.554 | 0.526 | 0.534 | 0.521 | 0.572 | 0.549 | 0.566 | 0.520 | 0.416 | 0.373 | 0.355 | 0.329 | 0.360 | 0.374 | 0.385 | 
| Path BH | 1.000 | 0.976 | 0.958 | 1.042 | 1.250 | 1.492 | 1.512 | 1.439 | 1.829 | 1.624 | 1.833 | 1.724 | 1.717 | 1.968 | 1.954 | 1.996 | 1.987 | 1.964 | 1.993 | 1.743 | 1.956 | 2.011 | 2.325 | 2.939 | 3.030 | 2.736 | 3.054 | 3.229 | 3.312 | 3.076 | 3.170 | 3.465 | 3.733 | 3.573 | 3.543 | 3.561 | 3.434 | 3.188 | 3.109 | 2.913 | 3.119 | 3.204 | 3.646 | 3.392 | 3.312 | 3.524 | 3.654 | 3.661 | 3.602 | 3.714 | 3.579 | 3.322 | 3.024 | 3.475 | 3.848 | 4.189 | 3.780 | 3.734 | 4.085 | 3.873 | 3.495 | 3.912 | 3.320 | 3.321 | 3.411 | 3.508 | 3.439 | 3.511 | 3.155 | 3.109 | 2.972 | 2.503 | 2.555 | 2.527 | 2.328 | 2.644 | 2.675 | 2.772 | 2.763 | 2.768 | 
| Path BI | 1.000 | 0.915 | 0.861 | 0.895 | 1.007 | 0.983 | 0.979 | 0.998 | 0.994 | 0.905 | 0.898 | 0.853 | 0.718 | 0.716 | 0.704 | 0.941 | 0.914 | 0.919 | 0.941 | 0.977 | 1.007 | 1.036 | 0.955 | 0.739 | 0.797 | 0.881 | 0.916 | 0.818 | 0.761 | 0.719 | 0.818 | 0.817 | 0.825 | 1.189 | 1.162 | 1.222 | 1.188 | 1.263 | 1.151 | 1.056 | 1.073 | 1.100 | 1.052 | 1.042 | 1.105 | 1.091 | 1.170 | 1.043 | 0.866 | 0.737 | 0.737 | 0.697 | 0.623 | 0.608 | 0.597 | 0.649 | 0.779 | 0.930 | 0.942 | 0.897 | 1.139 | 1.012 | 1.142 | 1.074 | 1.070 | 0.946 | 1.062 | 1.091 | 1.262 | 1.595 | 1.644 | 1.485 | 1.805 | 1.899 | 2.030 | 1.865 | 1.829 | 1.955 | 1.998 | 2.027 | 
| Path BJ | 1.000 | 1.023 | 1.212 | 1.514 | 1.528 | 1.497 | 1.699 | 1.735 | 1.761 | 1.736 | 1.733 | 1.820 | 1.690 | 1.752 | 1.661 | 1.499 | 1.678 | 1.424 | 1.425 | 1.463 | 1.431 | 1.277 | 1.157 | 1.028 | 1.127 | 1.123 | 1.208 | 1.212 | 1.332 | 1.382 | 1.210 | 1.031 | 1.078 | 1.049 | 1.195 | 1.209 | 1.657 | 1.679 | 1.702 | 2.001 | 1.776 | 2.005 | 1.885 | 1.878 | 1.962 | 1.815 | 1.806 | 1.938 | 1.798 | 1.688 | 1.734 | 1.433 | 1.412 | 1.410 | 1.279 | 1.071 | 1.115 | 1.245 | 1.294 | 1.554 | 1.794 | 1.875 | 1.852 | 1.699 | 1.860 | 1.805 | 1.556 | 1.578 | 1.773 | 1.830 | 2.329 | 2.520 | 2.510 | 2.514 | 2.459 | 2.562 | 2.390 | 2.407 | 2.562 | 2.746 | 
| Path BK | 1.000 | 0.998 | 1.048 | 0.973 | 0.977 | 1.086 | 0.983 | 0.922 | 0.955 | 0.835 | 0.827 | 0.703 | 0.684 | 0.690 | 0.581 | 0.593 | 0.587 | 0.540 | 0.614 | 0.621 | 0.644 | 0.672 | 0.648 | 0.657 | 0.645 | 0.847 | 0.877 | 0.936 | 0.952 | 0.951 | 0.862 | 0.722 | 0.751 | 0.840 | 0.872 | 1.047 | 1.209 | 1.264 | 1.248 | 1.226 | 1.294 | 1.171 | 1.226 | 1.276 | 1.123 | 1.073 | 1.100 | 0.965 | 0.963 | 0.853 | 0.853 | 0.899 | 0.840 | 0.826 | 0.858 | 0.843 | 1.085 | 1.101 | 1.111 | 1.131 | 1.179 | 1.207 | 1.206 | 1.077 | 1.002 | 0.880 | 0.893 | 0.781 | 0.876 | 0.901 | 1.042 | 1.317 | 1.357 | 1.226 | 1.490 | 1.568 | 1.676 | 1.540 | 1.556 | 2.295 | 
| Path BL | 1.000 | 1.038 | 0.909 | 0.774 | 0.810 | 0.788 | 0.897 | 0.908 | 1.244 | 1.261 | 1.278 | 1.300 | 1.336 | 1.294 | 1.228 | 1.282 | 1.231 | 1.161 | 1.104 | 0.989 | 0.884 | 0.954 | 0.884 | 0.878 | 0.951 | 1.046 | 0.983 | 0.924 | 0.921 | 0.962 | 0.890 | 0.885 | 0.950 | 0.881 | 0.827 | 0.850 | 0.702 | 0.730 | 0.667 | 0.584 | 0.720 | 0.777 | 0.776 | 0.754 | 0.757 | 0.832 | 0.863 | 0.756 | 0.644 | 0.673 | 0.655 | 0.747 | 0.784 | 0.784 | 0.809 | 0.780 | 0.778 | 0.829 | 0.888 | 0.882 | 0.854 | 0.867 | 0.864 | 0.807 | 0.760 | 0.697 | 0.661 | 0.669 | 0.741 | 0.661 | 0.662 | 0.664 | 0.736 | 0.743 | 0.656 | 0.676 | 0.499 | 0.452 | 0.470 | 0.439 | 
| Path BM | 1.000 | 0.987 | 1.010 | 1.088 | 1.095 | 1.039 | 1.084 | 1.041 | 0.982 | 0.933 | 0.836 | 0.748 | 0.807 | 0.796 | 0.796 | 0.839 | 0.874 | 0.745 | 0.775 | 0.781 | 0.833 | 0.882 | 0.784 | 0.792 | 0.565 | 0.510 | 0.504 | 0.494 | 0.528 | 0.510 | 0.475 | 0.518 | 0.476 | 0.457 | 0.477 | 0.448 | 0.411 | 0.355 | 0.321 | 0.354 | 0.353 | 0.348 | 0.417 | 0.464 | 0.443 | 0.457 | 0.448 | 0.497 | 0.497 | 0.449 | 0.392 | 0.397 | 0.399 | 0.467 | 0.570 | 0.593 | 0.538 | 0.676 | 0.701 | 0.758 | 0.694 | 0.678 | 0.740 | 0.710 | 0.637 | 0.654 | 0.663 | 0.651 | 0.855 | 0.839 | 0.873 | 0.860 | 0.918 | 0.933 | 0.932 | 0.845 | 0.708 | 0.737 | 0.686 | 0.600 | 
| Path BN | 1.000 | 1.027 | 1.004 | 0.897 | 0.812 | 0.722 | 0.791 | 0.789 | 0.805 | 0.778 | 0.764 | 0.816 | 0.806 | 0.839 | 0.761 | 0.807 | 0.834 | 0.975 | 1.190 | 1.240 | 1.125 | 1.412 | 1.466 | 1.584 | 1.450 | 1.416 | 1.223 | 1.272 | 1.162 | 1.101 | 1.115 | 1.235 | 1.102 | 1.103 | 1.107 | 1.227 | 1.238 | 1.094 | 1.126 | 1.055 | 1.234 | 1.505 | 1.568 | 1.422 | 1.786 | 1.853 | 2.002 | 1.833 | 1.791 | 1.956 | 1.878 | 1.684 | 1.837 | 1.706 | 1.712 | 1.903 | 1.723 | 1.616 | 1.674 | 1.464 | 1.449 | 1.231 | 1.200 | 1.137 | 1.269 | 1.333 | 1.238 | 1.352 | 1.329 | 1.569 | 1.435 | 1.351 | 1.405 | 1.580 | 1.543 | 1.536 | 1.565 | 1.560 | 1.899 | 2.044 | 
| Path BO | 1.000 | 0.998 | 1.055 | 1.227 | 1.140 | 1.217 | 1.159 | 1.203 | 1.238 | 1.045 | 1.210 | 1.178 | 1.051 | 1.034 | 1.075 | 1.059 | 1.131 | 1.150 | 1.149 | 1.042 | 0.873 | 0.908 | 1.014 | 1.054 | 1.265 | 1.461 | 1.480 | 1.556 | 1.513 | 1.608 | 1.465 | 1.403 | 1.491 | 1.606 | 1.956 | 2.105 | 2.210 | 2.137 | 2.755 | 2.491 | 2.348 | 2.233 | 1.999 | 1.788 | 1.930 | 1.789 | 1.775 | 1.923 | 2.115 | 2.133 | 2.107 | 2.105 | 2.116 | 2.198 | 2.270 | 2.376 | 2.329 | 2.378 | 2.137 | 2.106 | 2.013 | 1.695 | 1.730 | 1.712 | 1.576 | 1.913 | 1.870 | 1.966 | 1.912 | 2.032 | 1.851 | 1.773 | 1.884 | 2.030 | 2.471 | 2.660 | 2.793 | 2.700 | 2.906 | 3.051 | 
| Path BP | 1.000 | 1.020 | 1.016 | 0.988 | 0.995 | 1.014 | 1.291 | 1.278 | 1.313 | 1.268 | 1.456 | 1.415 | 1.295 | 1.354 | 1.540 | 1.433 | 1.399 | 1.489 | 1.544 | 1.547 | 1.522 | 1.569 | 1.512 | 1.404 | 1.378 | 1.236 | 1.059 | 1.059 | 0.956 | 0.836 | 0.845 | 0.839 | 0.947 | 0.956 | 1.329 | 1.320 | 1.348 | 1.342 | 1.327 | 1.486 | 1.428 | 1.346 | 1.280 | 1.146 | 1.025 | 1.107 | 1.026 | 1.018 | 1.102 | 1.213 | 1.223 | 1.208 | 1.192 | 1.212 | 1.242 | 1.188 | 1.176 | 1.247 | 1.231 | 1.320 | 1.178 | 0.978 | 0.832 | 0.832 | 0.787 | 0.790 | 1.006 | 1.088 | 1.083 | 1.085 | 1.062 | 1.106 | 1.032 | 1.039 | 1.075 | 1.268 | 1.521 | 1.597 | 1.609 | 1.665 | 
| Path BQ | 1.000 | 1.020 | 1.016 | 0.988 | 0.995 | 1.014 | 1.291 | 1.278 | 1.313 | 1.268 | 1.456 | 1.415 | 1.295 | 1.270 | 1.268 | 1.332 | 1.236 | 1.241 | 1.379 | 1.248 | 1.171 | 1.213 | 1.061 | 1.050 | 0.892 | 0.869 | 0.894 | 0.923 | 0.966 | 0.947 | 0.967 | 0.869 | 0.856 | 0.818 | 0.689 | 0.704 | 0.696 | 0.641 | 0.728 | 0.708 | 0.693 | 0.770 | 0.770 | 0.695 | 0.607 | 0.614 | 0.610 | 0.688 | 0.695 | 0.966 | 0.960 | 0.980 | 1.161 | 1.175 | 1.217 | 1.271 | 1.226 | 1.242 | 1.220 | 1.601 | 1.571 | 1.635 | 1.610 | 1.720 | 1.748 | 1.588 | 1.688 | 1.624 | 1.516 | 1.691 | 1.669 | 1.790 | 1.778 | 1.748 | 1.760 | 1.798 | 2.332 | 2.318 | 2.377 | 2.403 | 
| Path BR | 1.000 | 1.074 | 1.057 | 1.043 | 1.067 | 1.150 | 1.157 | 1.098 | 1.146 | 1.101 | 1.038 | 0.987 | 0.884 | 0.845 | 0.942 | 0.930 | 0.997 | 0.991 | 0.974 | 0.981 | 1.002 | 1.300 | 1.292 | 1.304 | 1.317 | 1.453 | 1.424 | 1.329 | 1.483 | 1.464 | 1.569 | 1.559 | 1.533 | 1.543 | 1.577 | 2.045 | 2.033 | 2.052 | 2.073 | 2.030 | 2.052 | 3.026 | 2.851 | 3.005 | 2.929 | 3.181 | 2.835 | 2.765 | 2.716 | 2.954 | 3.544 | 4.231 | 4.197 | 4.359 | 4.502 | 4.713 | 4.620 | 4.716 | 4.238 | 4.176 | 3.992 | 3.362 | 3.432 | 3.395 | 3.127 | 2.909 | 3.240 | 3.311 | 3.394 | 3.430 | 3.432 | 3.527 | 3.468 | 4.637 | 4.501 | 4.525 | 4.637 | 4.813 | 4.962 | 4.481 | 
| Path BS | 1.000 | 0.929 | 1.014 | 0.997 | 1.177 | 1.077 | 1.014 | 1.054 | 1.186 | 1.158 | 1.153 | 1.175 | 1.171 | 1.093 | 1.090 | 1.112 | 1.074 | 1.056 | 1.127 | 1.114 | 1.189 | 1.066 | 0.976 | 0.744 | 0.739 | 0.710 | 0.652 | 0.650 | 0.607 | 0.572 | 0.504 | 0.476 | 0.487 | 0.446 | 0.484 | 0.496 | 0.530 | 0.534 | 0.546 | 0.516 | 0.481 | 0.485 | 0.502 | 0.592 | 0.710 | 0.745 | 0.698 | 0.802 | 0.888 | 0.967 | 0.872 | 0.862 | 0.954 | 0.918 | 0.856 | 0.956 | 0.943 | 1.011 | 1.005 | 0.988 | 0.995 | 1.016 | 1.318 | 1.310 | 1.322 | 1.510 | 1.843 | 1.920 | 1.742 | 2.187 | 2.269 | 2.452 | 2.245 | 2.193 | 2.395 | 2.299 | 2.062 | 2.303 | 2.169 | 2.286 | 
| Path BT | 1.000 | 1.194 | 1.209 | 1.151 | 1.463 | 1.299 | 1.466 | 1.379 | 1.374 | 1.435 | 1.327 | 1.321 | 1.417 | 1.311 | 1.218 | 1.301 | 1.239 | 1.286 | 1.323 | 1.117 | 1.293 | 1.260 | 1.123 | 1.112 | 1.097 | 0.956 | 0.965 | 0.922 | 0.913 | 0.968 | 0.956 | 1.025 | 0.915 | 0.759 | 0.646 | 0.646 | 0.611 | 0.608 | 0.610 | 0.652 | 0.642 | 0.770 | 0.857 | 0.818 | 0.844 | 0.827 | 0.918 | 0.918 | 0.828 | 0.724 | 0.732 | 0.727 | 0.793 | 0.814 | 0.751 | 0.837 | 0.855 | 0.876 | 0.886 | 0.886 | 0.911 | 0.895 | 1.197 | 1.162 | 1.168 | 1.082 | 1.173 | 1.204 | 1.287 | 1.296 | 1.324 | 1.314 | 1.301 | 1.605 | 1.732 | 1.730 | 1.682 | 1.688 | 1.659 | 1.771 | 
| Path BU | 1.000 | 0.957 | 0.949 | 0.954 | 0.920 | 0.854 | 0.833 | 0.655 | 0.689 | 0.707 | 0.653 | 0.727 | 0.743 | 0.719 | 0.765 | 0.795 | 0.822 | 0.718 | 0.737 | 0.763 | 0.789 | 0.842 | 0.750 | 0.717 | 0.464 | 0.494 | 0.520 | 0.532 | 0.631 | 0.788 | 0.795 | 0.779 | 0.884 | 0.903 | 0.916 | 0.903 | 0.901 | 0.947 | 0.879 | 0.815 | 0.630 | 0.679 | 0.751 | 0.769 | 0.777 | 1.146 | 1.080 | 1.138 | 1.109 | 1.205 | 1.073 | 1.047 | 1.094 | 1.081 | 1.154 | 1.035 | 0.948 | 0.722 | 0.717 | 0.689 | 0.675 | 0.693 | 0.732 | 0.751 | 0.698 | 0.737 | 0.762 | 0.735 | 0.790 | 0.777 | 0.767 | 0.785 | 0.846 | 0.851 | 0.807 | 0.843 | 0.809 | 0.763 | 0.771 | 1.058 | 
| Path BV | 1.000 | 1.170 | 1.427 | 1.487 | 1.349 | 1.693 | 1.757 | 1.899 | 1.738 | 1.698 | 1.854 | 1.780 | 1.597 | 1.787 | 2.173 | 2.286 | 2.443 | 2.245 | 2.201 | 2.354 | 2.272 | 2.117 | 2.308 | 2.123 | 2.036 | 2.126 | 2.113 | 2.223 | 2.376 | 2.183 | 2.141 | 2.289 | 2.210 | 2.059 | 2.244 | 2.064 | 1.980 | 2.067 | 1.942 | 1.927 | 1.935 | 2.016 | 2.029 | 1.997 | 2.075 | 2.038 | 2.622 | 2.660 | 2.685 | 2.734 | 2.849 | 2.918 | 2.861 | 2.834 | 2.830 | 3.183 | 3.001 | 2.900 | 3.083 | 3.202 | 3.307 | 3.462 | 3.394 | 3.465 | 3.114 | 4.605 | 4.338 | 4.573 | 4.457 | 4.840 | 4.314 | 4.208 | 4.133 | 4.495 | 5.393 | 6.438 | 6.520 | 6.207 | 6.430 | 7.113 | 
| Lower percentile | 1.000 | 0.884 | 0.856 | 0.793 | 0.810 | 0.733 | 0.737 | 0.670 | 0.688 | 0.690 | 0.653 | 0.704 | 0.680 | 0.694 | 0.681 | 0.707 | 0.665 | 0.649 | 0.620 | 0.644 | 0.605 | 0.617 | 0.560 | 0.537 | 0.489 | 0.501 | 0.513 | 0.499 | 0.490 | 0.453 | 0.475 | 0.479 | 0.450 | 0.448 | 0.478 | 0.405 | 0.418 | 0.421 | 0.399 | 0.389 | 0.354 | 0.357 | 0.348 | 0.366 | 0.367 | 0.364 | 0.335 | 0.322 | 0.308 | 0.308 | 0.327 | 0.322 | 0.351 | 0.332 | 0.344 | 0.341 | 0.333 | 0.306 | 0.282 | 0.259 | 0.252 | 0.275 | 0.273 | 0.352 | 0.360 | 0.358 | 0.345 | 0.302 | 0.306 | 0.298 | 0.278 | 0.304 | 0.273 | 0.284 | 0.279 | 0.265 | 0.290 | 0.286 | 0.281 | 0.296 | 
| Median | 1.000 | 1.020 | 1.016 | 1.026 | 1.061 | 1.066 | 1.087 | 1.076 | 1.137 | 1.120 | 1.130 | 1.103 | 1.103 | 1.063 | 1.083 | 1.045 | 1.046 | 1.053 | 1.105 | 1.036 | 1.077 | 1.105 | 1.109 | 1.075 | 1.108 | 1.126 | 1.127 | 1.177 | 1.137 | 1.098 | 1.151 | 1.151 | 1.113 | 1.097 | 1.190 | 1.224 | 1.223 | 1.265 | 1.252 | 1.197 | 1.255 | 1.306 | 1.361 | 1.440 | 1.415 | 1.309 | 1.356 | 1.371 | 1.219 | 1.209 | 1.260 | 1.243 | 1.329 | 1.402 | 1.430 | 1.394 | 1.297 | 1.246 | 1.225 | 1.287 | 1.218 | 1.214 | 1.219 | 1.245 | 1.288 | 1.325 | 1.333 | 1.393 | 1.379 | 1.573 | 1.502 | 1.478 | 1.484 | 1.634 | 1.727 | 1.682 | 1.712 | 1.718 | 1.705 | 1.926 | 
| Upper percentile | 1.000 | 1.190 | 1.426 | 1.475 | 1.523 | 1.660 | 1.683 | 1.870 | 1.817 | 1.729 | 1.878 | 1.869 | 2.014 | 2.139 | 2.165 | 2.293 | 2.372 | 2.272 | 2.519 | 3.022 | 3.106 | 2.875 | 3.280 | 3.095 | 3.179 | 3.397 | 3.775 | 3.667 | 3.603 | 3.739 | 3.975 | 4.002 | 3.941 | 4.052 | 3.888 | 3.656 | 3.579 | 3.493 | 4.276 | 4.340 | 4.374 | 4.908 | 5.027 | 4.982 | 5.503 | 5.540 | 4.995 | 5.122 | 4.760 | 4.690 | 4.620 | 4.608 | 5.506 | 5.750 | 5.744 | 6.659 | 6.772 | 7.486 | 7.126 | 7.574 | 7.053 | 7.098 | 6.925 | 7.057 | 6.412 | 6.680 | 6.720 | 6.892 | 6.703 | 6.292 | 6.454 | 6.582 | 7.725 | 7.668 | 8.317 | 7.339 | 7.356 | 7.469 | 6.423 | 7.031 | 
| Original history | 1.000 | 0.876 | 0.746 | 0.780 | 0.759 | 0.865 | 0.875 | 1.199 | 1.215 | 1.232 | 1.253 | 1.288 | 1.222 | 1.159 | 1.194 | 1.222 | 1.448 | 1.808 | 1.825 | 1.788 | 2.029 | 2.072 | 2.103 | 2.073 | 2.069 | 2.174 | 2.018 | 2.025 | 2.251 | 2.038 | 1.912 | 1.980 | 1.732 | 1.714 | 1.457 | 1.419 | 1.345 | 1.501 | 1.425 | 1.446 | 1.412 | 1.550 | 1.488 | 1.533 | 1.408 | 1.128 | 1.011 | 0.960 | 0.892 | 0.974 | 0.958 | 1.131 | 1.034 | 0.974 | 1.012 | 1.139 | 1.112 | 1.107 | 1.128 | 1.124 | 1.024 | 1.015 | 0.964 | 0.812 | 0.863 | 0.830 | 0.775 | 0.865 | 0.854 | 0.915 | 0.909 | 0.894 | 0.900 | 0.919 | 1.193 | 1.186 | 1.196 | 1.209 | 1.334 | 1.292 | 

**Chart data $\cdot$ Pool-return differences across rebuilt histories $\cdot$ 90-day blocks**

Summary of pool-return differences
| Statistic | LP/xyk difference, percentage points per year | 
| --- | --- |
| Minimum | −21.06 | 
| Lower quartile | −0.55 | 
| Median | +1.77 | 
| Upper quartile | +3.10 | 
| Maximum | +19.28 | 
| Original history | +1.65 | 

Proposal minus current LP/xyk, percentage points per year
| LP/xyk difference, percentage points per year | Pair kept in this analysis? | 
| --- | --- |
| +2.41 | Yes | 
| −9.80 | Yes | 
| −10.16 | Yes | 
| −0.64 | Yes | 
| undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| +0.93 | Yes | 
| −0.90 | Yes | 
| +1.58 | Yes | 
| +1.54 | Yes | 
| +5.32 | Yes | 
| −2.28 | Yes | 
| +1.74 | Yes | 
| +1.77 | Yes | 
| −7.44 | Yes | 
| +2.04 | Yes | 
| −7.20 | Yes | 
| +14.76 | Yes | 
| +2.67 | Yes | 
| +1.57 | Yes | 
| −7.63 | Yes | 
| −0.58 | Yes | 
| +1.82 | Yes | 
| +6.39 | Yes | 
| +10.37 | Yes | 
| +1.54 | Yes | 
| −6.82 | Yes | 
| +1.52 | Yes | 
| +1.94 | Yes | 
| +5.09 | Yes | 
| +11.97 | Yes | 
| −21.06 | Yes | 
| +3.13 | Yes | 
| +2.19 | Yes | 
| +3.26 | Yes | 
| +17.01 | Yes | 
| +1.64 | Yes | 
| +8.92 | Yes | 
| +1.71 | Yes | 
| +1.98 | Yes | 
| +3.07 | Yes | 
| +3.38 | Yes | 
| +1.77 | Yes | 
| +1.59 | Yes | 
| +1.86 | Yes | 
| −4.97 | Yes | 
| +1.90 | Yes | 
| −0.52 | Yes | 
| +19.28 | Yes | 

**Chart data $\cdot$ Prices on rebuilt histories $\cdot$ 30-day blocks**

Price divided by starting price, sampled weekly
| Rebuilt history | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | 
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Path AA | 1.000 | 0.862 | 0.874 | 0.982 | 1.014 | 0.947 | 0.945 | 0.993 | 0.921 | 0.846 | 0.755 | 0.627 | 0.533 | 0.513 | 0.504 | 0.596 | 0.545 | 0.513 | 0.568 | 0.618 | 0.558 | 0.551 | 0.492 | 0.618 | 0.641 | 0.693 | 0.563 | 0.563 | 0.578 | 0.566 | 0.501 | 0.490 | 0.517 | 0.468 | 0.490 | 0.451 | 0.458 | 0.447 | 0.491 | 0.471 | 0.447 | 0.454 | 0.443 | 0.430 | 0.456 | 0.471 | 0.551 | 0.672 | 0.624 | 0.586 | 0.602 | 0.497 | 0.501 | 0.489 | 0.534 | 0.513 | 0.461 | 0.462 | 0.419 | 0.444 | 0.468 | 0.507 | 0.558 | 0.563 | 0.556 | 0.581 | 0.600 | 0.628 | 0.616 | 0.713 | 0.743 | 0.674 | 0.846 | 0.978 | 0.927 | 0.837 | 0.937 | 0.795 | 0.707 | 0.676 | 
| Path AB | 1.000 | 1.007 | 1.419 | 1.359 | 1.390 | 1.473 | 1.454 | 1.334 | 1.461 | 1.142 | 1.231 | 1.361 | 1.393 | 1.384 | 1.415 | 1.417 | 1.389 | 1.365 | 1.407 | 1.538 | 1.657 | 1.586 | 1.522 | 1.413 | 1.378 | 1.083 | 1.131 | 1.119 | 1.150 | 1.110 | 1.344 | 1.040 | 1.121 | 1.239 | 1.268 | 1.294 | 1.332 | 1.228 | 0.950 | 0.995 | 0.975 | 1.000 | 1.058 | 1.152 | 1.185 | 1.001 | 1.159 | 1.129 | 1.133 | 1.062 | 1.032 | 0.985 | 0.972 | 0.937 | 0.870 | 0.848 | 0.761 | 0.766 | 0.753 | 0.783 | 0.794 | 0.812 | 0.832 | 0.841 | 0.842 | 0.796 | 0.515 | 0.549 | 0.550 | 0.565 | 0.612 | 0.673 | 0.678 | 0.680 | 0.666 | 0.680 | 0.611 | 0.602 | 0.625 | 0.547 | 
| Path AC | 1.000 | 1.010 | 1.455 | 1.422 | 1.495 | 1.685 | 1.535 | 1.470 | 1.562 | 1.533 | 1.610 | 1.495 | 1.500 | 1.718 | 1.623 | 1.847 | 1.846 | 1.864 | 2.327 | 2.350 | 2.302 | 2.612 | 2.609 | 2.542 | 2.409 | 2.688 | 3.003 | 2.759 | 2.705 | 2.893 | 2.870 | 2.597 | 2.719 | 2.830 | 2.492 | 2.572 | 2.630 | 2.410 | 2.614 | 2.724 | 2.962 | 3.554 | 4.244 | 4.581 | 4.712 | 4.650 | 4.645 | 4.664 | 4.808 | 5.255 | 5.663 | 5.419 | 4.800 | 5.019 | 4.882 | 5.563 | 5.697 | 6.041 | 5.963 | 6.396 | 5.760 | 5.283 | 4.564 | 4.131 | 4.410 | 3.582 | 3.620 | 3.597 | 4.059 | 3.859 | 3.789 | 3.398 | 2.995 | 3.207 | 3.090 | 2.869 | 2.817 | 2.526 | 2.698 | 2.400 | 
| Path AD | 1.000 | 0.893 | 0.831 | 0.785 | 0.893 | 0.907 | 1.089 | 1.257 | 1.315 | 1.220 | 1.256 | 1.158 | 0.895 | 1.049 | 1.081 | 1.113 | 1.026 | 0.793 | 0.795 | 0.779 | 0.766 | 0.816 | 0.849 | 0.806 | 0.679 | 0.722 | 0.628 | 0.570 | 0.604 | 0.625 | 0.715 | 0.625 | 0.642 | 0.664 | 0.686 | 0.943 | 0.936 | 0.956 | 0.952 | 0.914 | 0.913 | 0.864 | 0.860 | 0.888 | 0.896 | 0.913 | 0.951 | 0.974 | 0.973 | 1.094 | 1.032 | 0.997 | 1.079 | 1.055 | 1.113 | 1.007 | 1.073 | 1.087 | 1.203 | 1.074 | 1.099 | 1.224 | 1.250 | 1.282 | 1.295 | 1.253 | 1.248 | 1.303 | 1.206 | 1.302 | 1.278 | 1.442 | 1.452 | 1.883 | 2.001 | 1.925 | 1.797 | 2.004 | 1.765 | 1.685 | 
| Path AE | 1.000 | 1.264 | 1.303 | 1.177 | 1.430 | 1.272 | 1.216 | 0.787 | 0.839 | 0.842 | 0.896 | 0.891 | 0.853 | 0.879 | 0.893 | 0.875 | 0.768 | 0.716 | 0.700 | 0.738 | 0.668 | 0.699 | 0.762 | 0.754 | 0.775 | 0.748 | 0.840 | 0.876 | 0.897 | 0.896 | 0.905 | 0.923 | 0.919 | 0.894 | 0.900 | 0.822 | 0.803 | 0.877 | 0.842 | 0.797 | 0.759 | 0.965 | 0.856 | 0.965 | 0.958 | 0.921 | 0.902 | 0.925 | 0.932 | 0.965 | 1.138 | 1.364 | 1.514 | 1.636 | 1.497 | 1.463 | 1.953 | 1.896 | 1.906 | 1.953 | 1.993 | 1.930 | 1.825 | 1.748 | 1.508 | 1.708 | 1.518 | 1.533 | 1.094 | 1.149 | 1.196 | 1.054 | 1.006 | 1.116 | 1.246 | 1.230 | 1.318 | 1.310 | 1.571 | 1.876 | 
| Path AF | 1.000 | 1.000 | 1.054 | 1.099 | 0.936 | 1.072 | 1.079 | 1.521 | 1.457 | 1.610 | 1.568 | 1.398 | 1.384 | 1.473 | 1.414 | 1.457 | 1.339 | 1.072 | 1.016 | 1.135 | 1.077 | 1.093 | 1.080 | 1.297 | 1.498 | 1.566 | 1.439 | 1.498 | 1.398 | 1.408 | 1.612 | 1.785 | 1.593 | 1.595 | 1.599 | 1.672 | 1.659 | 1.607 | 1.631 | 1.652 | 1.856 | 1.916 | 2.438 | 2.526 | 2.356 | 2.373 | 2.456 | 2.897 | 3.350 | 3.263 | 2.909 | 2.881 | 3.793 | 3.721 | 3.872 | 3.814 | 3.467 | 3.380 | 2.965 | 3.154 | 3.273 | 2.969 | 3.150 | 3.254 | 3.807 | 3.940 | 3.936 | 3.952 | 3.705 | 3.579 | 4.078 | 4.124 | 5.654 | 5.921 | 5.847 | 5.364 | 5.872 | 5.602 | 5.271 | 5.251 | 
| Path AG | 1.000 | 1.094 | 1.017 | 0.959 | 1.081 | 1.089 | 1.534 | 1.469 | 1.502 | 1.540 | 1.196 | 1.281 | 1.326 | 1.149 | 1.081 | 1.077 | 1.124 | 1.040 | 1.078 | 1.113 | 1.165 | 1.142 | 1.330 | 1.380 | 1.491 | 1.365 | 1.371 | 1.491 | 1.789 | 2.136 | 2.158 | 2.332 | 2.134 | 2.085 | 2.277 | 1.709 | 1.545 | 1.556 | 1.637 | 1.557 | 1.315 | 1.522 | 1.483 | 1.350 | 1.417 | 1.370 | 1.767 | 1.613 | 1.786 | 1.944 | 1.754 | 1.733 | 1.560 | 1.429 | 1.089 | 1.081 | 0.983 | 1.046 | 1.087 | 1.123 | 1.004 | 1.018 | 0.999 | 1.312 | 1.288 | 1.356 | 1.365 | 1.343 | 1.395 | 1.373 | 1.371 | 1.244 | 1.042 | 1.044 | 1.043 | 1.045 | 0.948 | 1.006 | 1.034 | 0.874 | 
| Path AH | 1.000 | 1.067 | 1.092 | 1.093 | 1.071 | 1.475 | 1.494 | 1.515 | 1.541 | 1.679 | 1.764 | 1.652 | 1.899 | 2.530 | 2.310 | 2.401 | 2.371 | 2.317 | 2.323 | 2.576 | 2.598 | 2.297 | 2.188 | 2.171 | 2.352 | 2.587 | 2.464 | 2.210 | 2.468 | 2.061 | 2.142 | 2.153 | 2.076 | 1.928 | 1.880 | 1.848 | 1.925 | 1.796 | 1.809 | 1.892 | 2.666 | 2.555 | 2.612 | 2.697 | 2.893 | 2.581 | 2.143 | 1.824 | 1.594 | 1.637 | 1.693 | 1.751 | 1.697 | 1.767 | 1.649 | 1.661 | 1.817 | 1.663 | 1.625 | 1.774 | 1.620 | 1.546 | 1.481 | 1.589 | 1.809 | 1.749 | 1.796 | 2.044 | 1.902 | 1.681 | 1.733 | 1.772 | 2.101 | 2.639 | 2.041 | 2.200 | 2.433 | 2.490 | 2.552 | 2.649 | 
| Path AI | 1.000 | 1.005 | 0.969 | 0.900 | 0.878 | 0.916 | 0.818 | 0.819 | 0.821 | 0.922 | 0.806 | 0.798 | 0.678 | 0.632 | 0.533 | 0.617 | 0.601 | 0.536 | 0.539 | 0.552 | 0.573 | 0.591 | 0.575 | 0.602 | 0.590 | 0.603 | 0.588 | 0.575 | 0.607 | 0.549 | 0.521 | 0.472 | 0.465 | 0.432 | 0.463 | 0.480 | 0.501 | 0.481 | 0.454 | 0.411 | 0.462 | 0.436 | 0.421 | 0.448 | 0.402 | 0.397 | 0.379 | 0.319 | 0.329 | 0.360 | 0.388 | 0.371 | 0.391 | 0.361 | 0.279 | 0.301 | 0.291 | 0.299 | 0.309 | 0.320 | 0.351 | 0.341 | 0.344 | 0.350 | 0.446 | 0.491 | 0.429 | 0.440 | 0.455 | 0.475 | 0.489 | 0.449 | 0.360 | 0.310 | 0.341 | 0.344 | 0.340 | 0.339 | 0.376 | 0.409 | 
| Path AJ | 1.000 | 1.122 | 1.154 | 1.334 | 1.686 | 1.750 | 1.992 | 1.990 | 2.010 | 3.013 | 2.966 | 2.927 | 2.994 | 3.118 | 2.981 | 2.953 | 3.131 | 3.090 | 3.985 | 3.638 | 3.781 | 3.734 | 3.649 | 3.598 | 3.591 | 3.772 | 3.825 | 4.120 | 5.017 | 5.399 | 5.639 | 6.406 | 6.482 | 6.716 | 7.012 | 6.185 | 6.094 | 5.825 | 4.906 | 5.053 | 4.862 | 4.538 | 5.062 | 5.104 | 4.682 | 4.044 | 3.661 | 3.908 | 4.121 | 4.016 | 4.362 | 3.887 | 3.794 | 4.037 | 4.016 | 3.842 | 4.021 | 3.735 | 4.079 | 4.010 | 4.478 | 4.474 | 4.518 | 6.510 | 6.364 | 7.274 | 7.252 | 7.403 | 7.150 | 7.821 | 7.638 | 7.604 | 7.747 | 7.724 | 8.004 | 8.357 | 8.060 | 8.168 | 8.294 | 8.097 | 
| Path AK | 1.000 | 1.039 | 1.073 | 1.123 | 1.101 | 1.106 | 1.109 | 1.006 | 1.067 | 0.974 | 0.920 | 1.047 | 1.046 | 1.131 | 1.072 | 1.197 | 1.136 | 1.153 | 1.167 | 1.292 | 1.154 | 1.155 | 1.118 | 1.649 | 1.553 | 1.637 | 1.530 | 1.635 | 1.503 | 1.473 | 1.620 | 1.636 | 1.167 | 1.055 | 1.063 | 1.132 | 1.290 | 1.519 | 1.620 | 1.846 | 1.887 | 1.934 | 1.954 | 2.100 | 2.121 | 2.077 | 2.358 | 2.408 | 2.441 | 2.464 | 2.509 | 2.615 | 2.683 | 2.671 | 2.647 | 2.643 | 2.678 | 2.562 | 2.653 | 2.935 | 3.023 | 3.003 | 3.067 | 3.053 | 3.018 | 3.315 | 3.440 | 3.013 | 2.567 | 2.882 | 3.102 | 3.257 | 3.149 | 3.518 | 3.755 | 3.368 | 3.084 | 2.351 | 2.575 | 2.567 | 
| Path AL | 1.000 | 1.001 | 1.004 | 1.113 | 1.123 | 1.285 | 1.290 | 1.344 | 1.353 | 1.379 | 1.260 | 1.194 | 1.209 | 1.199 | 1.365 | 1.364 | 1.377 | 1.984 | 1.934 | 1.926 | 1.962 | 1.956 | 1.934 | 2.144 | 2.163 | 1.912 | 1.886 | 1.848 | 2.052 | 2.053 | 1.878 | 1.694 | 1.481 | 1.497 | 1.487 | 1.553 | 1.373 | 1.414 | 1.043 | 0.984 | 0.896 | 0.889 | 0.844 | 0.648 | 0.687 | 0.610 | 0.616 | 0.440 | 0.341 | 0.365 | 0.379 | 0.342 | 0.359 | 0.342 | 0.434 | 0.386 | 0.438 | 0.439 | 0.398 | 0.422 | 0.431 | 0.423 | 0.380 | 0.335 | 0.366 | 0.491 | 0.497 | 0.504 | 0.513 | 0.453 | 0.410 | 0.365 | 0.400 | 0.424 | 0.427 | 0.436 | 0.565 | 0.562 | 0.538 | 0.534 | 
| Path AM | 1.000 | 0.999 | 0.892 | 0.830 | 0.784 | 0.783 | 0.785 | 0.712 | 0.755 | 0.737 | 0.817 | 0.729 | 0.730 | 0.632 | 0.638 | 0.634 | 0.716 | 0.723 | 0.705 | 0.692 | 0.753 | 0.903 | 1.023 | 1.005 | 1.319 | 1.294 | 1.294 | 1.355 | 1.328 | 1.356 | 1.268 | 1.275 | 1.210 | 1.263 | 1.213 | 1.299 | 1.389 | 1.276 | 1.251 | 1.246 | 1.191 | 1.003 | 1.024 | 1.026 | 1.082 | 1.054 | 1.145 | 1.020 | 1.085 | 1.128 | 1.165 | 1.018 | 1.062 | 0.952 | 1.063 | 0.888 | 1.028 | 0.873 | 0.873 | 0.896 | 0.885 | 0.872 | 1.045 | 1.162 | 1.109 | 0.998 | 1.127 | 1.060 | 1.056 | 1.139 | 1.680 | 1.582 | 1.668 | 1.563 | 1.655 | 1.472 | 1.486 | 1.060 | 0.990 | 1.104 | 
| Path AN | 1.000 | 1.114 | 1.138 | 1.167 | 1.179 | 1.130 | 1.175 | 1.202 | 1.202 | 1.285 | 1.300 | 1.782 | 1.805 | 1.802 | 1.825 | 1.737 | 2.208 | 1.960 | 2.004 | 2.376 | 2.966 | 2.995 | 3.037 | 3.022 | 2.987 | 3.032 | 2.938 | 2.949 | 3.239 | 3.362 | 2.863 | 2.941 | 2.839 | 3.259 | 3.170 | 3.201 | 3.180 | 3.127 | 3.148 | 3.143 | 3.270 | 3.343 | 3.344 | 3.551 | 3.780 | 3.759 | 3.597 | 3.724 | 3.872 | 4.649 | 5.368 | 5.613 | 5.726 | 5.859 | 6.313 | 6.351 | 6.187 | 5.782 | 5.446 | 4.798 | 4.443 | 4.429 | 4.032 | 4.000 | 3.799 | 4.221 | 4.873 | 5.095 | 5.031 | 4.684 | 5.231 | 4.368 | 4.534 | 4.728 | 4.646 | 4.960 | 4.901 | 5.231 | 4.867 | 4.752 | 
| Path AO | 1.000 | 1.050 | 1.015 | 1.309 | 1.195 | 1.452 | 1.496 | 1.351 | 1.643 | 1.971 | 1.896 | 1.770 | 1.974 | 2.220 | 2.083 | 2.157 | 1.886 | 1.868 | 1.934 | 2.140 | 2.201 | 2.172 | 2.138 | 2.168 | 2.435 | 2.514 | 2.296 | 2.132 | 2.197 | 2.402 | 2.473 | 2.253 | 2.158 | 2.294 | 2.471 | 2.636 | 2.965 | 2.895 | 2.882 | 2.825 | 2.801 | 2.815 | 2.715 | 2.579 | 2.408 | 2.686 | 2.652 | 2.843 | 2.925 | 2.697 | 2.086 | 2.249 | 2.172 | 2.183 | 2.104 | 1.954 | 1.839 | 1.758 | 1.741 | 1.847 | 1.852 | 1.802 | 1.814 | 1.848 | 2.353 | 2.198 | 2.497 | 2.527 | 2.618 | 2.476 | 2.485 | 2.761 | 2.500 | 2.238 | 2.399 | 2.381 | 2.307 | 2.341 | 2.401 | 2.426 | 
| Path AP | 1.000 | 0.975 | 0.855 | 0.909 | 0.945 | 0.978 | 0.965 | 0.964 | 0.968 | 1.046 | 1.071 | 1.082 | 1.596 | 1.485 | 1.461 | 1.518 | 1.491 | 1.919 | 2.034 | 2.008 | 2.154 | 1.921 | 1.985 | 2.005 | 2.213 | 2.143 | 2.185 | 2.234 | 2.047 | 2.221 | 2.318 | 2.027 | 2.187 | 2.223 | 2.279 | 1.987 | 1.906 | 1.990 | 1.870 | 1.569 | 1.742 | 1.743 | 1.573 | 1.595 | 1.594 | 1.570 | 1.881 | 2.093 | 2.325 | 2.326 | 2.099 | 1.835 | 2.004 | 1.841 | 1.806 | 1.931 | 1.906 | 1.709 | 1.565 | 1.193 | 1.137 | 1.173 | 1.130 | 1.129 | 1.202 | 1.284 | 1.252 | 1.359 | 1.212 | 1.175 | 1.134 | 1.302 | 1.267 | 1.264 | 1.304 | 1.660 | 1.796 | 1.789 | 1.564 | 1.688 | 
| Path AQ | 1.000 | 1.107 | 1.205 | 1.087 | 1.074 | 1.027 | 0.995 | 1.010 | 1.006 | 1.031 | 0.939 | 0.900 | 0.956 | 0.938 | 0.945 | 0.962 | 1.226 | 1.214 | 1.280 | 1.247 | 1.354 | 1.207 | 1.238 | 1.239 | 1.214 | 1.194 | 1.277 | 1.255 | 1.482 | 1.355 | 1.246 | 1.410 | 1.415 | 1.475 | 1.484 | 1.998 | 2.027 | 2.046 | 2.084 | 2.131 | 1.884 | 1.939 | 1.431 | 1.383 | 1.441 | 1.307 | 1.641 | 1.703 | 1.699 | 1.505 | 1.506 | 1.586 | 1.493 | 1.531 | 1.343 | 1.340 | 1.267 | 1.494 | 1.792 | 1.882 | 1.851 | 1.983 | 2.053 | 1.856 | 2.100 | 2.086 | 2.061 | 2.092 | 1.830 | 1.966 | 1.884 | 2.020 | 2.301 | 2.470 | 2.240 | 2.813 | 2.919 | 3.154 | 2.960 | 3.065 | 
| Path AR | 1.000 | 0.957 | 0.949 | 0.954 | 0.920 | 0.849 | 0.836 | 0.777 | 0.832 | 0.860 | 0.922 | 0.915 | 0.886 | 0.936 | 0.932 | 0.921 | 0.935 | 0.818 | 0.815 | 0.851 | 0.787 | 0.783 | 0.922 | 0.959 | 0.990 | 0.865 | 0.955 | 0.972 | 1.014 | 1.038 | 1.066 | 0.920 | 0.932 | 1.048 | 1.081 | 0.974 | 1.020 | 1.062 | 0.935 | 0.915 | 0.914 | 0.913 | 0.915 | 0.914 | 0.913 | 0.816 | 0.759 | 0.717 | 0.731 | 0.728 | 0.708 | 0.713 | 0.711 | 0.760 | 0.734 | 0.684 | 0.733 | 0.721 | 0.744 | 0.717 | 0.704 | 0.691 | 0.780 | 0.785 | 1.106 | 0.973 | 0.922 | 0.951 | 0.973 | 1.111 | 1.119 | 1.101 | 1.144 | 1.112 | 1.125 | 1.542 | 1.562 | 1.584 | 1.582 | 1.496 | 
| Path AS | 1.000 | 0.958 | 0.980 | 0.979 | 0.977 | 0.978 | 1.034 | 1.060 | 0.985 | 1.156 | 1.216 | 1.300 | 1.194 | 1.232 | 1.210 | 1.292 | 1.277 | 1.363 | 1.564 | 1.521 | 1.392 | 1.375 | 1.138 | 1.272 | 1.321 | 1.587 | 1.946 | 2.017 | 2.021 | 1.988 | 2.175 | 2.241 | 2.306 | 2.126 | 1.645 | 1.748 | 1.745 | 1.833 | 1.702 | 1.572 | 1.442 | 1.245 | 1.127 | 1.389 | 1.448 | 1.235 | 1.284 | 1.295 | 1.156 | 1.157 | 1.160 | 1.286 | 1.215 | 1.085 | 1.009 | 0.953 | 0.930 | 0.994 | 1.001 | 1.023 | 0.991 | 0.969 | 1.018 | 0.990 | 1.052 | 0.904 | 0.959 | 0.991 | 1.159 | 1.231 | 1.387 | 1.481 | 1.511 | 1.541 | 1.709 | 1.724 | 1.524 | 1.569 | 1.580 | 1.610 | 
| Path AT | 1.000 | 0.942 | 0.979 | 1.101 | 1.075 | 1.098 | 1.125 | 1.076 | 1.066 | 1.060 | 1.101 | 1.137 | 1.190 | 1.153 | 0.957 | 0.815 | 0.815 | 0.770 | 0.823 | 0.738 | 0.676 | 0.515 | 0.519 | 0.553 | 0.549 | 0.577 | 0.519 | 0.522 | 0.533 | 0.692 | 0.675 | 0.636 | 0.560 | 0.529 | 0.541 | 0.614 | 0.617 | 0.642 | 0.647 | 0.661 | 0.570 | 0.578 | 0.650 | 0.709 | 0.633 | 0.633 | 0.635 | 0.704 | 0.857 | 0.922 | 0.969 | 0.936 | 0.965 | 0.897 | 0.848 | 0.965 | 0.891 | 0.852 | 0.551 | 0.588 | 0.591 | 0.617 | 0.571 | 0.568 | 0.610 | 0.580 | 0.570 | 0.511 | 0.450 | 0.482 | 0.492 | 0.490 | 0.476 | 0.499 | 0.577 | 0.729 | 0.752 | 0.679 | 0.605 | 0.590 | 
| Path AU | 1.000 | 0.974 | 0.923 | 1.031 | 0.978 | 1.218 | 1.256 | 1.134 | 1.379 | 1.590 | 1.504 | 1.497 | 1.501 | 1.570 | 1.675 | 1.656 | 1.767 | 1.585 | 1.435 | 1.276 | 1.398 | 1.393 | 1.373 | 1.433 | 1.377 | 1.298 | 1.253 | 1.280 | 1.660 | 1.650 | 1.679 | 1.599 | 2.032 | 1.804 | 2.037 | 2.013 | 2.232 | 2.251 | 1.990 | 2.134 | 2.225 | 1.896 | 1.973 | 1.829 | 1.811 | 1.539 | 1.499 | 1.421 | 1.206 | 1.206 | 1.239 | 1.212 | 1.196 | 1.196 | 1.260 | 1.314 | 1.293 | 1.467 | 1.498 | 1.520 | 1.531 | 1.790 | 2.185 | 2.276 | 2.065 | 2.163 | 2.142 | 2.114 | 1.841 | 2.062 | 2.033 | 2.029 | 2.131 | 2.027 | 2.204 | 2.645 | 3.158 | 3.198 | 3.232 | 4.767 | 
| Path AV | 1.000 | 1.022 | 1.325 | 1.317 | 1.329 | 1.325 | 1.253 | 1.248 | 1.251 | 1.299 | 1.005 | 1.084 | 1.198 | 1.185 | 1.214 | 1.161 | 1.150 | 1.219 | 1.268 | 1.426 | 1.392 | 1.386 | 1.409 | 1.395 | 1.377 | 1.199 | 1.453 | 1.329 | 1.251 | 1.301 | 1.321 | 1.423 | 1.432 | 1.359 | 1.418 | 1.428 | 1.356 | 1.285 | 1.324 | 1.400 | 1.547 | 1.584 | 1.601 | 2.425 | 2.479 | 2.480 | 2.556 | 2.464 | 2.576 | 2.544 | 2.334 | 2.555 | 2.376 | 2.333 | 2.537 | 3.044 | 3.014 | 3.228 | 3.343 | 3.022 | 3.261 | 3.384 | 3.481 | 2.940 | 3.403 | 3.261 | 3.605 | 3.690 | 3.730 | 4.985 | 5.096 | 5.098 | 5.256 | 5.368 | 5.731 | 5.862 | 5.869 | 5.751 | 5.348 | 5.726 | 
| Path AW | 1.000 | 0.940 | 0.937 | 0.978 | 0.905 | 1.033 | 1.020 | 1.093 | 1.086 | 1.099 | 1.443 | 1.416 | 1.473 | 1.563 | 1.663 | 1.724 | 1.728 | 1.700 | 1.731 | 1.804 | 1.848 | 1.846 | 1.791 | 1.671 | 1.683 | 1.742 | 1.754 | 1.939 | 1.985 | 2.006 | 2.912 | 2.988 | 3.193 | 3.216 | 3.285 | 3.322 | 3.616 | 3.263 | 3.223 | 2.659 | 2.408 | 2.371 | 2.205 | 2.265 | 2.158 | 2.239 | 2.304 | 1.946 | 1.608 | 1.672 | 1.528 | 1.447 | 1.576 | 1.692 | 1.569 | 1.473 | 1.581 | 1.562 | 1.667 | 1.495 | 1.508 | 1.430 | 1.290 | 1.444 | 1.225 | 1.197 | 1.284 | 1.191 | 1.118 | 1.578 | 1.567 | 1.601 | 1.593 | 1.531 | 1.424 | 1.345 | 1.531 | 1.530 | 1.470 | 1.441 | 
| Path AX | 1.000 | 1.063 | 0.968 | 0.927 | 0.986 | 1.017 | 0.997 | 1.018 | 0.915 | 0.869 | 0.868 | 0.870 | 0.789 | 0.762 | 0.786 | 0.859 | 0.925 | 0.886 | 0.939 | 0.927 | 0.994 | 0.887 | 0.831 | 0.837 | 0.866 | 1.022 | 1.138 | 1.130 | 1.275 | 1.288 | 1.892 | 1.849 | 1.951 | 1.765 | 1.848 | 2.067 | 1.984 | 1.780 | 1.987 | 1.878 | 1.476 | 1.554 | 1.595 | 1.434 | 1.258 | 1.255 | 1.111 | 1.112 | 1.123 | 1.124 | 1.155 | 1.136 | 1.146 | 1.165 | 1.194 | 1.142 | 1.053 | 1.137 | 1.041 | 1.017 | 1.095 | 1.145 | 1.131 | 1.038 | 1.136 | 1.046 | 1.087 | 1.068 | 1.374 | 1.501 | 1.540 | 1.646 | 1.658 | 1.613 | 1.687 | 1.666 | 1.528 | 1.673 | 1.868 | 1.844 | 
| Path AY | 1.000 | 1.031 | 0.994 | 0.922 | 0.906 | 0.861 | 0.769 | 0.696 | 0.619 | 0.623 | 0.614 | 0.587 | 0.494 | 0.496 | 0.490 | 0.489 | 0.482 | 0.577 | 0.505 | 0.518 | 0.536 | 0.554 | 0.547 | 0.523 | 0.406 | 0.435 | 0.454 | 0.447 | 0.477 | 0.485 | 0.473 | 0.427 | 0.478 | 0.406 | 0.406 | 0.401 | 0.460 | 0.447 | 0.409 | 0.384 | 0.367 | 0.237 | 0.253 | 0.257 | 0.233 | 0.249 | 0.254 | 0.255 | 0.259 | 0.255 | 0.254 | 0.267 | 0.227 | 0.193 | 0.193 | 0.183 | 0.169 | 0.185 | 0.184 | 0.188 | 0.172 | 0.149 | 0.151 | 0.169 | 0.175 | 0.197 | 0.235 | 0.238 | 0.227 | 0.278 | 0.255 | 0.250 | 0.268 | 0.255 | 0.243 | 0.252 | 0.259 | 0.219 | 0.221 | 0.230 | 
| Path AZ | 1.000 | 1.095 | 1.044 | 1.001 | 1.073 | 0.955 | 0.841 | 0.920 | 0.856 | 0.809 | 0.817 | 1.135 | 1.128 | 1.127 | 1.140 | 1.563 | 1.584 | 1.606 | 1.724 | 1.710 | 1.657 | 1.681 | 1.687 | 1.784 | 2.074 | 1.928 | 1.931 | 1.725 | 1.562 | 1.388 | 1.588 | 1.538 | 1.454 | 1.393 | 1.201 | 1.134 | 0.941 | 0.801 | 0.801 | 0.754 | 0.774 | 0.714 | 0.795 | 0.749 | 0.748 | 0.747 | 0.749 | 0.680 | 0.501 | 0.454 | 0.447 | 0.416 | 0.468 | 0.444 | 0.421 | 0.434 | 0.429 | 0.447 | 0.499 | 0.519 | 0.494 | 0.536 | 0.550 | 0.587 | 0.592 | 0.513 | 0.496 | 0.527 | 0.547 | 0.551 | 0.551 | 0.521 | 0.518 | 0.596 | 0.726 | 0.781 | 0.820 | 0.793 | 0.825 | 0.922 | 
| Path BA | 1.000 | 1.037 | 1.039 | 1.022 | 1.054 | 1.065 | 1.105 | 1.139 | 1.172 | 1.105 | 1.135 | 1.292 | 1.202 | 1.084 | 1.063 | 1.106 | 1.090 | 1.164 | 1.254 | 1.200 | 1.190 | 1.196 | 1.133 | 1.377 | 1.449 | 1.549 | 1.553 | 1.504 | 1.423 | 1.363 | 1.181 | 1.067 | 1.297 | 1.364 | 1.458 | 1.298 | 1.286 | 1.363 | 1.345 | 1.492 | 1.468 | 1.962 | 1.905 | 1.804 | 1.806 | 1.811 | 2.008 | 2.025 | 2.111 | 2.029 | 1.913 | 1.819 | 1.866 | 1.542 | 1.603 | 1.465 | 1.283 | 1.296 | 1.912 | 1.801 | 1.763 | 1.742 | 1.586 | 1.556 | 1.756 | 1.810 | 1.866 | 1.799 | 1.796 | 1.759 | 1.760 | 1.854 | 1.933 | 1.837 | 1.623 | 1.671 | 1.234 | 1.117 | 1.078 | 1.237 | 
| Path BB | 1.000 | 1.052 | 1.125 | 1.033 | 1.013 | 1.011 | 1.081 | 1.043 | 0.972 | 0.917 | 0.832 | 0.883 | 0.912 | 1.061 | 1.050 | 1.079 | 1.042 | 1.196 | 1.229 | 1.209 | 1.616 | 1.569 | 1.516 | 1.565 | 1.639 | 1.606 | 1.903 | 2.117 | 2.020 | 2.085 | 2.018 | 2.181 | 1.996 | 1.950 | 2.130 | 2.072 | 2.039 | 2.102 | 2.026 | 2.167 | 2.126 | 2.212 | 2.179 | 2.207 | 2.191 | 2.106 | 2.064 | 2.116 | 1.981 | 2.277 | 2.521 | 2.744 | 3.642 | 3.535 | 3.554 | 3.642 | 3.507 | 3.702 | 3.349 | 3.506 | 3.599 | 2.794 | 2.992 | 3.099 | 2.801 | 2.467 | 2.102 | 2.198 | 2.138 | 2.450 | 2.400 | 2.107 | 1.963 | 1.837 | 1.786 | 1.898 | 1.729 | 1.656 | 1.809 | 1.736 | 
| Path BC | 1.000 | 1.081 | 0.989 | 0.966 | 1.055 | 1.144 | 1.154 | 1.140 | 1.139 | 1.191 | 1.279 | 1.259 | 1.243 | 1.001 | 1.067 | 1.068 | 1.111 | 1.135 | 1.060 | 1.183 | 1.168 | 1.252 | 1.271 | 1.242 | 1.356 | 1.302 | 1.168 | 1.043 | 0.944 | 0.839 | 0.902 | 0.821 | 0.815 | 0.774 | 0.652 | 0.651 | 0.658 | 0.658 | 0.677 | 0.715 | 0.730 | 0.705 | 0.693 | 0.715 | 0.647 | 0.732 | 0.735 | 0.765 | 0.782 | 0.802 | 0.810 | 0.811 | 0.804 | 0.720 | 0.644 | 0.695 | 0.706 | 0.724 | 0.765 | 0.785 | 0.759 | 0.805 | 0.794 | 0.852 | 0.760 | 0.774 | 0.815 | 0.850 | 0.725 | 0.825 | 0.792 | 0.710 | 0.793 | 0.766 | 0.818 | 0.834 | 0.831 | 0.808 | 0.876 | 0.963 | 
| Path BD | 1.000 | 0.881 | 0.964 | 0.896 | 0.845 | 0.918 | 0.819 | 0.680 | 0.579 | 0.634 | 0.642 | 0.651 | 0.663 | 0.631 | 0.674 | 0.679 | 0.694 | 0.689 | 0.702 | 0.894 | 0.885 | 0.909 | 0.706 | 0.639 | 0.629 | 0.585 | 0.652 | 0.645 | 0.688 | 0.617 | 0.593 | 0.521 | 0.485 | 0.424 | 0.458 | 0.481 | 0.425 | 0.437 | 0.323 | 0.297 | 0.339 | 0.343 | 0.470 | 0.488 | 0.493 | 0.435 | 0.448 | 0.331 | 0.332 | 0.353 | 0.351 | 0.336 | 0.387 | 0.392 | 0.406 | 0.424 | 0.402 | 0.417 | 0.410 | 0.527 | 0.514 | 0.508 | 0.556 | 0.527 | 0.475 | 0.474 | 0.498 | 0.485 | 0.515 | 0.502 | 0.488 | 0.556 | 0.563 | 0.831 | 0.820 | 0.880 | 0.785 | 0.651 | 0.728 | 0.718 | 
| Path BE | 1.000 | 1.135 | 1.159 | 1.176 | 1.159 | 0.965 | 1.002 | 1.018 | 0.998 | 1.034 | 1.193 | 1.248 | 1.232 | 1.264 | 1.229 | 1.125 | 1.111 | 1.011 | 1.263 | 1.275 | 1.249 | 1.418 | 1.596 | 1.657 | 1.707 | 1.756 | 1.490 | 1.609 | 1.491 | 1.479 | 1.571 | 1.482 | 1.670 | 1.783 | 1.819 | 1.884 | 1.789 | 1.695 | 1.747 | 1.887 | 2.009 | 2.154 | 2.138 | 2.140 | 1.808 | 2.092 | 2.038 | 1.817 | 1.753 | 1.776 | 1.744 | 2.290 | 2.251 | 2.181 | 2.214 | 2.206 | 2.115 | 1.940 | 1.675 | 1.517 | 1.538 | 1.514 | 1.494 | 1.529 | 1.648 | 1.670 | 1.597 | 1.582 | 1.677 | 1.781 | 1.751 | 1.763 | 1.801 | 2.380 | 2.155 | 2.022 | 2.093 | 1.831 | 1.906 | 1.729 | 
| Path BF | 1.000 | 0.995 | 1.068 | 0.991 | 0.930 | 0.933 | 0.934 | 0.914 | 0.952 | 1.004 | 1.017 | 1.126 | 1.005 | 1.127 | 1.153 | 1.166 | 1.719 | 1.620 | 1.573 | 1.581 | 1.620 | 1.682 | 1.801 | 1.806 | 1.922 | 1.912 | 2.017 | 1.704 | 1.972 | 1.921 | 1.808 | 1.877 | 1.934 | 1.990 | 1.835 | 1.750 | 1.945 | 1.761 | 1.652 | 1.916 | 2.132 | 2.034 | 2.099 | 2.247 | 2.167 | 2.196 | 2.156 | 2.832 | 2.576 | 2.528 | 2.853 | 2.873 | 3.019 | 2.984 | 3.184 | 2.856 | 2.855 | 3.140 | 3.167 | 3.129 | 3.082 | 3.432 | 3.508 | 3.596 | 3.634 | 3.205 | 3.334 | 3.361 | 3.584 | 3.300 | 3.523 | 3.357 | 3.483 | 3.542 | 3.786 | 3.479 | 3.411 | 3.647 | 3.678 | 3.633 | 
| Path BG | 1.000 | 1.066 | 1.067 | 1.110 | 1.135 | 1.118 | 1.191 | 1.277 | 1.267 | 1.253 | 1.204 | 1.180 | 1.210 | 1.247 | 1.293 | 1.331 | 1.124 | 1.301 | 1.320 | 1.302 | 1.299 | 1.365 | 1.414 | 1.416 | 1.387 | 1.364 | 1.389 | 1.533 | 1.484 | 1.404 | 1.351 | 1.408 | 1.442 | 1.440 | 1.287 | 1.407 | 1.447 | 1.428 | 1.427 | 1.650 | 1.509 | 1.421 | 1.477 | 1.640 | 1.616 | 1.726 | 1.754 | 1.752 | 1.683 | 1.587 | 1.509 | 1.351 | 1.228 | 1.173 | 1.203 | 1.055 | 1.106 | 1.117 | 1.609 | 1.573 | 1.593 | 1.684 | 1.958 | 1.820 | 1.943 | 1.870 | 1.803 | 1.675 | 1.633 | 1.317 | 1.121 | 1.121 | 1.060 | 0.993 | 1.121 | 1.054 | 1.050 | 1.097 | 1.078 | 1.415 | 
| Path BH | 1.000 | 0.976 | 0.958 | 1.042 | 1.250 | 1.460 | 1.527 | 1.508 | 1.383 | 1.429 | 1.520 | 1.512 | 1.447 | 1.484 | 1.470 | 1.468 | 1.651 | 1.557 | 1.406 | 1.709 | 1.798 | 1.921 | 1.853 | 1.851 | 1.859 | 1.742 | 1.697 | 1.721 | 1.750 | 1.799 | 1.696 | 1.688 | 1.812 | 1.680 | 1.577 | 1.639 | 1.709 | 1.456 | 1.515 | 1.616 | 1.741 | 1.666 | 1.652 | 1.704 | 1.770 | 2.126 | 2.454 | 2.566 | 2.626 | 2.654 | 3.914 | 3.687 | 3.983 | 3.703 | 3.965 | 4.072 | 4.210 | 4.206 | 3.757 | 3.494 | 3.329 | 3.251 | 3.459 | 3.586 | 3.593 | 3.647 | 4.155 | 4.202 | 5.761 | 6.307 | 6.259 | 6.063 | 6.153 | 6.190 | 6.170 | 5.617 | 5.572 | 5.292 | 4.504 | 4.503 | 
| Path BI | 1.000 | 0.915 | 0.861 | 0.895 | 1.007 | 0.973 | 0.991 | 1.262 | 1.250 | 1.269 | 1.151 | 0.964 | 1.003 | 1.133 | 1.177 | 1.216 | 1.063 | 1.091 | 1.041 | 0.998 | 1.070 | 1.219 | 1.097 | 1.164 | 1.203 | 1.407 | 1.736 | 1.613 | 1.722 | 1.641 | 1.661 | 1.532 | 1.706 | 1.744 | 1.788 | 2.068 | 2.042 | 2.189 | 2.175 | 2.170 | 2.181 | 2.235 | 2.320 | 2.417 | 2.458 | 2.527 | 2.398 | 2.273 | 2.610 | 2.538 | 2.323 | 2.295 | 2.148 | 2.227 | 2.231 | 2.195 | 2.080 | 2.059 | 1.750 | 1.705 | 1.669 | 1.593 | 1.634 | 1.434 | 1.430 | 1.385 | 1.286 | 1.325 | 1.449 | 1.475 | 1.647 | 1.376 | 1.428 | 1.431 | 1.424 | 1.407 | 1.429 | 1.249 | 1.288 | 1.408 | 
| Path BJ | 1.000 | 1.023 | 1.212 | 1.514 | 1.528 | 1.580 | 1.462 | 1.455 | 1.561 | 1.359 | 1.410 | 1.453 | 1.495 | 1.387 | 1.459 | 1.560 | 1.433 | 1.405 | 1.367 | 1.251 | 1.236 | 1.125 | 1.105 | 0.926 | 0.963 | 1.076 | 1.122 | 1.166 | 1.204 | 1.260 | 1.206 | 1.208 | 1.189 | 1.226 | 1.181 | 1.225 | 1.223 | 1.375 | 1.297 | 1.396 | 1.336 | 1.325 | 1.331 | 1.367 | 1.335 | 1.421 | 1.473 | 1.476 | 1.643 | 1.567 | 1.617 | 1.585 | 1.648 | 1.841 | 1.913 | 2.297 | 2.910 | 3.023 | 3.630 | 4.191 | 3.964 | 3.979 | 4.422 | 4.003 | 3.756 | 3.922 | 3.867 | 3.860 | 4.054 | 4.516 | 4.032 | 4.036 | 4.048 | 4.258 | 3.968 | 4.325 | 3.978 | 3.816 | 4.388 | 4.859 | 
| Path BK | 1.000 | 0.998 | 1.048 | 0.973 | 0.977 | 0.844 | 0.798 | 0.816 | 0.748 | 0.773 | 0.853 | 0.826 | 0.781 | 0.745 | 0.783 | 0.727 | 0.729 | 0.810 | 0.806 | 0.793 | 0.798 | 0.815 | 0.930 | 0.932 | 0.845 | 0.897 | 0.970 | 1.235 | 1.336 | 1.330 | 1.306 | 1.214 | 1.147 | 1.306 | 1.305 | 1.430 | 1.629 | 1.919 | 2.045 | 2.209 | 2.271 | 2.626 | 3.319 | 3.287 | 3.561 | 3.916 | 3.950 | 3.902 | 4.205 | 4.648 | 4.758 | 4.809 | 6.518 | 6.349 | 5.661 | 5.606 | 6.180 | 5.160 | 5.356 | 5.446 | 5.155 | 5.183 | 5.310 | 5.512 | 5.680 | 4.767 | 4.959 | 5.542 | 5.756 | 5.603 | 5.777 | 5.567 | 5.168 | 5.254 | 6.310 | 7.285 | 7.617 | 7.522 | 7.631 | 7.605 | 
| Path BL | 1.000 | 1.038 | 0.909 | 0.774 | 0.810 | 0.811 | 0.795 | 0.812 | 0.729 | 0.688 | 0.679 | 0.663 | 0.700 | 0.631 | 0.643 | 0.819 | 0.811 | 0.834 | 0.835 | 0.889 | 0.884 | 0.846 | 0.763 | 0.743 | 0.704 | 0.786 | 0.840 | 0.798 | 0.756 | 0.779 | 0.840 | 0.810 | 0.821 | 0.806 | 1.059 | 1.057 | 1.160 | 1.114 | 1.148 | 1.050 | 1.163 | 1.038 | 1.039 | 1.075 | 0.971 | 1.180 | 1.242 | 1.327 | 1.340 | 1.863 | 1.851 | 1.890 | 2.093 | 2.036 | 2.164 | 1.971 | 1.762 | 1.750 | 1.733 | 2.138 | 2.345 | 2.050 | 2.213 | 2.249 | 2.305 | 2.075 | 1.844 | 2.020 | 2.014 | 2.180 | 1.883 | 1.705 | 1.820 | 1.684 | 1.935 | 2.143 | 2.332 | 2.104 | 1.654 | 1.740 | 
| Path BM | 1.000 | 0.987 | 1.010 | 1.088 | 1.095 | 0.994 | 1.061 | 1.085 | 1.086 | 0.961 | 0.960 | 1.008 | 0.936 | 0.904 | 0.888 | 0.894 | 0.914 | 1.185 | 1.212 | 1.437 | 1.794 | 1.811 | 1.770 | 1.839 | 1.807 | 2.325 | 2.417 | 2.209 | 2.093 | 2.119 | 2.219 | 2.193 | 2.226 | 1.947 | 2.185 | 2.333 | 2.333 | 2.406 | 2.319 | 2.247 | 2.225 | 2.360 | 2.329 | 2.394 | 2.490 | 2.511 | 2.677 | 2.834 | 2.962 | 2.856 | 2.895 | 2.842 | 2.706 | 2.876 | 2.767 | 2.583 | 2.959 | 2.930 | 3.107 | 3.067 | 3.273 | 3.276 | 3.286 | 3.643 | 3.675 | 3.407 | 3.219 | 3.664 | 3.661 | 4.052 | 3.957 | 3.940 | 4.014 | 3.897 | 3.823 | 3.978 | 3.918 | 4.184 | 4.311 | 3.961 | 
| Path BN | 1.000 | 1.027 | 1.004 | 0.897 | 0.812 | 0.790 | 0.757 | 0.804 | 0.866 | 0.814 | 0.812 | 0.719 | 0.720 | 0.717 | 0.817 | 0.963 | 1.026 | 1.024 | 1.081 | 0.978 | 1.024 | 1.066 | 0.877 | 0.874 | 0.865 | 0.864 | 0.983 | 1.200 | 1.249 | 1.133 | 1.343 | 1.335 | 1.278 | 1.323 | 1.464 | 1.928 | 1.953 | 1.980 | 2.014 | 1.815 | 1.938 | 1.915 | 2.044 | 1.870 | 1.856 | 1.798 | 1.825 | 1.818 | 1.835 | 1.854 | 2.046 | 1.982 | 2.016 | 1.438 | 1.300 | 1.310 | 1.334 | 1.273 | 1.314 | 1.287 | 1.434 | 1.437 | 1.414 | 1.458 | 1.405 | 1.387 | 1.196 | 1.212 | 1.362 | 1.323 | 1.343 | 1.174 | 1.317 | 1.286 | 1.433 | 1.464 | 1.501 | 1.517 | 1.708 | 1.824 | 
| Path BO | 1.000 | 0.998 | 1.055 | 1.227 | 1.140 | 1.338 | 1.301 | 1.306 | 1.434 | 1.530 | 1.511 | 1.386 | 1.518 | 1.450 | 1.320 | 1.309 | 1.243 | 1.047 | 1.115 | 1.156 | 1.158 | 1.139 | 1.364 | 1.285 | 1.355 | 1.320 | 1.369 | 1.426 | 1.294 | 1.624 | 1.689 | 1.846 | 1.989 | 1.904 | 1.888 | 1.845 | 1.940 | 1.664 | 1.341 | 1.334 | 1.418 | 1.527 | 1.860 | 2.133 | 1.522 | 1.375 | 1.385 | 1.457 | 1.435 | 1.416 | 1.449 | 1.561 | 1.512 | 1.522 | 1.575 | 1.858 | 1.833 | 1.770 | 1.739 | 1.857 | 1.876 | 1.885 | 1.818 | 1.688 | 1.646 | 1.497 | 1.482 | 1.260 | 1.227 | 1.261 | 1.423 | 1.437 | 1.998 | 1.974 | 2.249 | 2.275 | 3.119 | 3.160 | 3.251 | 3.208 | 
| Path BP | 1.000 | 1.020 | 1.016 | 0.988 | 0.995 | 1.075 | 1.069 | 1.023 | 1.060 | 1.167 | 1.211 | 1.061 | 0.904 | 0.970 | 0.967 | 0.880 | 0.873 | 0.829 | 0.786 | 0.877 | 0.832 | 0.845 | 0.835 | 1.003 | 1.158 | 1.211 | 1.168 | 1.204 | 1.231 | 1.460 | 1.780 | 1.968 | 2.014 | 2.036 | 3.002 | 2.722 | 2.390 | 2.226 | 1.946 | 2.141 | 2.130 | 2.038 | 2.110 | 2.297 | 2.262 | 2.711 | 3.016 | 2.878 | 2.543 | 2.618 | 1.932 | 1.750 | 1.676 | 1.826 | 1.680 | 1.611 | 1.576 | 1.538 | 1.689 | 1.621 | 1.718 | 1.951 | 1.974 | 2.046 | 2.136 | 2.191 | 2.342 | 2.152 | 2.110 | 2.272 | 2.259 | 2.279 | 2.303 | 2.381 | 2.082 | 2.336 | 2.402 | 2.777 | 3.488 | 3.620 | 
| Path BQ | 1.000 | 1.020 | 1.016 | 0.988 | 0.995 | 0.979 | 1.071 | 1.015 | 0.916 | 1.037 | 1.013 | 1.008 | 1.027 | 1.022 | 1.033 | 1.140 | 1.104 | 1.044 | 1.176 | 1.256 | 1.281 | 1.276 | 1.157 | 1.181 | 1.168 | 1.076 | 1.151 | 1.234 | 1.226 | 1.205 | 1.207 | 1.361 | 1.453 | 1.482 | 1.476 | 1.417 | 1.456 | 1.405 | 1.614 | 1.559 | 1.588 | 1.583 | 1.441 | 1.548 | 1.519 | 1.714 | 1.726 | 2.432 | 2.199 | 2.303 | 2.397 | 2.111 | 1.844 | 1.882 | 1.862 | 1.715 | 1.789 | 1.655 | 1.647 | 1.768 | 1.721 | 1.990 | 2.515 | 2.593 | 2.341 | 2.489 | 2.354 | 2.343 | 2.349 | 2.436 | 2.433 | 2.430 | 2.436 | 2.503 | 2.493 | 2.425 | 2.442 | 2.488 | 2.715 | 2.669 | 
| Path BR | 1.000 | 1.074 | 1.057 | 1.043 | 1.067 | 1.192 | 1.219 | 1.249 | 1.262 | 1.251 | 1.180 | 1.329 | 1.420 | 1.410 | 1.424 | 1.979 | 1.966 | 2.008 | 2.137 | 2.216 | 2.220 | 2.184 | 1.939 | 2.103 | 2.159 | 2.307 | 2.276 | 2.390 | 2.310 | 2.979 | 2.289 | 2.409 | 2.473 | 2.282 | 2.541 | 2.718 | 2.654 | 2.642 | 2.692 | 2.558 | 2.730 | 2.698 | 2.880 | 2.618 | 2.482 | 2.558 | 2.616 | 3.101 | 2.885 | 2.726 | 3.102 | 3.100 | 3.326 | 3.620 | 3.267 | 3.227 | 3.416 | 3.485 | 3.471 | 3.376 | 3.282 | 3.164 | 3.159 | 3.363 | 3.605 | 3.705 | 3.390 | 3.349 | 3.049 | 3.042 | 2.959 | 2.980 | 3.035 | 3.842 | 3.563 | 3.345 | 3.437 | 2.839 | 3.079 | 3.159 | 
| Path BS | 1.000 | 0.929 | 1.014 | 0.997 | 1.177 | 1.148 | 1.271 | 1.135 | 1.136 | 1.103 | 1.063 | 0.987 | 0.963 | 0.896 | 0.816 | 0.782 | 0.831 | 0.895 | 0.966 | 0.895 | 0.888 | 0.962 | 1.140 | 1.367 | 1.436 | 1.345 | 1.318 | 1.313 | 1.315 | 1.286 | 1.253 | 1.303 | 1.190 | 1.128 | 1.142 | 1.212 | 1.109 | 1.096 | 0.998 | 1.025 | 1.013 | 1.081 | 0.970 | 0.956 | 0.990 | 1.095 | 1.127 | 1.112 | 1.072 | 0.996 | 0.971 | 0.763 | 0.816 | 0.772 | 0.739 | 0.637 | 0.652 | 0.659 | 0.903 | 0.915 | 0.930 | 0.915 | 0.951 | 0.934 | 1.202 | 1.301 | 1.401 | 1.706 | 1.836 | 1.929 | 1.846 | 1.831 | 1.840 | 1.782 | 1.866 | 1.942 | 1.710 | 1.633 | 1.753 | 1.739 | 
| Path BT | 1.000 | 1.194 | 1.209 | 1.151 | 1.463 | 1.423 | 1.443 | 1.423 | 1.420 | 1.356 | 1.329 | 1.306 | 1.392 | 1.378 | 1.388 | 1.418 | 1.839 | 1.828 | 1.865 | 1.845 | 1.699 | 1.930 | 1.816 | 1.802 | 1.952 | 2.147 | 2.117 | 2.067 | 2.269 | 2.178 | 2.320 | 2.104 | 2.642 | 2.742 | 2.963 | 3.038 | 3.342 | 3.370 | 3.329 | 3.120 | 2.820 | 3.190 | 3.203 | 3.114 | 3.357 | 3.712 | 3.799 | 3.840 | 3.521 | 3.855 | 3.678 | 3.524 | 4.208 | 3.842 | 3.993 | 3.943 | 4.042 | 4.340 | 4.273 | 4.216 | 4.378 | 4.338 | 4.332 | 4.871 | 4.593 | 4.764 | 4.452 | 4.194 | 3.695 | 4.161 | 4.318 | 4.666 | 4.271 | 4.090 | 4.365 | 3.915 | 3.585 | 2.733 | 2.685 | 2.919 | 
| Path BU | 1.000 | 0.957 | 0.949 | 0.954 | 0.920 | 0.853 | 0.808 | 0.902 | 0.856 | 0.810 | 0.881 | 1.057 | 1.262 | 1.244 | 1.088 | 1.099 | 1.092 | 1.232 | 1.313 | 1.304 | 1.371 | 1.176 | 1.201 | 1.286 | 1.321 | 1.503 | 1.380 | 1.658 | 1.914 | 2.001 | 2.050 | 1.805 | 1.724 | 1.768 | 1.551 | 1.604 | 1.954 | 2.102 | 2.208 | 1.935 | 1.989 | 1.956 | 2.614 | 2.638 | 2.626 | 2.633 | 2.802 | 2.787 | 2.799 | 2.623 | 2.547 | 2.433 | 2.516 | 2.138 | 2.083 | 1.974 | 2.164 | 2.217 | 2.301 | 2.371 | 2.395 | 2.092 | 2.148 | 2.222 | 2.298 | 2.511 | 2.532 | 2.502 | 2.499 | 2.534 | 2.477 | 2.604 | 2.533 | 2.478 | 2.515 | 2.455 | 2.695 | 2.587 | 2.927 | 2.939 | 
| Path BV | 1.000 | 1.170 | 1.427 | 1.487 | 1.349 | 1.559 | 1.812 | 1.684 | 1.798 | 1.890 | 1.930 | 1.958 | 1.931 | 2.067 | 2.121 | 2.267 | 2.283 | 2.332 | 2.168 | 2.321 | 2.384 | 2.713 | 3.449 | 3.494 | 3.543 | 3.604 | 3.613 | 3.844 | 3.986 | 3.994 | 4.263 | 3.899 | 3.672 | 3.818 | 4.293 | 4.008 | 4.430 | 4.535 | 4.583 | 5.916 | 5.595 | 5.359 | 4.621 | 4.354 | 4.558 | 4.468 | 4.562 | 4.099 | 4.835 | 5.798 | 6.089 | 5.702 | 5.610 | 5.243 | 4.939 | 4.351 | 4.259 | 4.424 | 4.569 | 4.783 | 4.585 | 4.711 | 4.546 | 5.220 | 5.077 | 4.788 | 4.199 | 4.468 | 4.642 | 4.365 | 4.431 | 3.874 | 4.348 | 4.204 | 3.862 | 3.093 | 2.774 | 2.634 | 2.759 | 2.871 | 
| Lower percentile | 1.000 | 0.884 | 0.856 | 0.793 | 0.810 | 0.794 | 0.771 | 0.699 | 0.638 | 0.643 | 0.649 | 0.631 | 0.556 | 0.534 | 0.510 | 0.599 | 0.555 | 0.543 | 0.544 | 0.564 | 0.561 | 0.552 | 0.524 | 0.562 | 0.556 | 0.579 | 0.526 | 0.529 | 0.541 | 0.552 | 0.505 | 0.475 | 0.479 | 0.426 | 0.459 | 0.456 | 0.458 | 0.447 | 0.417 | 0.388 | 0.381 | 0.359 | 0.425 | 0.433 | 0.412 | 0.403 | 0.391 | 0.321 | 0.330 | 0.354 | 0.356 | 0.337 | 0.364 | 0.345 | 0.301 | 0.316 | 0.311 | 0.320 | 0.325 | 0.338 | 0.365 | 0.356 | 0.350 | 0.337 | 0.380 | 0.477 | 0.440 | 0.448 | 0.451 | 0.457 | 0.424 | 0.379 | 0.367 | 0.330 | 0.356 | 0.360 | 0.379 | 0.378 | 0.404 | 0.431 | 
| Median | 1.000 | 1.020 | 1.016 | 1.026 | 1.061 | 1.068 | 1.085 | 1.089 | 1.086 | 1.104 | 1.143 | 1.136 | 1.196 | 1.141 | 1.114 | 1.150 | 1.124 | 1.175 | 1.242 | 1.253 | 1.265 | 1.235 | 1.255 | 1.372 | 1.378 | 1.364 | 1.385 | 1.495 | 1.483 | 1.434 | 1.616 | 1.568 | 1.537 | 1.546 | 1.519 | 1.655 | 1.684 | 1.636 | 1.634 | 1.633 | 1.665 | 1.705 | 1.627 | 1.754 | 1.693 | 1.720 | 1.796 | 1.818 | 1.726 | 1.815 | 1.749 | 1.750 | 1.686 | 1.729 | 1.626 | 1.636 | 1.776 | 1.659 | 1.682 | 1.736 | 1.693 | 1.766 | 1.816 | 1.718 | 1.783 | 1.780 | 1.800 | 1.752 | 1.813 | 1.770 | 1.756 | 1.768 | 1.887 | 1.860 | 1.968 | 1.982 | 1.945 | 1.918 | 1.838 | 1.834 | 
| Upper percentile | 1.000 | 1.190 | 1.426 | 1.475 | 1.523 | 1.666 | 1.764 | 1.656 | 1.771 | 1.956 | 1.924 | 1.927 | 1.967 | 2.476 | 2.277 | 2.377 | 2.356 | 2.329 | 2.327 | 2.541 | 2.902 | 2.946 | 3.377 | 3.412 | 3.446 | 3.504 | 3.506 | 3.688 | 3.855 | 3.883 | 4.027 | 3.740 | 3.588 | 3.720 | 4.117 | 3.888 | 4.287 | 4.331 | 4.364 | 4.718 | 4.583 | 4.366 | 4.555 | 4.541 | 4.660 | 4.394 | 4.455 | 4.066 | 4.702 | 5.149 | 5.611 | 5.579 | 5.706 | 5.751 | 5.534 | 5.598 | 6.096 | 5.673 | 5.431 | 5.332 | 5.055 | 5.100 | 4.561 | 5.461 | 5.574 | 4.784 | 4.944 | 5.464 | 5.760 | 6.183 | 6.174 | 5.976 | 6.066 | 6.143 | 6.285 | 7.036 | 7.312 | 7.212 | 7.232 | 7.276 | 
| Original history | 1.000 | 0.876 | 0.746 | 0.780 | 0.759 | 0.865 | 0.875 | 1.199 | 1.215 | 1.232 | 1.253 | 1.288 | 1.222 | 1.159 | 1.194 | 1.222 | 1.448 | 1.808 | 1.825 | 1.788 | 2.029 | 2.072 | 2.103 | 2.073 | 2.069 | 2.174 | 2.018 | 2.025 | 2.251 | 2.038 | 1.912 | 1.980 | 1.732 | 1.714 | 1.457 | 1.419 | 1.345 | 1.501 | 1.425 | 1.446 | 1.412 | 1.550 | 1.488 | 1.533 | 1.408 | 1.128 | 1.011 | 0.960 | 0.892 | 0.974 | 0.958 | 1.131 | 1.034 | 0.974 | 1.012 | 1.139 | 1.112 | 1.107 | 1.128 | 1.124 | 1.024 | 1.015 | 0.964 | 0.812 | 0.863 | 0.830 | 0.775 | 0.865 | 0.854 | 0.915 | 0.909 | 0.894 | 0.900 | 0.919 | 1.193 | 1.186 | 1.196 | 1.209 | 1.334 | 1.292 | 

**Chart data $\cdot$ Pool-return differences across rebuilt histories $\cdot$ 30-day blocks**

Summary of pool-return differences
| Statistic | LP/xyk difference, percentage points per year | 
| --- | --- |
| Minimum | −26.09 | 
| Lower quartile | −1.85 | 
| Median | +0.91 | 
| Upper quartile | +1.95 | 
| Maximum | +29.12 | 
| Original history | +1.65 | 

Proposal minus current LP/xyk, percentage points per year
| LP/xyk difference, percentage points per year | Pair kept in this analysis? | 
| --- | --- |
| −2.03 | Yes | 
| +0.75 | Yes | 
| −1.95 | Yes | 
| +1.38 | Yes | 
| +1.27 | Yes | 
| −26.09 | Yes | 
| +1.25 | Yes | 
| +0.53 | Yes | 
| +0.12 | Yes | 
| +29.12 | Yes | 
| −1.76 | Yes | 
| +1.20 | Yes | 
| +0.91 | Yes | 
| −20.27 | Yes | 
| +2.42 | Yes | 
| −1.48 | Yes | 
| +2.21 | Yes | 
| +1.99 | Yes | 
| +1.38 | Yes | 
| +1.29 | Yes | 
| −0.68 | Yes | 
| −19.97 | Yes | 
| −0.44 | Yes | 
| +1.15 | Yes | 
| undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| +5.06 | Yes | 
| −2.16 | Yes | 
| −0.77 | Yes | 
| +2.02 | Yes | 
| +0.17 | Yes | 
| +2.06 | Yes | 
| −8.14 | Yes | 
| +1.55 | Yes | 
| +1.17 | Yes | 
| +2.26 | Yes | 
| +12.22 | Yes | 
| +24.63 | Yes | 
| 0.00 | Yes | 
| −5.61 | Yes | 
| +2.00 | Yes | 
| −4.43 | Yes | 
| −20.89 | Yes | 
| +1.90 | Yes | 
| −9.69 | Yes | 
| −7.79 | Yes | 
| −0.19 | Yes | 
| +1.73 | Yes | 
| +10.43 | Yes | 

**Chart data $\cdot$ Prices on rebuilt histories $\cdot$ 1-day blocks**

Price divided by starting price, sampled weekly
| Rebuilt history | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | Weekly sample | 
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Path AA | 1.000 | 1.083 | 1.013 | 1.168 | 1.129 | 1.215 | 1.207 | 1.054 | 1.102 | 1.091 | 0.966 | 0.842 | 0.819 | 0.872 | 0.799 | 0.775 | 1.090 | 1.200 | 1.200 | 1.118 | 0.949 | 0.978 | 1.017 | 1.030 | 0.980 | 1.046 | 1.043 | 1.061 | 1.049 | 1.020 | 0.991 | 0.986 | 1.052 | 1.165 | 0.867 | 0.721 | 0.707 | 0.663 | 0.677 | 0.569 | 0.541 | 0.612 | 0.696 | 0.667 | 0.669 | 0.690 | 0.700 | 0.672 | 0.670 | 0.662 | 0.753 | 0.702 | 0.744 | 0.760 | 0.730 | 0.821 | 0.805 | 0.944 | 1.035 | 1.020 | 1.002 | 1.029 | 1.048 | 1.163 | 1.269 | 1.391 | 1.363 | 1.260 | 1.224 | 1.267 | 1.137 | 1.186 | 1.161 | 1.111 | 1.216 | 1.171 | 1.250 | 1.226 | 1.268 | 1.277 | 
| Path AB | 1.000 | 1.005 | 1.035 | 1.014 | 0.878 | 0.816 | 0.871 | 0.922 | 1.015 | 1.094 | 1.409 | 1.355 | 1.218 | 1.158 | 1.167 | 1.202 | 1.113 | 1.117 | 1.173 | 1.266 | 1.216 | 1.285 | 1.668 | 1.801 | 1.929 | 1.872 | 2.034 | 1.826 | 1.937 | 1.885 | 1.900 | 2.021 | 2.212 | 1.794 | 1.695 | 1.793 | 1.814 | 1.976 | 2.045 | 1.622 | 1.603 | 1.756 | 1.633 | 1.738 | 1.754 | 1.588 | 1.635 | 1.506 | 1.345 | 1.337 | 1.460 | 1.569 | 1.518 | 1.644 | 1.523 | 1.562 | 1.678 | 1.639 | 1.558 | 1.337 | 1.289 | 1.193 | 1.144 | 1.115 | 1.151 | 1.096 | 1.106 | 1.225 | 1.167 | 1.278 | 1.200 | 1.200 | 1.277 | 1.334 | 1.477 | 1.603 | 1.842 | 1.871 | 2.040 | 1.852 | 
| Path AC | 1.000 | 1.122 | 1.155 | 1.103 | 1.002 | 0.987 | 1.189 | 1.254 | 1.192 | 1.095 | 1.058 | 1.085 | 1.284 | 1.255 | 1.172 | 1.039 | 0.954 | 1.060 | 1.125 | 1.078 | 1.051 | 1.020 | 1.075 | 1.368 | 1.261 | 1.303 | 1.320 | 1.067 | 1.036 | 1.028 | 0.936 | 0.890 | 0.819 | 0.718 | 0.921 | 0.796 | 0.879 | 0.929 | 0.908 | 0.885 | 0.836 | 0.676 | 0.699 | 0.739 | 0.651 | 0.748 | 0.755 | 0.756 | 0.616 | 0.600 | 0.518 | 0.531 | 0.593 | 0.548 | 0.482 | 0.458 | 0.525 | 0.489 | 0.630 | 0.521 | 0.456 | 0.423 | 0.383 | 0.364 | 0.373 | 0.398 | 0.374 | 0.284 | 0.301 | 0.304 | 0.336 | 0.319 | 0.329 | 0.290 | 0.291 | 0.277 | 0.260 | 0.262 | 0.294 | 0.327 | 
| Path AD | 1.000 | 0.975 | 0.972 | 1.181 | 1.065 | 1.127 | 1.074 | 0.998 | 0.945 | 0.855 | 0.804 | 0.928 | 0.946 | 1.024 | 1.105 | 1.186 | 1.123 | 1.309 | 1.268 | 1.414 | 1.390 | 1.315 | 1.476 | 1.314 | 1.228 | 1.240 | 1.421 | 1.321 | 1.176 | 1.141 | 1.188 | 1.355 | 1.384 | 1.395 | 1.328 | 1.472 | 1.264 | 1.186 | 1.073 | 1.257 | 1.443 | 1.566 | 1.574 | 1.434 | 1.290 | 1.224 | 1.087 | 1.068 | 0.903 | 0.892 | 1.025 | 0.908 | 0.942 | 0.827 | 0.767 | 0.699 | 0.686 | 0.580 | 0.573 | 0.576 | 0.566 | 0.657 | 0.648 | 0.640 | 0.661 | 0.555 | 0.554 | 0.531 | 0.545 | 0.551 | 0.571 | 0.532 | 0.428 | 0.392 | 0.349 | 0.341 | 0.356 | 0.357 | 0.368 | 0.433 | 
| Path AE | 1.000 | 1.165 | 1.165 | 1.333 | 1.412 | 1.401 | 1.493 | 1.648 | 1.703 | 1.417 | 1.414 | 1.625 | 1.659 | 1.714 | 1.869 | 1.956 | 2.015 | 1.936 | 2.203 | 2.384 | 2.030 | 2.246 | 2.304 | 2.323 | 2.020 | 1.861 | 2.042 | 1.807 | 1.763 | 1.757 | 1.854 | 1.736 | 1.723 | 1.747 | 2.019 | 2.197 | 1.951 | 1.789 | 1.818 | 2.082 | 1.992 | 2.052 | 1.956 | 2.100 | 1.927 | 1.791 | 1.733 | 1.481 | 1.590 | 1.686 | 1.474 | 1.703 | 1.496 | 1.578 | 1.552 | 1.662 | 1.540 | 1.581 | 1.612 | 1.369 | 1.305 | 1.275 | 1.122 | 1.096 | 1.058 | 1.009 | 0.964 | 0.923 | 0.869 | 0.866 | 0.792 | 0.804 | 0.789 | 0.941 | 0.825 | 0.840 | 0.902 | 1.059 | 1.052 | 1.148 | 
| Path AF | 1.000 | 1.081 | 1.123 | 1.067 | 1.062 | 1.161 | 1.169 | 1.172 | 1.006 | 1.190 | 1.216 | 1.336 | 1.262 | 1.462 | 1.375 | 1.401 | 1.337 | 1.452 | 1.395 | 1.230 | 1.401 | 1.246 | 1.151 | 1.033 | 1.081 | 1.067 | 1.021 | 1.019 | 0.933 | 0.909 | 0.922 | 0.839 | 0.914 | 0.945 | 0.896 | 0.889 | 0.884 | 0.854 | 0.891 | 0.867 | 0.809 | 0.893 | 0.801 | 0.802 | 0.905 | 0.916 | 0.910 | 1.060 | 0.865 | 0.944 | 0.955 | 0.902 | 1.011 | 1.001 | 0.931 | 0.963 | 0.953 | 0.901 | 0.816 | 0.789 | 0.734 | 0.810 | 0.765 | 0.814 | 0.806 | 0.900 | 0.980 | 1.132 | 1.156 | 1.009 | 1.012 | 1.100 | 0.899 | 1.067 | 1.218 | 1.078 | 0.972 | 1.060 | 1.029 | 1.078 | 
| Path AG | 1.000 | 0.888 | 0.905 | 0.942 | 0.987 | 0.912 | 1.038 | 0.942 | 0.931 | 0.812 | 0.854 | 0.858 | 0.875 | 0.904 | 0.838 | 0.822 | 0.836 | 0.867 | 0.893 | 0.996 | 1.052 | 1.130 | 1.011 | 1.027 | 1.056 | 1.077 | 0.923 | 0.906 | 0.934 | 0.829 | 0.836 | 0.823 | 0.874 | 0.892 | 1.107 | 1.103 | 1.042 | 1.040 | 1.043 | 0.907 | 1.091 | 1.087 | 1.029 | 1.058 | 1.023 | 0.932 | 0.844 | 0.861 | 0.989 | 0.999 | 1.054 | 1.143 | 1.239 | 0.939 | 1.012 | 1.015 | 1.012 | 0.953 | 1.107 | 1.085 | 1.067 | 1.174 | 1.102 | 1.063 | 1.339 | 1.284 | 1.260 | 1.196 | 1.023 | 1.031 | 0.955 | 0.948 | 0.895 | 0.805 | 0.783 | 0.809 | 0.683 | 0.565 | 0.572 | 0.500 | 
| Path AH | 1.000 | 1.160 | 1.051 | 1.035 | 1.110 | 0.981 | 0.976 | 0.993 | 0.941 | 0.907 | 0.819 | 0.748 | 0.839 | 1.026 | 1.002 | 1.012 | 0.964 | 0.837 | 0.731 | 0.716 | 0.726 | 0.726 | 0.713 | 0.779 | 0.737 | 0.828 | 0.827 | 0.808 | 0.774 | 0.662 | 0.673 | 0.645 | 0.580 | 0.556 | 0.567 | 0.559 | 0.465 | 0.551 | 0.562 | 0.665 | 0.626 | 0.633 | 0.686 | 0.689 | 0.844 | 0.771 | 0.736 | 0.843 | 0.783 | 0.869 | 0.900 | 0.936 | 0.997 | 0.831 | 0.895 | 0.858 | 0.865 | 0.798 | 0.797 | 0.804 | 0.762 | 0.836 | 0.780 | 0.831 | 0.823 | 0.772 | 0.757 | 0.770 | 0.837 | 0.837 | 0.761 | 0.742 | 0.829 | 0.817 | 0.809 | 0.825 | 0.822 | 0.761 | 0.720 | 0.838 | 
| Path AI | 1.000 | 0.977 | 0.969 | 1.027 | 1.115 | 1.081 | 1.169 | 1.324 | 1.340 | 1.219 | 1.315 | 1.373 | 1.265 | 1.299 | 1.297 | 1.253 | 1.280 | 1.131 | 1.166 | 1.125 | 1.067 | 1.104 | 1.126 | 1.164 | 1.186 | 1.113 | 1.125 | 1.106 | 1.182 | 0.955 | 0.945 | 1.019 | 1.065 | 1.134 | 1.161 | 1.109 | 1.161 | 1.131 | 1.087 | 1.186 | 1.035 | 1.048 | 1.049 | 1.052 | 1.068 | 1.162 | 1.242 | 1.298 | 1.187 | 1.223 | 1.173 | 1.173 | 1.016 | 1.060 | 1.077 | 1.081 | 1.037 | 1.013 | 0.972 | 0.850 | 0.823 | 0.731 | 0.732 | 0.762 | 0.835 | 0.863 | 1.030 | 1.112 | 1.216 | 1.210 | 1.324 | 1.153 | 1.118 | 0.913 | 0.873 | 0.890 | 0.800 | 0.720 | 0.778 | 0.855 | 
| Path AJ | 1.000 | 1.046 | 1.050 | 1.040 | 0.989 | 0.978 | 1.018 | 0.957 | 0.856 | 0.963 | 0.933 | 0.954 | 0.939 | 0.991 | 1.000 | 0.961 | 1.228 | 1.204 | 1.357 | 1.238 | 1.211 | 1.292 | 1.303 | 1.373 | 1.451 | 1.421 | 1.350 | 1.317 | 1.242 | 1.420 | 1.493 | 1.561 | 1.409 | 1.319 | 1.352 | 1.364 | 1.306 | 1.437 | 1.412 | 1.496 | 1.586 | 1.820 | 1.883 | 2.194 | 1.942 | 1.991 | 1.986 | 1.809 | 1.880 | 1.911 | 1.800 | 2.131 | 2.339 | 2.545 | 2.482 | 2.489 | 2.354 | 2.486 | 2.464 | 2.167 | 2.307 | 2.248 | 2.381 | 2.854 | 3.074 | 2.632 | 2.603 | 2.398 | 2.450 | 2.406 | 2.427 | 2.331 | 2.156 | 2.486 | 2.606 | 2.588 | 2.838 | 3.271 | 3.666 | 3.623 | 
| Path AK | 1.000 | 0.923 | 0.872 | 0.747 | 0.724 | 0.700 | 0.834 | 0.795 | 1.049 | 0.942 | 1.066 | 1.046 | 1.136 | 1.064 | 0.999 | 0.975 | 0.727 | 0.641 | 0.585 | 0.508 | 0.532 | 0.502 | 0.413 | 0.330 | 0.454 | 0.430 | 0.444 | 0.412 | 0.399 | 0.358 | 0.383 | 0.360 | 0.363 | 0.395 | 0.456 | 0.485 | 0.491 | 0.478 | 0.619 | 0.546 | 0.526 | 0.512 | 0.535 | 0.516 | 0.524 | 0.609 | 0.616 | 0.635 | 0.628 | 0.595 | 0.652 | 0.709 | 0.658 | 0.675 | 0.733 | 0.608 | 0.594 | 0.632 | 0.654 | 0.541 | 0.496 | 0.523 | 0.490 | 0.439 | 0.446 | 0.381 | 0.385 | 0.424 | 0.459 | 0.436 | 0.473 | 0.478 | 0.560 | 0.534 | 0.714 | 0.749 | 0.786 | 0.794 | 0.654 | 0.714 | 
| Path AL | 1.000 | 0.976 | 0.901 | 0.750 | 0.569 | 0.612 | 0.574 | 0.590 | 0.567 | 0.648 | 0.646 | 0.805 | 1.022 | 1.016 | 1.052 | 1.137 | 1.276 | 1.179 | 1.173 | 1.183 | 1.041 | 1.121 | 1.044 | 1.011 | 0.953 | 1.058 | 0.947 | 0.996 | 0.993 | 0.961 | 0.954 | 0.864 | 0.822 | 0.712 | 0.751 | 0.719 | 0.799 | 0.826 | 0.739 | 0.828 | 0.728 | 0.964 | 0.961 | 0.933 | 0.976 | 1.054 | 1.110 | 1.157 | 1.174 | 1.417 | 1.655 | 1.922 | 2.220 | 2.528 | 2.213 | 2.513 | 2.418 | 2.153 | 2.143 | 2.129 | 2.338 | 2.273 | 2.730 | 2.933 | 2.481 | 2.718 | 3.127 | 3.342 | 2.968 | 2.995 | 2.706 | 2.608 | 2.617 | 2.265 | 2.207 | 2.453 | 2.155 | 2.046 | 1.836 | 1.787 | 
| Path AM | 1.000 | 1.083 | 1.242 | 1.252 | 1.343 | 1.295 | 1.221 | 1.195 | 1.217 | 1.125 | 1.092 | 1.034 | 1.108 | 1.059 | 1.015 | 1.100 | 1.021 | 0.962 | 0.957 | 0.863 | 0.838 | 0.791 | 0.762 | 0.736 | 0.613 | 0.525 | 0.508 | 0.618 | 0.605 | 0.777 | 0.793 | 0.777 | 0.690 | 0.730 | 0.887 | 0.846 | 0.830 | 0.752 | 0.832 | 0.818 | 0.996 | 1.114 | 1.167 | 1.191 | 1.204 | 1.282 | 1.307 | 1.317 | 1.316 | 1.285 | 1.373 | 1.251 | 1.221 | 1.125 | 1.073 | 1.062 | 0.974 | 0.942 | 1.086 | 1.064 | 1.103 | 1.126 | 1.108 | 1.010 | 1.071 | 1.040 | 1.309 | 1.291 | 1.377 | 1.369 | 1.273 | 1.076 | 1.130 | 1.238 | 1.407 | 1.338 | 1.364 | 1.309 | 1.308 | 1.338 | 
| Path AN | 1.000 | 0.985 | 0.963 | 0.960 | 0.824 | 0.798 | 0.710 | 0.665 | 0.758 | 0.871 | 1.011 | 0.981 | 0.946 | 1.060 | 1.076 | 1.180 | 1.127 | 1.190 | 1.224 | 1.154 | 1.158 | 1.170 | 1.127 | 1.458 | 1.685 | 1.868 | 1.770 | 1.841 | 1.760 | 1.793 | 2.128 | 2.307 | 2.101 | 1.775 | 1.790 | 1.489 | 1.881 | 1.660 | 1.717 | 1.767 | 1.930 | 1.829 | 1.823 | 1.885 | 1.857 | 1.826 | 1.650 | 1.687 | 1.555 | 1.612 | 1.587 | 1.327 | 1.329 | 1.433 | 1.328 | 1.500 | 1.479 | 1.552 | 1.329 | 1.486 | 1.443 | 1.617 | 1.454 | 1.455 | 1.536 | 1.558 | 1.613 | 1.557 | 1.843 | 1.700 | 1.974 | 2.019 | 1.901 | 1.716 | 1.586 | 1.759 | 1.722 | 1.744 | 2.028 | 1.912 | 
| Path AO | 1.000 | 1.052 | 1.016 | 1.046 | 1.058 | 1.000 | 1.144 | 1.256 | 1.423 | 1.501 | 1.431 | 1.343 | 1.309 | 1.340 | 1.489 | 1.512 | 1.674 | 1.743 | 1.755 | 2.034 | 2.009 | 1.940 | 1.922 | 1.854 | 1.739 | 1.762 | 1.771 | 1.986 | 1.772 | 1.645 | 1.531 | 1.540 | 1.381 | 1.500 | 1.359 | 1.518 | 1.558 | 1.490 | 1.339 | 1.387 | 1.325 | 1.294 | 1.257 | 1.324 | 1.496 | 1.516 | 1.648 | 1.646 | 1.721 | 1.685 | 1.794 | 1.903 | 2.115 | 1.868 | 2.347 | 2.071 | 2.472 | 2.630 | 2.564 | 2.622 | 2.629 | 3.066 | 3.682 | 3.886 | 3.354 | 3.034 | 3.127 | 3.368 | 3.620 | 3.046 | 2.941 | 2.865 | 3.115 | 3.077 | 2.773 | 2.772 | 2.821 | 2.769 | 2.830 | 2.789 | 
| Path AP | 1.000 | 1.127 | 1.169 | 1.199 | 1.185 | 1.135 | 1.519 | 1.284 | 1.270 | 1.312 | 1.210 | 0.994 | 1.233 | 1.158 | 1.099 | 0.967 | 1.120 | 1.045 | 0.870 | 0.888 | 1.066 | 1.078 | 1.078 | 1.327 | 1.305 | 1.192 | 1.032 | 1.272 | 1.218 | 1.207 | 1.067 | 0.927 | 1.103 | 0.928 | 1.010 | 0.889 | 0.753 | 0.823 | 0.706 | 0.681 | 0.697 | 0.739 | 0.658 | 0.594 | 0.545 | 0.571 | 0.554 | 0.574 | 0.617 | 0.602 | 0.585 | 0.594 | 0.484 | 0.473 | 0.450 | 0.452 | 0.486 | 0.478 | 0.491 | 0.451 | 0.389 | 0.341 | 0.343 | 0.361 | 0.391 | 0.375 | 0.401 | 0.355 | 0.389 | 0.377 | 0.400 | 0.381 | 0.379 | 0.377 | 0.371 | 0.422 | 0.431 | 0.422 | 0.555 | 0.545 | 
| Path AQ | 1.000 | 1.041 | 1.128 | 1.164 | 1.167 | 1.124 | 1.231 | 1.212 | 1.196 | 1.175 | 1.158 | 1.183 | 1.107 | 0.944 | 0.933 | 0.903 | 0.673 | 0.640 | 0.711 | 0.689 | 0.725 | 0.891 | 0.859 | 0.760 | 0.815 | 0.790 | 1.046 | 1.048 | 0.956 | 1.084 | 1.071 | 1.000 | 1.094 | 1.095 | 0.988 | 1.065 | 1.016 | 0.951 | 1.024 | 1.108 | 1.184 | 1.038 | 1.134 | 0.987 | 1.060 | 1.048 | 1.072 | 1.097 | 1.009 | 0.928 | 1.096 | 1.141 | 1.107 | 1.287 | 1.401 | 1.480 | 1.782 | 1.751 | 1.787 | 1.971 | 1.954 | 1.863 | 1.725 | 1.505 | 1.418 | 1.382 | 1.272 | 1.430 | 1.569 | 1.739 | 1.731 | 1.832 | 1.794 | 1.542 | 1.731 | 1.866 | 1.926 | 2.008 | 1.750 | 1.737 | 
| Path AR | 1.000 | 0.926 | 0.962 | 1.010 | 1.001 | 0.931 | 1.002 | 1.095 | 1.086 | 1.200 | 1.400 | 1.320 | 1.320 | 1.392 | 1.329 | 1.207 | 1.250 | 1.197 | 1.219 | 1.283 | 1.283 | 1.084 | 1.220 | 1.043 | 0.977 | 0.881 | 0.966 | 1.141 | 1.277 | 1.029 | 1.125 | 1.196 | 1.327 | 1.208 | 1.266 | 1.246 | 1.019 | 1.267 | 1.256 | 1.514 | 1.380 | 1.286 | 1.166 | 1.205 | 1.296 | 1.181 | 1.242 | 1.288 | 1.303 | 1.337 | 1.565 | 1.615 | 1.731 | 1.631 | 1.502 | 1.438 | 1.517 | 1.516 | 1.502 | 1.376 | 1.334 | 1.553 | 1.642 | 1.561 | 1.624 | 1.960 | 1.730 | 1.784 | 2.096 | 2.286 | 2.212 | 2.117 | 2.030 | 1.790 | 1.934 | 2.042 | 1.974 | 1.934 | 2.076 | 2.192 | 
| Path AS | 1.000 | 1.116 | 1.092 | 1.063 | 1.042 | 0.985 | 1.058 | 0.983 | 1.100 | 1.230 | 1.387 | 1.119 | 1.255 | 1.292 | 1.402 | 1.431 | 1.397 | 1.402 | 1.126 | 1.015 | 0.924 | 0.932 | 1.053 | 1.064 | 1.073 | 1.139 | 1.207 | 1.304 | 1.198 | 1.056 | 1.165 | 1.139 | 1.219 | 1.395 | 1.488 | 1.515 | 1.510 | 1.510 | 1.672 | 1.731 | 1.442 | 1.483 | 1.512 | 1.441 | 1.470 | 1.458 | 1.548 | 1.584 | 1.706 | 1.648 | 1.581 | 1.762 | 1.746 | 1.841 | 2.105 | 1.559 | 1.448 | 1.411 | 1.450 | 1.547 | 1.649 | 1.788 | 1.947 | 2.048 | 2.493 | 2.477 | 1.990 | 1.910 | 1.729 | 1.683 | 1.851 | 1.646 | 1.651 | 1.513 | 1.560 | 1.510 | 1.353 | 1.141 | 1.262 | 1.637 | 
| Path AT | 1.000 | 0.888 | 0.924 | 0.929 | 0.990 | 0.878 | 0.953 | 1.077 | 1.068 | 0.968 | 0.939 | 0.780 | 0.969 | 0.930 | 0.922 | 0.976 | 1.106 | 1.200 | 1.129 | 1.129 | 1.108 | 0.998 | 1.060 | 1.185 | 1.419 | 1.521 | 1.744 | 1.692 | 1.499 | 1.375 | 1.664 | 1.655 | 1.554 | 1.421 | 1.439 | 1.444 | 1.217 | 1.369 | 1.676 | 1.575 | 1.682 | 1.791 | 1.585 | 1.455 | 1.394 | 1.335 | 1.375 | 1.480 | 1.287 | 1.360 | 1.470 | 1.409 | 1.337 | 1.342 | 1.413 | 1.138 | 1.011 | 1.010 | 1.091 | 1.017 | 0.962 | 0.922 | 0.846 | 0.918 | 0.865 | 0.859 | 0.865 | 0.816 | 0.884 | 0.835 | 0.841 | 0.704 | 0.689 | 0.602 | 0.567 | 0.585 | 0.556 | 0.525 | 0.485 | 0.482 | 
| Path AU | 1.000 | 0.977 | 0.961 | 1.045 | 1.106 | 1.042 | 1.054 | 0.960 | 0.994 | 1.086 | 1.113 | 1.133 | 1.132 | 1.023 | 0.994 | 0.976 | 1.094 | 1.039 | 0.851 | 0.917 | 0.944 | 0.902 | 1.196 | 1.310 | 1.262 | 1.262 | 1.202 | 1.368 | 1.431 | 1.512 | 1.481 | 1.519 | 1.361 | 1.365 | 1.294 | 1.535 | 1.447 | 1.465 | 1.256 | 1.427 | 1.334 | 1.381 | 1.501 | 1.382 | 1.250 | 1.608 | 1.589 | 1.339 | 1.251 | 1.257 | 1.261 | 1.368 | 1.452 | 1.702 | 1.331 | 1.201 | 1.479 | 1.452 | 1.278 | 1.339 | 1.367 | 1.490 | 1.513 | 1.777 | 1.804 | 1.947 | 2.042 | 2.425 | 2.617 | 2.807 | 3.050 | 3.245 | 3.697 | 3.776 | 4.053 | 4.244 | 4.662 | 5.302 | 5.672 | 4.955 | 
| Path AV | 1.000 | 1.056 | 1.107 | 1.016 | 1.163 | 1.188 | 1.096 | 1.185 | 1.264 | 1.196 | 1.157 | 1.087 | 1.156 | 1.052 | 1.211 | 1.208 | 1.251 | 1.452 | 1.507 | 1.470 | 1.359 | 1.436 | 1.628 | 1.698 | 1.781 | 2.022 | 1.958 | 2.239 | 2.212 | 2.811 | 2.631 | 2.596 | 2.292 | 2.289 | 2.550 | 2.749 | 2.614 | 2.916 | 2.930 | 2.890 | 3.025 | 3.008 | 3.017 | 2.745 | 3.022 | 3.117 | 3.246 | 3.385 | 3.102 | 2.995 | 3.079 | 3.216 | 3.409 | 3.316 | 2.952 | 3.046 | 3.001 | 3.502 | 3.557 | 3.797 | 4.380 | 4.022 | 4.096 | 4.241 | 4.639 | 4.428 | 4.529 | 4.928 | 5.021 | 5.296 | 4.752 | 4.513 | 4.601 | 4.889 | 5.002 | 5.676 | 6.442 | 6.084 | 6.536 | 7.265 | 
| Path AW | 1.000 | 1.165 | 1.111 | 1.434 | 1.636 | 1.540 | 1.502 | 1.596 | 1.567 | 1.581 | 1.613 | 2.076 | 2.242 | 2.205 | 2.006 | 1.869 | 2.143 | 2.003 | 2.138 | 2.324 | 2.146 | 2.137 | 1.817 | 1.823 | 1.779 | 1.801 | 1.707 | 1.732 | 1.624 | 1.423 | 1.476 | 1.621 | 1.694 | 1.808 | 1.768 | 1.638 | 1.618 | 1.677 | 1.712 | 1.563 | 1.440 | 1.212 | 1.162 | 1.241 | 1.195 | 1.455 | 1.445 | 1.437 | 1.493 | 1.586 | 1.505 | 1.559 | 1.454 | 1.600 | 1.436 | 1.309 | 1.396 | 1.180 | 1.164 | 1.209 | 1.145 | 1.180 | 1.166 | 1.327 | 1.532 | 1.536 | 1.432 | 1.481 | 1.456 | 1.485 | 1.557 | 1.554 | 1.651 | 1.648 | 2.247 | 2.290 | 2.563 | 2.416 | 2.473 | 2.664 | 
| Path AX | 1.000 | 1.018 | 0.916 | 0.870 | 0.897 | 1.085 | 1.279 | 1.172 | 1.172 | 1.130 | 1.176 | 1.517 | 1.358 | 1.679 | 1.670 | 1.741 | 1.372 | 1.397 | 1.747 | 1.498 | 1.695 | 1.751 | 1.912 | 2.207 | 2.375 | 2.302 | 2.450 | 2.508 | 2.707 | 2.476 | 2.498 | 2.477 | 2.483 | 2.283 | 2.480 | 2.758 | 2.758 | 3.364 | 3.212 | 3.180 | 3.090 | 3.078 | 2.964 | 3.143 | 3.140 | 2.865 | 2.965 | 3.490 | 3.342 | 3.725 | 3.346 | 4.354 | 5.038 | 5.053 | 6.201 | 6.301 | 5.733 | 5.711 | 5.774 | 6.084 | 5.625 | 5.889 | 6.224 | 5.098 | 5.345 | 5.895 | 5.492 | 5.206 | 4.240 | 4.579 | 4.495 | 3.934 | 4.034 | 4.112 | 3.842 | 3.713 | 3.864 | 3.876 | 3.549 | 4.268 | 
| Path AY | 1.000 | 0.973 | 0.900 | 1.010 | 1.057 | 1.175 | 1.188 | 1.274 | 1.344 | 1.413 | 1.539 | 1.222 | 1.120 | 0.991 | 1.030 | 0.866 | 0.926 | 0.892 | 0.864 | 0.905 | 0.899 | 1.001 | 0.996 | 1.096 | 1.397 | 1.274 | 1.238 | 1.377 | 1.487 | 1.302 | 1.492 | 1.625 | 1.513 | 1.195 | 1.209 | 1.332 | 1.210 | 1.303 | 1.341 | 1.250 | 1.130 | 1.189 | 1.111 | 1.169 | 1.300 | 1.260 | 1.429 | 1.359 | 1.280 | 1.244 | 1.338 | 1.478 | 1.480 | 1.868 | 1.762 | 1.635 | 1.970 | 2.074 | 2.139 | 2.003 | 1.995 | 1.928 | 1.973 | 1.910 | 1.722 | 2.039 | 2.670 | 2.338 | 2.387 | 2.663 | 2.283 | 2.230 | 2.135 | 2.010 | 2.102 | 2.422 | 2.097 | 1.999 | 2.111 | 2.330 | 
| Path AZ | 1.000 | 1.052 | 0.795 | 0.784 | 0.830 | 0.821 | 0.692 | 0.695 | 0.749 | 0.802 | 0.847 | 0.768 | 0.767 | 0.711 | 0.798 | 0.638 | 0.662 | 0.793 | 0.883 | 0.971 | 0.933 | 0.952 | 1.044 | 1.083 | 1.195 | 1.301 | 1.393 | 1.474 | 1.560 | 1.625 | 1.507 | 1.437 | 1.392 | 1.373 | 1.422 | 1.550 | 1.530 | 1.326 | 1.325 | 1.419 | 1.394 | 1.362 | 1.353 | 1.279 | 1.236 | 1.187 | 1.225 | 1.419 | 1.670 | 1.433 | 1.409 | 1.418 | 1.389 | 1.316 | 1.363 | 1.395 | 1.385 | 1.419 | 1.403 | 1.457 | 1.356 | 1.309 | 1.207 | 1.250 | 1.292 | 1.304 | 1.206 | 1.166 | 1.137 | 1.157 | 1.062 | 0.930 | 0.867 | 0.896 | 0.803 | 0.711 | 0.865 | 0.816 | 0.739 | 0.619 | 
| Path BA | 1.000 | 1.060 | 0.967 | 0.992 | 1.041 | 1.023 | 1.087 | 1.105 | 1.411 | 1.274 | 1.347 | 1.313 | 1.322 | 1.389 | 1.474 | 1.579 | 1.532 | 1.494 | 1.309 | 1.188 | 1.196 | 1.173 | 1.231 | 1.192 | 1.141 | 1.409 | 1.587 | 1.589 | 1.630 | 1.544 | 1.548 | 1.666 | 1.611 | 1.665 | 1.575 | 1.575 | 1.491 | 1.420 | 1.590 | 1.695 | 1.888 | 1.831 | 1.904 | 1.840 | 1.739 | 1.877 | 1.938 | 1.997 | 2.293 | 2.316 | 2.627 | 2.799 | 2.979 | 2.418 | 2.964 | 2.844 | 2.782 | 2.947 | 3.011 | 3.053 | 2.549 | 2.132 | 2.357 | 2.305 | 2.268 | 2.327 | 2.320 | 2.380 | 2.253 | 2.589 | 2.629 | 3.029 | 3.345 | 3.559 | 4.046 | 4.137 | 3.959 | 4.031 | 4.955 | 4.609 | 
| Path BB | 1.000 | 0.977 | 0.878 | 1.090 | 1.066 | 1.012 | 1.213 | 1.104 | 1.207 | 1.231 | 1.262 | 1.302 | 1.290 | 1.161 | 1.106 | 1.038 | 1.041 | 1.078 | 1.102 | 1.107 | 1.368 | 1.347 | 1.345 | 1.284 | 1.469 | 1.391 | 1.448 | 1.698 | 2.035 | 2.028 | 1.954 | 2.019 | 1.954 | 1.709 | 1.903 | 2.079 | 2.147 | 2.238 | 2.294 | 2.069 | 1.696 | 1.630 | 1.447 | 1.613 | 1.617 | 1.380 | 1.473 | 1.488 | 1.484 | 1.394 | 1.244 | 1.208 | 1.403 | 1.363 | 1.345 | 1.417 | 1.527 | 1.783 | 2.301 | 2.271 | 2.444 | 3.123 | 3.100 | 3.535 | 3.482 | 3.318 | 3.192 | 3.230 | 3.369 | 3.591 | 3.773 | 3.683 | 3.772 | 3.612 | 3.462 | 4.245 | 4.206 | 4.232 | 4.202 | 3.925 | 
| Path BC | 1.000 | 0.957 | 1.200 | 1.255 | 1.373 | 1.381 | 1.353 | 1.297 | 1.379 | 1.170 | 1.251 | 1.174 | 1.144 | 1.169 | 1.496 | 1.435 | 1.335 | 1.339 | 1.198 | 1.401 | 1.295 | 1.220 | 0.991 | 1.020 | 0.957 | 0.973 | 1.006 | 1.064 | 1.361 | 1.464 | 1.559 | 1.391 | 1.627 | 1.757 | 1.878 | 1.912 | 2.264 | 2.322 | 2.359 | 2.468 | 2.531 | 2.037 | 2.327 | 2.231 | 2.224 | 2.195 | 1.948 | 1.906 | 1.978 | 2.166 | 1.969 | 1.956 | 1.995 | 1.914 | 1.941 | 2.137 | 2.462 | 2.576 | 3.313 | 3.358 | 2.904 | 2.957 | 3.124 | 2.841 | 2.849 | 2.805 | 2.661 | 2.505 | 2.418 | 2.237 | 2.550 | 2.531 | 2.880 | 2.657 | 2.470 | 2.457 | 2.276 | 2.064 | 2.227 | 2.166 | 
| Path BD | 1.000 | 0.998 | 0.986 | 1.064 | 1.157 | 1.001 | 1.000 | 0.995 | 0.921 | 0.993 | 0.924 | 1.039 | 1.103 | 1.044 | 1.112 | 0.983 | 0.969 | 0.846 | 0.782 | 0.873 | 0.936 | 1.046 | 1.099 | 1.036 | 0.909 | 0.896 | 0.959 | 1.021 | 1.127 | 1.163 | 1.265 | 1.276 | 1.260 | 1.298 | 1.351 | 1.670 | 1.815 | 1.741 | 1.910 | 1.818 | 1.680 | 1.636 | 1.823 | 1.741 | 1.726 | 1.746 | 1.921 | 1.937 | 1.897 | 1.904 | 2.259 | 2.714 | 2.843 | 3.122 | 3.662 | 3.213 | 3.192 | 3.150 | 3.397 | 3.523 | 3.271 | 3.056 | 3.347 | 3.952 | 4.053 | 3.823 | 3.778 | 4.037 | 4.080 | 3.467 | 2.856 | 2.583 | 2.716 | 3.031 | 2.812 | 2.814 | 2.243 | 2.509 | 2.258 | 2.000 | 
| Path BE | 1.000 | 1.091 | 1.024 | 1.238 | 1.422 | 1.292 | 1.381 | 1.332 | 1.086 | 1.153 | 1.400 | 1.542 | 1.402 | 1.425 | 1.683 | 1.628 | 1.510 | 1.523 | 1.410 | 1.493 | 1.928 | 1.936 | 2.123 | 2.080 | 2.186 | 2.015 | 2.029 | 1.859 | 1.821 | 1.713 | 1.818 | 1.738 | 1.760 | 1.859 | 1.808 | 1.921 | 2.265 | 2.239 | 2.152 | 1.715 | 1.879 | 1.851 | 1.798 | 1.658 | 1.576 | 1.657 | 1.667 | 1.644 | 2.087 | 2.210 | 2.195 | 2.391 | 2.402 | 2.376 | 2.474 | 2.500 | 2.510 | 2.248 | 2.436 | 2.290 | 2.347 | 2.429 | 2.263 | 2.594 | 2.513 | 2.495 | 2.454 | 2.382 | 2.244 | 2.119 | 1.899 | 1.816 | 1.864 | 2.042 | 2.211 | 2.060 | 2.003 | 2.117 | 2.389 | 2.478 | 
| Path BF | 1.000 | 0.991 | 0.875 | 0.821 | 0.831 | 0.725 | 0.788 | 0.731 | 0.776 | 0.738 | 0.682 | 0.719 | 0.691 | 0.655 | 0.614 | 0.665 | 0.640 | 0.672 | 0.728 | 0.752 | 0.710 | 0.786 | 0.807 | 0.836 | 0.991 | 1.085 | 1.035 | 0.994 | 1.018 | 0.949 | 0.850 | 0.832 | 0.863 | 0.820 | 0.861 | 0.819 | 0.797 | 0.782 | 0.744 | 0.716 | 0.674 | 0.624 | 0.520 | 0.545 | 0.535 | 0.592 | 0.600 | 0.612 | 0.714 | 0.616 | 0.641 | 0.669 | 0.649 | 0.653 | 0.626 | 0.685 | 0.631 | 0.729 | 0.732 | 0.688 | 0.749 | 0.752 | 0.870 | 0.894 | 0.868 | 0.905 | 0.850 | 0.812 | 0.808 | 0.697 | 0.677 | 0.759 | 0.809 | 0.891 | 0.870 | 0.826 | 0.771 | 0.831 | 0.812 | 0.849 | 
| Lower percentile | 1.000 | 0.888 | 0.854 | 0.749 | 0.689 | 0.680 | 0.665 | 0.648 | 0.708 | 0.718 | 0.674 | 0.741 | 0.750 | 0.698 | 0.756 | 0.659 | 0.657 | 0.641 | 0.682 | 0.648 | 0.670 | 0.676 | 0.646 | 0.645 | 0.577 | 0.503 | 0.494 | 0.572 | 0.558 | 0.594 | 0.608 | 0.581 | 0.531 | 0.520 | 0.542 | 0.542 | 0.485 | 0.535 | 0.606 | 0.563 | 0.537 | 0.589 | 0.532 | 0.539 | 0.532 | 0.588 | 0.590 | 0.604 | 0.617 | 0.599 | 0.570 | 0.580 | 0.568 | 0.531 | 0.475 | 0.457 | 0.516 | 0.487 | 0.554 | 0.505 | 0.441 | 0.405 | 0.374 | 0.363 | 0.387 | 0.380 | 0.383 | 0.339 | 0.369 | 0.361 | 0.385 | 0.367 | 0.367 | 0.357 | 0.336 | 0.326 | 0.334 | 0.336 | 0.351 | 0.409 | 
| Median | 1.000 | 1.029 | 0.999 | 1.043 | 1.060 | 1.017 | 1.091 | 1.100 | 1.093 | 1.127 | 1.157 | 1.103 | 1.140 | 1.062 | 1.105 | 1.118 | 1.121 | 1.185 | 1.169 | 1.127 | 1.087 | 1.112 | 1.113 | 1.175 | 1.212 | 1.251 | 1.223 | 1.311 | 1.260 | 1.255 | 1.370 | 1.373 | 1.371 | 1.342 | 1.339 | 1.458 | 1.285 | 1.347 | 1.332 | 1.423 | 1.387 | 1.328 | 1.305 | 1.302 | 1.293 | 1.308 | 1.402 | 1.389 | 1.309 | 1.349 | 1.435 | 1.414 | 1.427 | 1.505 | 1.407 | 1.427 | 1.479 | 1.484 | 1.427 | 1.372 | 1.345 | 1.400 | 1.330 | 1.391 | 1.475 | 1.463 | 1.397 | 1.456 | 1.512 | 1.584 | 1.644 | 1.600 | 1.651 | 1.528 | 1.573 | 1.681 | 1.782 | 1.807 | 1.793 | 1.762 | 
| Upper percentile | 1.000 | 1.165 | 1.210 | 1.356 | 1.470 | 1.432 | 1.506 | 1.608 | 1.598 | 1.519 | 1.556 | 1.727 | 1.790 | 1.825 | 1.900 | 1.888 | 2.044 | 1.951 | 2.153 | 2.338 | 2.056 | 2.162 | 2.164 | 2.233 | 2.229 | 2.085 | 2.134 | 2.300 | 2.323 | 2.551 | 2.528 | 2.504 | 2.335 | 2.285 | 2.496 | 2.751 | 2.647 | 3.017 | 2.993 | 2.955 | 3.040 | 3.024 | 2.976 | 2.834 | 3.049 | 2.921 | 3.028 | 3.409 | 3.156 | 3.159 | 3.139 | 3.472 | 3.775 | 3.707 | 4.233 | 3.908 | 3.764 | 3.999 | 4.056 | 4.312 | 4.660 | 4.442 | 4.575 | 4.434 | 4.798 | 4.758 | 4.746 | 4.991 | 4.416 | 4.741 | 4.553 | 4.064 | 4.161 | 4.287 | 4.267 | 4.567 | 5.063 | 5.478 | 5.867 | 5.475 | 
| Original history | 1.000 | 0.876 | 0.746 | 0.780 | 0.759 | 0.865 | 0.875 | 1.199 | 1.215 | 1.232 | 1.253 | 1.288 | 1.222 | 1.159 | 1.194 | 1.222 | 1.448 | 1.808 | 1.825 | 1.788 | 2.029 | 2.072 | 2.103 | 2.073 | 2.069 | 2.174 | 2.018 | 2.025 | 2.251 | 2.038 | 1.912 | 1.980 | 1.732 | 1.714 | 1.457 | 1.419 | 1.345 | 1.501 | 1.425 | 1.446 | 1.412 | 1.550 | 1.488 | 1.533 | 1.408 | 1.128 | 1.011 | 0.960 | 0.892 | 0.974 | 0.958 | 1.131 | 1.034 | 0.974 | 1.012 | 1.139 | 1.112 | 1.107 | 1.128 | 1.124 | 1.024 | 1.015 | 0.964 | 0.812 | 0.863 | 0.830 | 0.775 | 0.865 | 0.854 | 0.915 | 0.909 | 0.894 | 0.900 | 0.919 | 1.193 | 1.186 | 1.196 | 1.209 | 1.334 | 1.292 | 

**Chart data $\cdot$ Pool-return differences across rebuilt histories $\cdot$ 1-day blocks**

Summary of pool-return differences
| Statistic | LP/xyk difference, percentage points per year | 
| --- | --- |
| Minimum | −22.31 | 
| Lower quartile | −1.75 | 
| Median | +0.33 | 
| Upper quartile | +1.21 | 
| Maximum | +10.86 | 
| Original history | +1.65 | 

Proposal minus current LP/xyk, percentage points per year
| LP/xyk difference, percentage points per year | Pair kept in this analysis? | 
| --- | --- |
| +1.20 | Yes | 
| −0.18 | Yes | 
| undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| +1.15 | Yes | 
| +0.94 | Yes | 
| +0.54 | Yes | 
| +2.00 | Yes | 
| −1.75 | Yes | 
| +1.21 | Yes | 
| +6.91 | Yes | 
| −6.62 | Yes | 
| +10.86 | Yes | 
| −2.13 | Yes | 
| −1.22 | Yes | 
| −0.27 | Yes | 
| −5.98 | Yes | 
| +0.94 | Yes | 
| +1.75 | Yes | 
| undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| −9.95 | Yes | 
| −22.31 | Yes | 
| +0.33 | Yes | 
| −2.50 | Yes | 
| +0.98 | Yes | 
| −1.66 | Yes | 
| −20.00 | Yes | 
| −0.52 | Yes | 
| +4.72 | Yes | 
| +0.09 | Yes | 
| +1.36 | Yes | 
| +1.66 | Yes |


# E. Tests of the YB proposal {#proposal}

**The proposal’s results depend on [financing](./#glossary/financing), update timing and the market history.**

- [E1 The proposal’s original test and its separate changes](./#proposal/test) — The original gain disappears in tested variants using recorded operation times.
- [E2 The early gain comes from changing financing](./#proposal/channels) — Financing changes explain the early [LP/xyk](./#glossary/lp-xyk) advantage.
- [E3 Customers receive worse prices in the quote test](./#proposal/demand) — The proposal raises the cost of the tested customer trades.
- [E4 Selected settings on unused and older data](./#proposal/selection) — Selected settings show no reliable advantage after matching financing on unused data.


# E1 The proposal’s original test and its separate changes {#proposal/test}

**The proposal’s original gain disappears in the tested variants using recorded operation times.**

The original test uses the [arbitrage](./#glossary/arbitrage)-only setup. Arbitrage means trading price differences between markets for profit. The timing tests change when the pool can update.

An [LP](./#glossary/lp) owns a share of the pool. [LP/xyk](./#glossary/lp-xyk) measures share growth above a reference, after [donation](./#glossary/donation) charges. The reference pool charges no trading fees. Both pools face the same market prices.

Rates use [percentage points](./#glossary/percentage-point) per year, or pp/yr. The [rate conventions](./#settings) explain the logarithmic calculation.

**Measure:** LP/xyk difference, in percentage points per year.

**Compared:** The full proposal and each partial package with deployed current settings.

**Same for both:** The tuning price history, or each shared rebuilt history.

**Higher means:** A larger advantage for the changed package.

The YB holder borrows to own pool shares. Its remaining wealth is the share value after subtracting debt. Holder growth here is measured in [ETH](./#glossary/eth), Ethereum’s asset.

The original test supplies hourly update opportunities. Its tuning history runs from 2025-03-24 to 30 September 2026.

| Test: proposal minus current settings | LP/xyk, pp/yr | Holder wealth in ETH: growth difference, pp/yr | 
| --- | --- | --- |
| Post’s test | +1.65 | +4.48 | 
| Timing test without recorded user-update times | +2.12 | +5.09 | 
| Timing test with recorded user-update times | [−0.18, −0.04] | [+0.54, +0.67] | 

The claimed LP/xyk gain is +1.65 pp/yr. The claimed gain in holder growth is +4.48 pp/yr. Both compare the proposal with current settings.

Without recorded user-update times, the timing simulator gives +2.12 pp/yr of LP/xyk advantage. With those times, the smallest and largest results are [−0.18, −0.04] pp/yr.

Timing variants also change starting times and use observed [crvUSD](./#glossary/crvusd) prices. crvUSD is the borrowing token. Variants labelled “with updates” add recorded user-operation opportunities. They do not copy users’ asset transfers.

Ranges show the lowest and highest outcomes across those variants. On the final rally, the proposal stops moving [price_scale](./#glossary/price_scale), its price centre. Growth in [market value](./#glossary/market-value) per share then falls below current settings.

The pool’s internal profit records measure something other than market value. The holder’s wealth after debt is also a separate measure. Those measures can show different advantages.

### Which changes account for the original result?

A component test applies only part of the proposal. Changing [financing](./#glossary/financing) parameters alone lowers LP/xyk on the tuning history. Changing only the external-price policy also lowers it. Combining the changes produces the original gain.

> **Common misunderstanding:** “Each part of the proposal adds to its gain.”
>
> **What is true.**
>
> On the tuning history, changing financing alone lowers LP/xyk. Changing only the external-price rules also lowers it. Only the combination produces the original gain.

| Setting | Deployed current | Proposed, rounded | 
| --- | --- | --- |
| Rules for external prices | Pool rules based on its traded prices | External price [reports](./#glossary/report) guide fees and the pool’s central price | 
| Donation rate, %/yr | 5 | 1.2 | 
| Recorded profit protected from spending, % | 45 | 42.9 | 
| [LevAMM](./#glossary/levamm) fee, % | 1.3 | 1.5 | 

Donations supply outside capital to the pool. Reserved profit is the share of recorded profit protected against spending on price-centre moves. LevAMM manages the debt-financed YB holding.

“Parameters only” is the financing-only package. It changes donations, reserved profit and the LevAMM fee. “External-price policy only” changes the rules using external reference prices. “Keep current” leaves the named setting unchanged and applies the other changes.

| Changes applied | Arbitrage only: LP/xyk difference, pp/yr | Arbitrage only: holder-growth difference in ETH, pp/yr | Timing variants: LP/xyk difference, pp/yr | Timing variants: holder-growth difference in ETH, pp/yr | 
| --- | --- | --- | --- | --- |
| Full proposal | +1.65 | +4.48 | −0.18 to −0.04 | +0.54 to +0.67 | 
| Parameters only | −3.03 | −2.34 | −1.95 to −1.48 | −0.39 to +0.02 | 
| Proposal, keeping current donations | −2.54 | −7.39 | −2.40 to −2.18 | −7.31 to −6.45 | 
| Proposal, keeping current reserved profit | −1.29 | +2.34 | −4.76 to −3.76 | −6.39 to −4.24 | 
| Proposal, keeping the current LevAMM fee | +1.82 | +5.04 | −0.61 to −0.21 | −0.47 to +0.04 | 
| External-price policy only | −2.13 | −6.39 | −1.85 to −1.72 | −5.83 to −5.15 | 

The separate parts lose more LP/xyk than the post’s claimed gain. Parameters alone give −3.03 pp/yr. The external-price policy alone gives −2.13 pp/yr. The full proposal gains +1.65 pp/yr under arbitrage only.

The full proposal also gains when it keeps the current LevAMM fee under arbitrage only. The [settings table](./#settings) defines the forum proposal’s complete package.

### The same changes on rebuilt histories

**Measure:** Separate pool and holder growth differences, in percentage points per year.

**Compared:** Each package with deployed current settings.

**Same for both:** Each shared rebuilt path from the tuning history.

**Higher means:** A larger advantage for the changed package.

Each treatment has 100 rebuilt paths. The full proposal has a positive median LP/xyk difference. Parameters alone and the external-price policy alone have negative medians.

**LP/xyk:** Markers show median differences from deployed current settings. The histories draw 180-day stretches from the tuning history. Intervals span the middle 95% of retained outcomes. The original-history result has a separate marker.

**LP/xyk:** A larger value favours the named package. This chart measures LP/xyk. The tables show retained and total pairs. Individual histories appear in More detail.

**[YB position](./#glossary/yb-position) in ETH:** Markers show median differences from deployed current settings. The histories draw 180-day stretches from the tuning history. Intervals span the middle 95% of retained outcomes. The original-history result has a separate marker.

**YB position in ETH:** A larger value favours the named package. This chart measures holder wealth in ETH. The tables show retained and total pairs. Individual histories appear in More detail.

The archive excludes a pair when either holder’s wealth after debt becomes zero or negative during its path. This exclusion also applies to pool-return summaries.

“Positive / retained” counts positive differences among retained pairs. “Retained / total” shows how many pairs remain after exclusions.

**More detail: summaries for each measure**

| Changes applied | Growth measure | Median difference, pp/yr | Middle 95% range, pp/yr | Positive differences / retained pairs | Retained pairs / all pairs | 
| --- | --- | --- | --- | --- | --- |
| Full proposal | LP/xyk | +1.90 | −7.89 to +7.12 | 84 of 100 | 100 of 100 | 
| Full proposal | Holder wealth in ETH | +5.44 | −14.11 to +14.91 | 88 of 100 | 100 of 100 | 
| Parameters only | LP/xyk | −2.51 | −29.57 to +2.30 | 29 of 95 | 95 of 100 | 
| Parameters only | Holder wealth in ETH | −2.84 | −63.71 to +7.75 | 43 of 95 | 95 of 100 | 
| External-price policy only | LP/xyk | −1.70 | −2.96 to +4.72 | 13 of 100 | 100 of 100 | 
| External-price policy only | Holder wealth in ETH | −5.74 | −8.89 to +6.63 | 11 of 100 | 100 of 100 | 

The histories draw 180-day stretches from the same tuning history.

**More detail: individual pool-return outcomes**

**LP/xyk:** Each point shows one retained paired history for the named package. The horizontal position shows the growth difference from current settings. The measure is LP/xyk.

**LP/xyk:** Diamonds mark the original-history outcomes. Rows keep the outcomes for each package together. The data table also identifies excluded pairs.

**More detail: individual holder outcomes**

**YB position in ETH:** Each point shows one retained paired history for the named package. The horizontal position shows the growth difference from current settings. The measure is holder wealth in ETH.

**YB position in ETH:** Diamonds mark the original-history outcomes. Rows keep the outcomes for each package together. The data table also identifies excluded pairs.

The timing simulator copies operation times without users’ asset amounts. It changes update timing instead of estimating customer demand. Modelling customer activity remains an open problem across the field.

These component tests start from a template and use the entire tuning history. The [financing test](./#proposal/channels) starts from observed [WETH](./#glossary/weth) reserves and available profit. It changes financing and price rules separately. The two tests answer different questions.

[← previous](./#resampling/why)[next $\to$](./#proposal/channels)

**Chart data $\cdot$ Combined changes and their separate parts: LP/xyk**

LP/xyk difference, percentage points per year
| Changes applied | Median LP/xyk difference, pp/yr | Middle 95% outcome range, LP/xyk difference, pp/yr | Original-history LP/xyk difference, pp/yr | Pairs kept / all pairs | 
| --- | --- | --- | --- | --- |
| Full proposal | +1.90 | −7.89 to +7.12 | +1.65 | 100 / 100 | 
| Parameters only | −2.51 | −29.57 to +2.30 | −3.03 | 95 / 100 | 
| External-price policy only | −1.70 | −2.96 to +4.72 | −2.13 | 100 / 100 | 

**Chart data $\cdot$ Combined changes and their separate parts: holder wealth in ETH**

Growth difference in holder wealth in ETH, percentage points per year
| Changes applied | Median Growth difference in holder wealth in ETH, pp/yr | Middle 95% outcome range, Growth difference in holder wealth in ETH, pp/yr | Original-history Growth difference in holder wealth in ETH, pp/yr | Pairs kept / all pairs | 
| --- | --- | --- | --- | --- |
| Full proposal | +5.44 | −14.11 to +14.91 | +4.48 | 100 / 100 | 
| Parameters only | −2.84 | −63.71 to +7.75 | −2.34 | 95 / 100 | 
| External-price policy only | −5.74 | −8.89 to +6.63 | −6.39 | 100 / 100 | 

**Chart data $\cdot$ Individual retained histories: LP/xyk**

LP/xyk difference, percentage points per year
| Changes applied | Outcome, LP/xyk difference, percentage points per year | Pair kept in this analysis? | 
| --- | --- | --- |
| Full proposal — original history | +1.65 | Yes | 
| Full proposal | +1.121 | Yes | 
| Full proposal | −33.370 | Yes | 
| Full proposal | −3.395 | Yes | 
| Full proposal | +1.855 | Yes | 
| Full proposal | +2.029 | Yes | 
| Full proposal | −2.011 | Yes | 
| Full proposal | +0.269 | Yes | 
| Full proposal | −10.082 | Yes | 
| Full proposal | +1.789 | Yes | 
| Full proposal | +2.926 | Yes | 
| Full proposal | +7.770 | Yes | 
| Full proposal | +1.651 | Yes | 
| Full proposal | +1.771 | Yes | 
| Full proposal | +2.790 | Yes | 
| Full proposal | +2.060 | Yes | 
| Full proposal | −11.157 | Yes | 
| Full proposal | +3.130 | Yes | 
| Full proposal | +1.782 | Yes | 
| Full proposal | +1.582 | Yes | 
| Full proposal | +1.971 | Yes | 
| Full proposal | +1.897 | Yes | 
| Full proposal | +4.618 | Yes | 
| Full proposal | +4.504 | Yes | 
| Full proposal | +3.077 | Yes | 
| Full proposal | +1.699 | Yes | 
| Full proposal | +16.272 | Yes | 
| Full proposal | +3.115 | Yes | 
| Full proposal | +2.542 | Yes | 
| Full proposal | +1.810 | Yes | 
| Full proposal | +0.225 | Yes | 
| Full proposal | −5.460 | Yes | 
| Full proposal | +2.214 | Yes | 
| Full proposal | +1.887 | Yes | 
| Full proposal | +2.725 | Yes | 
| Full proposal | +8.214 | Yes | 
| Full proposal | +2.574 | Yes | 
| Full proposal | +1.597 | Yes | 
| Full proposal | +1.697 | Yes | 
| Full proposal | +1.928 | Yes | 
| Full proposal | +2.149 | Yes | 
| Full proposal | +3.577 | Yes | 
| Full proposal | +1.612 | Yes | 
| Full proposal | +1.717 | Yes | 
| Full proposal | +3.095 | Yes | 
| Full proposal | +1.899 | Yes | 
| Full proposal | +1.820 | Yes | 
| Full proposal | +2.136 | Yes | 
| Full proposal | +3.099 | Yes | 
| Full proposal | +1.683 | Yes | 
| Full proposal | +2.327 | Yes | 
| Full proposal | +1.959 | Yes | 
| Full proposal | −2.197 | Yes | 
| Full proposal | +0.254 | Yes | 
| Full proposal | +1.627 | Yes | 
| Full proposal | +2.176 | Yes | 
| Full proposal | +1.403 | Yes | 
| Full proposal | +1.969 | Yes | 
| Full proposal | +5.821 | Yes | 
| Full proposal | +2.089 | Yes | 
| Full proposal | +3.026 | Yes | 
| Full proposal | +0.697 | Yes | 
| Full proposal | +2.461 | Yes | 
| Full proposal | +3.386 | Yes | 
| Full proposal | −2.003 | Yes | 
| Full proposal | +1.860 | Yes | 
| Full proposal | +1.786 | Yes | 
| Full proposal | +2.735 | Yes | 
| Full proposal | −2.538 | Yes | 
| Full proposal | −0.037 | Yes | 
| Full proposal | −3.192 | Yes | 
| Full proposal | +1.525 | Yes | 
| Full proposal | +1.777 | Yes | 
| Full proposal | +1.783 | Yes | 
| Full proposal | +1.992 | Yes | 
| Full proposal | +1.291 | Yes | 
| Full proposal | +2.705 | Yes | 
| Full proposal | +2.717 | Yes | 
| Full proposal | +2.864 | Yes | 
| Full proposal | +2.551 | Yes | 
| Full proposal | +3.285 | Yes | 
| Full proposal | +5.119 | Yes | 
| Full proposal | +1.634 | Yes | 
| Full proposal | +1.857 | Yes | 
| Full proposal | +6.068 | Yes | 
| Full proposal | +6.399 | Yes | 
| Full proposal | −2.097 | Yes | 
| Full proposal | −0.838 | Yes | 
| Full proposal | +3.095 | Yes | 
| Full proposal | −0.020 | Yes | 
| Full proposal | +2.946 | Yes | 
| Full proposal | +3.470 | Yes | 
| Full proposal | +1.951 | Yes | 
| Full proposal | +3.402 | Yes | 
| Full proposal | +1.486 | Yes | 
| Full proposal | +1.939 | Yes | 
| Full proposal | +2.941 | Yes | 
| Full proposal | −1.346 | Yes | 
| Full proposal | −1.822 | Yes | 
| Full proposal | +1.775 | Yes | 
| Full proposal | +0.350 | Yes | 
| Parameters only — original history | −3.03 | Yes | 
| Parameters only | −1.636 | Yes | 
| Parameters only | −20.535 | Yes | 
| Parameters only | −2.488 | Yes | 
| Parameters only | −39.275 | Yes | 
| Parameters only | +1.339 | Yes | 
| Parameters only | −1.780 | Yes | 
| Parameters only | −26.248 | Yes | 
| Parameters only | −0.728 | Yes | 
| Parameters only | +0.656 | Yes | 
| Parameters only | −14.184 | Yes | 
| Parameters only | −13.344 | Yes | 
| Parameters only | −1.113 | Yes | 
| Parameters only | −9.457 | Yes | 
| Parameters only | −0.467 | Yes | 
| Parameters only | −2.652 | Yes | 
| Parameters only | −17.222 | Yes | 
| Parameters only | +1.394 | Yes | 
| Parameters only | −0.110 | Yes | 
| Parameters only | +0.516 | Yes | 
| Parameters only | +2.085 | Yes | 
| Parameters only | +1.784 | Yes | 
| Parameters only | −20.463 | Yes | 
| Parameters only | −19.354 | Yes | 
| Parameters only | +1.389 | Yes | 
| Parameters only | +0.958 | Yes | 
| Parameters only | −8.098 | Yes | 
| Parameters only | −16.570 | Yes | 
| Parameters only | undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| Parameters only | +0.884 | Yes | 
| Parameters only | +2.411 | Yes | 
| Parameters only | +1.910 | Yes | 
| Parameters only | +0.580 | Yes | 
| Parameters only | +1.996 | Yes | 
| Parameters only | +1.387 | Yes | 
| Parameters only | −28.330 | Yes | 
| Parameters only | −7.161 | Yes | 
| Parameters only | −16.933 | Yes | 
| Parameters only | −3.586 | Yes | 
| Parameters only | −3.187 | Yes | 
| Parameters only | −1.348 | Yes | 
| Parameters only | −13.496 | Yes | 
| Parameters only | −11.720 | Yes | 
| Parameters only | −0.272 | Yes | 
| Parameters only | −29.953 | Yes | 
| Parameters only | +1.795 | Yes | 
| Parameters only | undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| Parameters only | +0.750 | Yes | 
| Parameters only | +2.595 | Yes | 
| Parameters only | undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| Parameters only | −13.389 | Yes | 
| Parameters only | −4.896 | Yes | 
| Parameters only | −0.884 | Yes | 
| Parameters only | −22.765 | Yes | 
| Parameters only | −0.102 | Yes | 
| Parameters only | −0.474 | Yes | 
| Parameters only | +0.607 | Yes | 
| Parameters only | −5.813 | Yes | 
| Parameters only | −0.817 | Yes | 
| Parameters only | +0.942 | Yes | 
| Parameters only | −12.183 | Yes | 
| Parameters only | −14.020 | Yes | 
| Parameters only | −5.786 | Yes | 
| Parameters only | −16.419 | Yes | 
| Parameters only | −6.840 | Yes | 
| Parameters only | −11.362 | Yes | 
| Parameters only | +0.616 | Yes | 
| Parameters only | undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| Parameters only | −28.870 | Yes | 
| Parameters only | −2.514 | Yes | 
| Parameters only | −2.102 | Yes | 
| Parameters only | −18.832 | Yes | 
| Parameters only | −13.875 | Yes | 
| Parameters only | +1.245 | Yes | 
| Parameters only | +0.353 | Yes | 
| Parameters only | −31.763 | Yes | 
| Parameters only | −12.645 | Yes | 
| Parameters only | −12.539 | Yes | 
| Parameters only | −2.743 | Yes | 
| Parameters only | −10.836 | Yes | 
| Parameters only | −13.019 | Yes | 
| Parameters only | −4.176 | Yes | 
| Parameters only | −1.497 | Yes | 
| Parameters only | −0.455 | Yes | 
| Parameters only | −7.703 | Yes | 
| Parameters only | −1.584 | Yes | 
| Parameters only | undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| Parameters only | −18.712 | Yes | 
| Parameters only | −25.786 | Yes | 
| Parameters only | −25.431 | Yes | 
| Parameters only | +0.013 | Yes | 
| Parameters only | +0.517 | Yes | 
| Parameters only | +2.001 | Yes | 
| Parameters only | −6.779 | Yes | 
| Parameters only | +1.467 | Yes | 
| Parameters only | +0.760 | Yes | 
| Parameters only | +2.940 | Yes | 
| Parameters only | −5.558 | Yes | 
| Parameters only | −1.104 | Yes | 
| Parameters only | +0.840 | Yes | 
| Parameters only | −17.882 | Yes | 
| External-price policy only — original history | −2.13 | Yes | 
| External-price policy only | −2.573 | Yes | 
| External-price policy only | −1.908 | Yes | 
| External-price policy only | −1.580 | Yes | 
| External-price policy only | +5.302 | Yes | 
| External-price policy only | −1.574 | Yes | 
| External-price policy only | −2.807 | Yes | 
| External-price policy only | −0.036 | Yes | 
| External-price policy only | −2.593 | Yes | 
| External-price policy only | −2.305 | Yes | 
| External-price policy only | −0.946 | Yes | 
| External-price policy only | +4.080 | Yes | 
| External-price policy only | −2.347 | Yes | 
| External-price policy only | −2.788 | Yes | 
| External-price policy only | −1.435 | Yes | 
| External-price policy only | −2.124 | Yes | 
| External-price policy only | −1.789 | Yes | 
| External-price policy only | −1.014 | Yes | 
| External-price policy only | −0.803 | Yes | 
| External-price policy only | −2.441 | Yes | 
| External-price policy only | −1.308 | Yes | 
| External-price policy only | −1.985 | Yes | 
| External-price policy only | +0.465 | Yes | 
| External-price policy only | +0.715 | Yes | 
| External-price policy only | −1.285 | Yes | 
| External-price policy only | −2.164 | Yes | 
| External-price policy only | +14.373 | Yes | 
| External-price policy only | −0.247 | Yes | 
| External-price policy only | −1.979 | Yes | 
| External-price policy only | −1.892 | Yes | 
| External-price policy only | −1.712 | Yes | 
| External-price policy only | −1.307 | Yes | 
| External-price policy only | −2.097 | Yes | 
| External-price policy only | −0.839 | Yes | 
| External-price policy only | −1.525 | Yes | 
| External-price policy only | +3.934 | Yes | 
| External-price policy only | −1.988 | Yes | 
| External-price policy only | −2.453 | Yes | 
| External-price policy only | −2.229 | Yes | 
| External-price policy only | −2.078 | Yes | 
| External-price policy only | −2.521 | Yes | 
| External-price policy only | −1.119 | Yes | 
| External-price policy only | −2.523 | Yes | 
| External-price policy only | −2.093 | Yes | 
| External-price policy only | +2.436 | Yes | 
| External-price policy only | −1.468 | Yes | 
| External-price policy only | −1.942 | Yes | 
| External-price policy only | −2.380 | Yes | 
| External-price policy only | −1.217 | Yes | 
| External-price policy only | −1.328 | Yes | 
| External-price policy only | −1.537 | Yes | 
| External-price policy only | −2.825 | Yes | 
| External-price policy only | −1.704 | Yes | 
| External-price policy only | −2.685 | Yes | 
| External-price policy only | −1.795 | Yes | 
| External-price policy only | −1.657 | Yes | 
| External-price policy only | −2.276 | Yes | 
| External-price policy only | −2.640 | Yes | 
| External-price policy only | +1.239 | Yes | 
| External-price policy only | −1.517 | Yes | 
| External-price policy only | −1.042 | Yes | 
| External-price policy only | −1.762 | Yes | 
| External-price policy only | −1.696 | Yes | 
| External-price policy only | −1.006 | Yes | 
| External-price policy only | −0.380 | Yes | 
| External-price policy only | −1.046 | Yes | 
| External-price policy only | −2.465 | Yes | 
| External-price policy only | −2.191 | Yes | 
| External-price policy only | +1.273 | Yes | 
| External-price policy only | −2.841 | Yes | 
| External-price policy only | −2.159 | Yes | 
| External-price policy only | −1.940 | Yes | 
| External-price policy only | −2.625 | Yes | 
| External-price policy only | −1.770 | Yes | 
| External-price policy only | −2.323 | Yes | 
| External-price policy only | −0.153 | Yes | 
| External-price policy only | −2.002 | Yes | 
| External-price policy only | −1.035 | Yes | 
| External-price policy only | −1.873 | Yes | 
| External-price policy only | −2.284 | Yes | 
| External-price policy only | −0.530 | Yes | 
| External-price policy only | +12.528 | Yes | 
| External-price policy only | −3.075 | Yes | 
| External-price policy only | −0.687 | Yes | 
| External-price policy only | +1.778 | Yes | 
| External-price policy only | +1.467 | Yes | 
| External-price policy only | −1.952 | Yes | 
| External-price policy only | −2.298 | Yes | 
| External-price policy only | −1.406 | Yes | 
| External-price policy only | −1.637 | Yes | 
| External-price policy only | −0.315 | Yes | 
| External-price policy only | −0.909 | Yes | 
| External-price policy only | −2.037 | Yes | 
| External-price policy only | −1.201 | Yes | 
| External-price policy only | +1.081 | Yes | 
| External-price policy only | −1.222 | Yes | 
| External-price policy only | −1.608 | Yes | 
| External-price policy only | −4.252 | Yes | 
| External-price policy only | −1.280 | Yes | 
| External-price policy only | −2.223 | Yes | 
| External-price policy only | −3.332 | Yes | 

**Chart data $\cdot$ Individual retained histories: holder wealth in ETH**

Growth difference in holder wealth in ETH, percentage points per year
| Changes applied | Outcome, Growth difference in holder wealth in ETH, percentage points per year | Pair kept in this analysis? | 
| --- | --- | --- |
| Full proposal — original history | +4.48 | Yes | 
| Full proposal | +3.443 | Yes | 
| Full proposal | −67.482 | Yes | 
| Full proposal | −1.486 | Yes | 
| Full proposal | +4.692 | Yes | 
| Full proposal | +5.396 | Yes | 
| Full proposal | +0.881 | Yes | 
| Full proposal | +2.530 | Yes | 
| Full proposal | −17.301 | Yes | 
| Full proposal | +5.642 | Yes | 
| Full proposal | +5.940 | Yes | 
| Full proposal | +16.808 | Yes | 
| Full proposal | +4.636 | Yes | 
| Full proposal | +5.342 | Yes | 
| Full proposal | +7.046 | Yes | 
| Full proposal | +6.006 | Yes | 
| Full proposal | −22.908 | Yes | 
| Full proposal | +7.173 | Yes | 
| Full proposal | +4.901 | Yes | 
| Full proposal | +4.954 | Yes | 
| Full proposal | +5.480 | Yes | 
| Full proposal | +5.469 | Yes | 
| Full proposal | +9.007 | Yes | 
| Full proposal | +11.124 | Yes | 
| Full proposal | +6.675 | Yes | 
| Full proposal | +5.418 | Yes | 
| Full proposal | +35.577 | Yes | 
| Full proposal | +6.112 | Yes | 
| Full proposal | +6.099 | Yes | 
| Full proposal | +4.868 | Yes | 
| Full proposal | +3.358 | Yes | 
| Full proposal | −10.584 | Yes | 
| Full proposal | +5.490 | Yes | 
| Full proposal | +5.337 | Yes | 
| Full proposal | +6.244 | Yes | 
| Full proposal | +14.217 | Yes | 
| Full proposal | +5.812 | Yes | 
| Full proposal | +4.845 | Yes | 
| Full proposal | +4.950 | Yes | 
| Full proposal | +5.783 | Yes | 
| Full proposal | +5.962 | Yes | 
| Full proposal | +9.383 | Yes | 
| Full proposal | +4.461 | Yes | 
| Full proposal | +4.918 | Yes | 
| Full proposal | +6.825 | Yes | 
| Full proposal | +5.446 | Yes | 
| Full proposal | +5.015 | Yes | 
| Full proposal | +6.014 | Yes | 
| Full proposal | +7.011 | Yes | 
| Full proposal | +4.717 | Yes | 
| Full proposal | +6.150 | Yes | 
| Full proposal | +4.780 | Yes | 
| Full proposal | −4.414 | Yes | 
| Full proposal | +2.676 | Yes | 
| Full proposal | +5.084 | Yes | 
| Full proposal | +4.793 | Yes | 
| Full proposal | +4.512 | Yes | 
| Full proposal | +5.551 | Yes | 
| Full proposal | +13.952 | Yes | 
| Full proposal | +5.829 | Yes | 
| Full proposal | +6.430 | Yes | 
| Full proposal | +1.329 | Yes | 
| Full proposal | +5.884 | Yes | 
| Full proposal | +7.453 | Yes | 
| Full proposal | −4.363 | Yes | 
| Full proposal | +4.921 | Yes | 
| Full proposal | +5.429 | Yes | 
| Full proposal | +6.251 | Yes | 
| Full proposal | −2.427 | Yes | 
| Full proposal | −1.219 | Yes | 
| Full proposal | −6.330 | Yes | 
| Full proposal | +5.489 | Yes | 
| Full proposal | +4.255 | Yes | 
| Full proposal | +5.172 | Yes | 
| Full proposal | +6.021 | Yes | 
| Full proposal | +3.589 | Yes | 
| Full proposal | +6.047 | Yes | 
| Full proposal | +6.624 | Yes | 
| Full proposal | +5.947 | Yes | 
| Full proposal | +5.844 | Yes | 
| Full proposal | +11.464 | Yes | 
| Full proposal | +13.134 | Yes | 
| Full proposal | +4.968 | Yes | 
| Full proposal | +5.605 | Yes | 
| Full proposal | +14.327 | Yes | 
| Full proposal | +15.431 | Yes | 
| Full proposal | −3.547 | Yes | 
| Full proposal | +0.018 | Yes | 
| Full proposal | +5.828 | Yes | 
| Full proposal | +2.288 | Yes | 
| Full proposal | +7.469 | Yes | 
| Full proposal | +8.544 | Yes | 
| Full proposal | +6.020 | Yes | 
| Full proposal | +8.368 | Yes | 
| Full proposal | +5.159 | Yes | 
| Full proposal | +5.360 | Yes | 
| Full proposal | +6.794 | Yes | 
| Full proposal | +1.420 | Yes | 
| Full proposal | −4.522 | Yes | 
| Full proposal | +5.171 | Yes | 
| Full proposal | +3.185 | Yes | 
| Parameters only — original history | −2.34 | Yes | 
| Parameters only | +1.885 | Yes | 
| Parameters only | −38.342 | Yes | 
| Parameters only | −0.895 | Yes | 
| Parameters only | −84.122 | Yes | 
| Parameters only | +5.603 | Yes | 
| Parameters only | +1.821 | Yes | 
| Parameters only | −54.814 | Yes | 
| Parameters only | +3.604 | Yes | 
| Parameters only | +6.046 | Yes | 
| Parameters only | −29.110 | Yes | 
| Parameters only | −27.293 | Yes | 
| Parameters only | +1.385 | Yes | 
| Parameters only | −14.211 | Yes | 
| Parameters only | +2.262 | Yes | 
| Parameters only | −4.121 | Yes | 
| Parameters only | −35.297 | Yes | 
| Parameters only | +5.294 | Yes | 
| Parameters only | +2.152 | Yes | 
| Parameters only | +4.350 | Yes | 
| Parameters only | +7.498 | Yes | 
| Parameters only | +6.639 | Yes | 
| Parameters only | −42.946 | Yes | 
| Parameters only | −41.397 | Yes | 
| Parameters only | +5.967 | Yes | 
| Parameters only | +6.017 | Yes | 
| Parameters only | −17.639 | Yes | 
| Parameters only | −35.535 | Yes | 
| Parameters only | undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| Parameters only | +5.210 | Yes | 
| Parameters only | +8.366 | Yes | 
| Parameters only | +6.527 | Yes | 
| Parameters only | +3.953 | Yes | 
| Parameters only | +7.225 | Yes | 
| Parameters only | +5.860 | Yes | 
| Parameters only | −62.521 | Yes | 
| Parameters only | −13.834 | Yes | 
| Parameters only | −35.180 | Yes | 
| Parameters only | −1.559 | Yes | 
| Parameters only | −16.195 | Yes | 
| Parameters only | +1.730 | Yes | 
| Parameters only | −27.170 | Yes | 
| Parameters only | −21.956 | Yes | 
| Parameters only | +3.269 | Yes | 
| Parameters only | −64.348 | Yes | 
| Parameters only | +7.349 | Yes | 
| Parameters only | undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| Parameters only | +5.849 | Yes | 
| Parameters only | +7.448 | Yes | 
| Parameters only | undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| Parameters only | −25.742 | Yes | 
| Parameters only | −19.759 | Yes | 
| Parameters only | −1.767 | Yes | 
| Parameters only | −44.095 | Yes | 
| Parameters only | +2.472 | Yes | 
| Parameters only | +2.713 | Yes | 
| Parameters only | +5.785 | Yes | 
| Parameters only | −26.439 | Yes | 
| Parameters only | +3.007 | Yes | 
| Parameters only | +5.067 | Yes | 
| Parameters only | −24.495 | Yes | 
| Parameters only | −30.953 | Yes | 
| Parameters only | −9.883 | Yes | 
| Parameters only | −32.472 | Yes | 
| Parameters only | −9.394 | Yes | 
| Parameters only | −22.690 | Yes | 
| Parameters only | +5.754 | Yes | 
| Parameters only | undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| Parameters only | −60.306 | Yes | 
| Parameters only | −0.277 | Yes | 
| Parameters only | −4.292 | Yes | 
| Parameters only | −37.726 | Yes | 
| Parameters only | −28.013 | Yes | 
| Parameters only | +5.796 | Yes | 
| Parameters only | +2.433 | Yes | 
| Parameters only | −70.039 | Yes | 
| Parameters only | −26.814 | Yes | 
| Parameters only | −24.916 | Yes | 
| Parameters only | −3.580 | Yes | 
| Parameters only | −20.288 | Yes | 
| Parameters only | −21.491 | Yes | 
| Parameters only | −7.472 | Yes | 
| Parameters only | +0.222 | Yes | 
| Parameters only | +0.119 | Yes | 
| Parameters only | −14.524 | Yes | 
| Parameters only | +0.012 | Yes | 
| Parameters only | undefined | Excluded: either holder’s wealth after debt reached zero or became negative | 
| Parameters only | −37.472 | Yes | 
| Parameters only | −53.854 | Yes | 
| Parameters only | −53.861 | Yes | 
| Parameters only | +2.795 | Yes | 
| Parameters only | +4.076 | Yes | 
| Parameters only | +7.880 | Yes | 
| Parameters only | −12.396 | Yes | 
| Parameters only | +5.357 | Yes | 
| Parameters only | +5.447 | Yes | 
| Parameters only | +8.121 | Yes | 
| Parameters only | −14.884 | Yes | 
| Parameters only | −2.840 | Yes | 
| Parameters only | +6.192 | Yes | 
| Parameters only | −33.707 | Yes | 
| External-price policy only — original history | −6.39 | Yes | 
| External-price policy only | −7.937 | Yes | 
| External-price policy only | −6.258 | Yes | 
| External-price policy only | −6.349 | Yes | 
| External-price policy only | +6.941 | Yes | 
| External-price policy only | −4.835 | Yes | 
| External-price policy only | −8.046 | Yes | 
| External-price policy only | −1.343 | Yes | 
| External-price policy only | −7.704 | Yes | 
| External-price policy only | −6.355 | Yes | 
| External-price policy only | −5.317 | Yes | 
| External-price policy only | +6.278 | Yes | 
| External-price policy only | −6.862 | Yes | 
| External-price policy only | −8.028 | Yes | 
| External-price policy only | −3.389 | Yes | 
| External-price policy only | −6.603 | Yes | 
| External-price policy only | −5.520 | Yes | 
| External-price policy only | −4.900 | Yes | 
| External-price policy only | −2.274 | Yes | 
| External-price policy only | −7.257 | Yes | 
| External-price policy only | −3.826 | Yes | 
| External-price policy only | −5.908 | Yes | 
| External-price policy only | −1.629 | Yes | 
| External-price policy only | −0.587 | Yes | 
| External-price policy only | −5.794 | Yes | 
| External-price policy only | −5.874 | Yes | 
| External-price policy only | +28.550 | Yes | 
| External-price policy only | −3.131 | Yes | 
| External-price policy only | −7.761 | Yes | 
| External-price policy only | −5.741 | Yes | 
| External-price policy only | −5.957 | Yes | 
| External-price policy only | −6.471 | Yes | 
| External-price policy only | −7.363 | Yes | 
| External-price policy only | −2.317 | Yes | 
| External-price policy only | −6.034 | Yes | 
| External-price policy only | +3.686 | Yes | 
| External-price policy only | −7.622 | Yes | 
| External-price policy only | −7.524 | Yes | 
| External-price policy only | −6.418 | Yes | 
| External-price policy only | −6.043 | Yes | 
| External-price policy only | −7.676 | Yes | 
| External-price policy only | −4.781 | Yes | 
| External-price policy only | −6.390 | Yes | 
| External-price policy only | −6.259 | Yes | 
| External-price policy only | +3.060 | Yes | 
| External-price policy only | −4.058 | Yes | 
| External-price policy only | −6.465 | Yes | 
| External-price policy only | −6.949 | Yes | 
| External-price policy only | −5.787 | Yes | 
| External-price policy only | −3.834 | Yes | 
| External-price policy only | −5.111 | Yes | 
| External-price policy only | −8.835 | Yes | 
| External-price policy only | −3.569 | Yes | 
| External-price policy only | −5.589 | Yes | 
| External-price policy only | −4.600 | Yes | 
| External-price policy only | −6.116 | Yes | 
| External-price policy only | −6.227 | Yes | 
| External-price policy only | −8.105 | Yes | 
| External-price policy only | +0.951 | Yes | 
| External-price policy only | −4.467 | Yes | 
| External-price policy only | −5.244 | Yes | 
| External-price policy only | −10.050 | Yes | 
| External-price policy only | −6.299 | Yes | 
| External-price policy only | −6.518 | Yes | 
| External-price policy only | −3.573 | Yes | 
| External-price policy only | −3.287 | Yes | 
| External-price policy only | −7.168 | Yes | 
| External-price policy only | −8.189 | Yes | 
| External-price policy only | +0.258 | Yes | 
| External-price policy only | −8.519 | Yes | 
| External-price policy only | −4.271 | Yes | 
| External-price policy only | −5.046 | Yes | 
| External-price policy only | −8.238 | Yes | 
| External-price policy only | −5.115 | Yes | 
| External-price policy only | −7.147 | Yes | 
| External-price policy only | −1.924 | Yes | 
| External-price policy only | −7.282 | Yes | 
| External-price policy only | −4.095 | Yes | 
| External-price policy only | −8.087 | Yes | 
| External-price policy only | −8.410 | Yes | 
| External-price policy only | +0.920 | Yes | 
| External-price policy only | +25.429 | Yes | 
| External-price policy only | −8.938 | Yes | 
| External-price policy only | −1.420 | Yes | 
| External-price policy only | +2.192 | Yes | 
| External-price policy only | +1.032 | Yes | 
| External-price policy only | −5.740 | Yes | 
| External-price policy only | −5.488 | Yes | 
| External-price policy only | −5.205 | Yes | 
| External-price policy only | −5.759 | Yes | 
| External-price policy only | −1.622 | Yes | 
| External-price policy only | −4.123 | Yes | 
| External-price policy only | −5.732 | Yes | 
| External-price policy only | −5.536 | Yes | 
| External-price policy only | −2.477 | Yes | 
| External-price policy only | −3.629 | Yes | 
| External-price policy only | −6.614 | Yes | 
| External-price policy only | −7.017 | Yes | 
| External-price policy only | −2.857 | Yes | 
| External-price policy only | −6.499 | Yes | 
| External-price policy only | −9.225 | Yes |


# E2 The early gain comes from changing financing {#proposal/channels}

**Changing [financing](./#glossary/financing) explains the early gain in [LP/xyk](./#glossary/lp-xyk).**

An [LP](./#glossary/lp) owns a share of the pool. LP/xyk measures share growth above a reference, after [donation](./#glossary/donation) charges. The reference pool charges no trading fees. Both pools face the same market prices.

Financing supplies pool capital through interest-funded donations.

Rates use [percentage points](./#glossary/percentage-point) per year, or pp/yr. The [rate conventions](./#settings) explain the logarithmic calculation.

[WETH](./#glossary/weth) is a token representing Ethereum’s [ETH](./#glossary/eth). These tests start from observed WETH pool states. The financing-only test keeps current price rules.

The early LP/xyk advantage comes after subtracting the donation charge. Donations supply capital through the YB holder’s interest payments. At longer horizons, the lower-financing pools [stall](./#glossary/stall) and their advantage turns negative.

**Measure:** Financing-only LP/xyk difference, in percentage points per year.

**Compared:** Current price rules with changed financing against deployed current settings.

**Same for both:** Observed WETH starting states, prices and recorded operation times, with a simulated YB holder.

**Higher means:** A larger advantage after the donation charge.

**Measure:** Full-proposal growth difference in [market value](./#glossary/market-value) per share, in percentage points per year.

**Compared:** The full proposal with deployed current settings.

**Same for both:** The same observed WETH starting states, prices and activity setup.

**Higher means:** Faster growth in market value per share under the proposal.

The left panel changes financing alone and measures LP/xyk. The right panel applies the full proposal and measures growth in market value per share. Both subtract deployed current settings. Positive differences favour the changed setting.

The simulations share observed WETH starts, market prices and recorded operation times. They simulate the YB holder. Each 60-day and 90-day average reuses one independent stretch of market history.

Changing financing raises LP/xyk at 7 and 30 days. The advantage turns negative at 60 and 90 days. The full proposal lowers growth in market value per share at every reported horizon.

> **Common misunderstanding:** “The proposal gains because its price rules trade better.”
>
> **What is true.**
>
> The early gain in LP/xyk comes from the financing change. Financing alone raises LP/xyk at 7 and 30 days. The advantage turns negative at 60 and 90 days. The longest horizons use one [effective market window](./#glossary/effective-market-window).
>
> The full proposal lowers growth in the market value of each share at every horizon.

Under the full proposal, that growth is 0.92 pp/yr lower at 7 days. It is 8.40 pp/yr lower at 90 days. The gap grows with the horizon.

| Measure: changed setting minus deployed current | 7 days | 30 days | 60 days | 90 days | 
| --- | --- | --- | --- | --- |
| Financing change alone: LP/xyk difference, pp/yr | +2.27 | +0.94 | −4.14 | −7.10 | 
| Full proposal: LP/xyk difference, pp/yr | +2.15 | +1.05 | — | — | 
| Full proposal: growth difference in market value per share, pp/yr | −0.92 | −2.61 | −3.45 | −8.40 | 
| Reduction in returned donation value / interest saved, % | 20 | 68 | 83 | 90 | 
| Financing change: difference in holder wealth after debt, ETH | +8.2 | +15.8 | −97.2 | −137.9 | 

### The holder’s wealth includes returned value

The YB holder owns pool shares financed with debt. Its remaining wealth subtracts that debt from the market value of its shares.

**Measure:** Difference in holder wealth after debt, in ETH.

**Compared:** Financing-only settings with deployed current settings.

**Same for both:** The same starts and periods, after all transfers and market effects.

**Higher means:** More remaining holder wealth after the financing change.

The financing change adds +15.8 ETH after 30 days. Its difference after 90 days is −137.9 ETH. Negative figures mean less remaining wealth than under current settings.

Lower interest also changes value returned through the pool. That returned value includes collections, allocation transfers and benefits from removing donated shares. The holder comparison includes these transfers, trading, fees and market effects.

Only lower-financing variants stall at longer horizons. Their slower growth in market value then outweighs the saved donation charge.

**More detail: returned value and overlapping histories**

Each 60-day and 90-day average uses one effective market window. The starting dates overlap enough to reuse one independent stretch of market history.

The returned-value ratio divides the reduction in returned value by interest saved for each starting state. The reported result averages those ratios. Returned value includes collections, allocation transfers and benefits from removing donated shares.

Holder wealth already includes those transfers and all market, execution and fee effects. Do not add the returned-value ratio to the holder result.

A separate test fixes financing and disables delivery of external price [reports](./#glossary/report). Its uncertainty intervals for changing the policy include both gains and losses.

Financing and price-centre moves contribute to returns. The total value of pool assets and the holder’s remaining wealth are reported separately.

### Recorded transfers answer a different question

The recorded-activity runs copy observed user transfers and donated coins. Those donated coins stay fixed between settings. The [ping](./#glossary/ping) runs copy operation times without user transfers. They simulate the YB holder’s financing.

With recorded transfers and [unlabelled contracts](./#glossary/unlabelled-contracts), whose trading purpose is unknown, the proposal gains +1.55 pp/yr at 7 days. Its gain is +1.08 pp/yr at 30 days. Both are LP/xyk differences from current settings with donated coins held fixed.

Pings with a simulated YB holder give +2.15 pp/yr at 7 days. That exceeds the post’s claimed gain.

### Windows without stalls form a selected subset

Among windows where neither pool stalls, the mean proposal-minus-current LP/xyk difference stays positive. Each horizon selects a different subset of runs.

| Horizon, days | Mean LP/xyk difference without stalls, pp/yr | 
| --- | --- |
| 7 | 1.57 | 
| 30 | 1.00 | 
| 90 | 1.18 | 

On the 556-day tuning history, the proposal’s final stall begins on 19 August. It continues to the endpoint. The final LP/xyk difference is negative. Selecting windows without stalls retains positive mean differences.

Stalls use the [shared price-gap rule](./#settings).

[← previous](./#proposal/test)[next $\to$](./#proposal/demand)

**Chart data $\cdot$ WETH: financing changes and the full proposal**

Difference from deployed current settings, percentage points per year. Each 60-day and 90-day average reuses one independent stretch of market history.
| Panel and line | Days since the starting state | Difference from deployed current settings, percentage points per year | 
| --- | --- | --- |
| Financing change: LP/xyk / Financing change alone: LP/xyk | 7 | +2.27 | 
| Financing change: LP/xyk / Financing change alone: LP/xyk | 30 | +0.94 | 
| Financing change: LP/xyk / Financing change alone: LP/xyk | 60 | −4.14 | 
| Financing change: LP/xyk / Financing change alone: LP/xyk | 90 | −7.10 | 
| Full proposal: market value per share / Full proposal: growth in market value per share | 7 | −0.92 | 
| Full proposal: market value per share / Full proposal: growth in market value per share | 30 | −2.61 | 
| Full proposal: market value per share / Full proposal: growth in market value per share | 60 | −3.45 | 
| Full proposal: market value per share / Full proposal: growth in market value per share | 90 | −8.40 | 
| Reference line | — | 0 |


# E3 Customers receive worse prices in the quote test {#proposal/demand}

**The proposal raises the cost of the tested customer trades.**

[Execution cost](./#glossary/execution-cost) compares the trade price with the market price. A higher cost means a worse deal for the customer. A [basis point](./#glossary/basis-point) is a hundredth of a [percentage point](./#glossary/percentage-point).

**Measure:** Execution cost, in basis points of order value.

**Compared:** The proposal with deployed current settings.

**Same for both:** Recorded [WETH](./#glossary/weth) customer order sizes and [replay](./#glossary/replay) periods.

**Higher means:** A worse price for the customer.

WETH represents Ethereum’s [ETH](./#glossary/eth). Median cost is 145 basis points under the proposal. It is 6.5 basis points under current settings. The proposal’s cost is more than twenty times higher.

A buyer pays more than the market reference price. A seller receives less than that reference price. The external reference is the market price outside the pool.

### Rejecting quotes changes the supplied activity

An [LP](./#glossary/lp) owns a share of the pool. [LP/xyk](./#glossary/lp-xyk) measures share growth above a reference, after [donation](./#glossary/donation) charges. The reference pool charges no trading fees. Both pools face the same market prices.

Rates use percentage points per year, or pp/yr. The [rate conventions](./#settings) explain the logarithmic calculation.

**Measure:** LP/xyk difference, in percentage points per year.

**Compared:** The proposal without tested customer trades against the stated current-settings control.

**Same for both:** The same monthly WETH windows.

**Higher means:** A larger proposal advantage in that imposed scenario.

The test removes all tested customer swaps, and swaps from [unlabelled contracts](./#glossary/unlabelled-contracts), from the proposal alone. Its 30-day LP/xyk still exceeds the current control by about 1.00 pp/yr.

The monthly rejection test covers customer trades routed through services and contracts with unknown purposes. It imposes refusal of quotes above a cost limit. It does not estimate customers’ choices.

### The smaller donation charge accounts for the LP/xyk gain

Growth in [market value](./#glossary/market-value) per share is lower than current settings in the monthly response tests. The proposal-minus-current difference ranges from −2.82 to −1.47 pp/yr.

The proposal’s donation charge is roughly 3.80 pp/yr smaller. That saving can make its LP/xyk advantage positive despite slower growth in market value. LP/xyk already includes the saving.

**More detail: customer choices remain unknown**

The test supplies trade-rejection rules and removes trades in the stated scenario. Customers may instead trade elsewhere, change amounts or change trading times. The test estimates neither actual demand nor [LT](./#glossary/lt) capital. LT is YieldBasis’s liquidity token.

The [financing](./#glossary/financing) reduction leaves an LP/xyk advantage over current settings. It does not establish that customers would keep trading these amounts. See the [customer-response question](./#simulation/limits).

[← previous](./#proposal/channels)[next $\to$](./#proposal/selection)


# E4 Selected settings on unused and older data {#proposal/selection}

**Unused-data tests show no reliable advantage beyond settings with the same [financing](./#glossary/financing).**

Financing supplies pool capital through interest-funded [donations](./#glossary/donation).

Selection chooses settings using training data. A [held-out test](./#glossary/held-out-test) measures them on data excluded from that choice. Each window compares settings chosen on other days with alternatives.

The YB holder owns pool shares financed with debt. Remaining wealth subtracts debt from the [market value](./#glossary/market-value) of those shares. Growth is measured in [ETH](./#glossary/eth), Ethereum’s asset.

Rates use [percentage points](./#glossary/percentage-point) per year, or pp/yr. The [rate conventions](./#settings) explain the logarithmic calculation.

**Measure:** Difference in growth of holder wealth in ETH, in percentage points per year.

**Compared:** The selected group with unrestricted random settings, then with matched alternatives.

**Same for both:** Identical test windows excluded from selection.

**Higher means:** A larger advantage for the selected group.

Matched alternatives share the donation rate and [reserved profit fraction](./#glossary/reserved-profit-fraction). Donations supply outside capital. The reserved fraction protects part of recorded profit from spending on price-centre moves.

The best 500 settings are selected using the other training days. Their average holder growth is then measured on the excluded test window.

| Comparison | Mean growth difference, pp/yr | One standard error, pp/yr | 95% confidence interval, pp/yr | 
| --- | --- | --- | --- |
| Selected minus unrestricted random settings | +7.02 | 5.21 | −1.86 to 17.84 | 
| Selected minus financing-matched settings | +1.45 | 10.90 | −18.78 to +23.20 | 

The observed mean advantage over unrestricted random settings is large. Its [confidence interval](./#glossary/confidence-interval) includes both gains and losses. A confidence interval describes uncertainty in the mean.

Matching financing reduces the mean advantage. The remaining difference is small compared with its [standard error](./#glossary/standard-error). A standard error measures uncertainty in an estimated mean. The matched difference cannot be distinguished from zero.

Matching financing reduces the observed mean advantage. The remaining difference is small compared with its standard error. Each bar compares growth in holder wealth after debt, measured in ETH, on windows excluded from selection.

Error bars show one standard error. Matching keeps the donation rate and reserved profit fraction equal. The nearby table gives confidence intervals.

The tested setting, numbered 534515, reaches the top tenth in 3 of 64 unused windows. Rankings transfer weakly from training days to excluded test windows. Their [rank correlation](./#glossary/rank-correlation) is 0.19 within exact donation-rate and reserved-profit pairs.

### The selected group performs worse on older data

**Measure:** Difference in growth of holder wealth in ETH, in percentage points per year.

**Compared:** Selected settings with alternatives sharing donation rates and reserved profit fractions.

**Same for both:** The older market windows.

**Higher means:** A larger advantage for selection.

| Comparison on older data | Holder-growth difference in ETH, pp/yr | 
| --- | --- |
| Selected minus matched settings: operation times only | −1.59 | 
| Selected minus matched settings: [arbitrage](./#glossary/arbitrage) only | −1.84 | 

Selected settings have lower mean holder growth than matched alternatives. [Stalls](./#glossary/stall) occur in 148 of 240 selected-setting runs. Matched alternatives stall in 109 runs.

> **Common misunderstanding:** “Settings that won on the tuning history will keep winning.”
>
> **What is true.**
>
> On data left out of the selection, the chosen settings show no reliable advantage over settings with the same financing. On older history, their mean advantage is negative.

**More detail: uncertainty and supplied inputs**

Error bars measure uncertainty in the mean difference. They allow for shared market moves across overlapping windows. The older-history comparison generates price [reports](./#glossary/report) and reuses observed operation times.

### A separate test compares the forum proposal with current settings

An [LP](./#glossary/lp) owns a share of the pool. [LP/xyk](./#glossary/lp-xyk) measures share growth above a reference, after donation charges. The reference pool charges no trading fees. Both pools face the same market prices.

**Measure:** Separate pool and holder growth differences, in percentage points per year.

**Compared:** The forum proposal with deployed [WETH](./#glossary/weth) current settings.

**Same for both:** The same older price history and generated reference-price reports.

**Higher means:** A larger advantage for the proposal.

The full older history lasts 478 days. The proposal gains +0.53 pp/yr of LP/xyk over current settings. Holder growth gains +3.17 pp/yr before the [LT](./#glossary/lt) administration fee.

The first half-year gives an LP/xyk loss of −0.88 pp/yr. A sharp market move and a stall occur in that period.

These 2023–2025 data predate tuning. Modelled external price reports reproduce observed errors. The modelled reports are smoother at short horizons.

The LP/xyk gain over the full older history is small compared with the post’s claim. Shorter windows include losses. Holder growth is measured in ETH before the LT administration fee. The test generates external reference-price reports.

Each window includes its starting date and excludes its ending date. The full window runs from 2023-12-01 to 2025-03-23.

- First shorter window: 2023-12-01 to 2024-05-29.
- Second shorter window: 2024-05-29 to 2024-11-25.

[Older-history results and ranges across report models](/yb-policy/#older).

Across report models, the smallest and largest full-period LP/xyk gains are [0.48, 0.53] pp/yr. For holder growth, the smallest and largest gains are [3.02, 3.17] pp/yr. The pool gain remains small compared with the post’s claim. The holder gains more than the pool measure.

The forum-proposal test compares different packages from the selected-versus-matched test above.

**More detail: possible bias from modelled reports**

On a window with recorded reports, modelled reports raise the proposal-minus-current LP/xyk difference by +0.09 pp/yr. Its standard error is 0.02 pp/yr.

The corresponding increase in holder-growth difference is +0.25 pp/yr. Its standard error is 0.09 pp/yr. The older-history results retain this possible bias. The bias on that older history is unknown.

[← previous](./#proposal/demand)[next $\to$](./#repeg/protection)

**Chart data $\cdot$ Matching financing reduces the observed selection advantage**

Holder-growth difference in ETH, percentage points per year
| Simulation or comparison | Mean on unused windows $\cdot$ Holder-growth difference in ETH, percentage points per year | One standard error, pp/yr | 
| --- | --- | --- |
| Selected minus unrestricted random settings | +7.02 | 5.21 | 
| Selected minus financing-matched settings | +1.45 | 10.90 | 

**Chart data $\cdot$ The older-history gain changes across time windows**

Proposal minus current growth, percentage points per year
| Simulation or comparison | LP/xyk $\cdot$ Proposal minus current growth, percentage points per year | Holder wealth in ETH $\cdot$ Proposal minus current growth, percentage points per year | 
| --- | --- | --- |
| 2023-12-01 to 2025-03-23 | +0.53 | +3.17 | 
| 2023-12-01 to 2024-05-29 | −0.88 | −1.27 | 
| 2024-05-29 to 2024-11-25 | +0.37 | +1.91 |


# F. The re-peg gate {#repeg}

**This chapter develops one point on each page.**

- [F1 The profit floor guards the books, then locks the pool](./#repeg/protection) — The profit floor protects the pool’s recorded value per share.
- [F2 Removing the floor in September](./#repeg/removal) — Removing the floor changes returns differently across pools on the same September price history.


# F1 The profit floor guards the books, then locks the pool {#repeg/protection}

**The profit floor protects the pool’s recorded value per share.**

**Measure:** growth difference above a fee-free reference pool ([M](./#glossary/m)), before [donation](./#glossary/donation) charges, in [percentage points](./#glossary/percentage-point) per year

**Compared:** the pool that keeps its profit floor with the same pool after removing that floor

**Same for both:** each test period with deliberately incorrect target prices

**Higher means:** keeping the floor gave faster growth in the [market value](./#glossary/market-value) of each share

The pool records an internal value per share called [virtual price](./#glossary/virtual-price). A [re-peg](./#glossary/re-peg) moves the pool’s centre price. Once the buffer above the floor is spent, the floor can block later re-pegs.

> **Common misunderstanding:** “The profit floor protects the market value of [LP](./#glossary/lp) shares.”
>
> **What is true.**
>
> The floor protects virtual price, the pool's internal accounting value per share. The market value of a share can still fall. Once the buffer above the floor is spent, the floor can block re-pegs and leave the pool [stalled](./#glossary/stall).

Before attempting a move, the pool checks the accounting value it holds. After calculating the move, it checks the value that would remain. Allowing one step below the protected floor leaves the pre-move check ready to refuse later steps. The target-error tests measure what this accounting protection does to wealth at market prices.

The gate first checks whether the pool has enough accounting value to attempt a re-peg. It then checks whether the proposed move and its allowed share [burn](./#glossary/burn) would leave enough value. Both checks protect the cumulative profit floor. Disabling the final check leaves the first check active.

Profit buffer

$\to$

Enough [headroom](./#glossary/headroom)? **Yes $\to$ re-peg allowed** **No $\to$ re-peg refused**

Keeping the floor raises growth in the market value of each [WETH](./#glossary/weth) pool share above floor removal in 7 of 12 tested cases. The gain is 0.10–0.38 pp/yr. In separate [BTC](./#glossary/btc) tests with targets deliberately offset by 2% up or down, keeping the floor beats removing it in 2 of 10 cases. A further test repeatedly moves the target in one direction until the 20% target limit stops that drift.

### Why stalls persist

**Measure:** re-peg attempts rejected by the pre-move check, out of all attempts in the trace

**Compared:** rejections after one permitted step below the floor with all attempts in the same trace

**Same for both:** the traced September [WBTC](./#glossary/wbtc) window

**Higher means:** the accounting floor refuses re-pegs more often

Skipping the second check allows one move below the minimum. The first check then blocks later moves until profits recover. In the traced WBTC case, almost every attempt stays blocked. The first check rejects 1,510 of 1,523 attempts.

Under the tested spending rule, multiplying [financing](./#glossary/financing) by 4 still leaves WBTC and [tBTC](./#glossary/tbtc) stalled through the September month. These runs test recovery from those starting states. The donation scan separately tests how often [episodes](./#glossary/episode) occur over rebuilt histories.

**More detail**

For [cbBTC](./#glossary/cbbtc) starting in August, the weaker gate permits re-centring. It raises M growth by 6.3 to 7.1 pp/yr compared with the current gate. YB-position growth rises by 14.4 to 16.6 pp/yr. 

The net [arbitrage](./#glossary/arbitrage) contribution differs by at most 0.075 pp/yr. Changed holdings account for most of the return difference.

### The accounting barrier

An allowed re-peg can spend below the old protected threshold. The experimental rule then lowers that threshold to the new virtual price. Later re-pegs can pass.

The pre-move check and the absolute virtual-price floor remain in force. No monthly spending cap was tested.

The remaining question concerns spending rules. How do they change recovery, market-valued wealth and losses from wrong target prices across different histories?

**More detail**

Headroom is virtual price divided by [lp_xcp_profit](./#glossary/lp_xcp_profit), minus 1. It measures the buffer above the protected floor. The distance between the pool’s centre price, [price_scale](./#glossary/price_scale), and the market price shows where trading capacity sits. A large accounting buffer can exist alongside a large market-price gap.

This breakdown uses re-pegs and the pool’s coin holdings. [Arbitrage fees](./#glossary/arbitrage-fees) and [execution costs](./#glossary/execution-cost) mostly cancel.

Return rates follow the [shared conventions](./#settings).

Stall and “both attached” labels use the [shared price-gap rule](./#settings).

[← previous](./#proposal/selection)[next $\to$](./#repeg/removal)


# F2 Removing the floor in September {#repeg/removal}

**Removing the floor changes returns differently across pools on the same September price history.**

**Measure:** growth difference above a fee-free reference pool ([M](./#glossary/m)), before [donation](./#glossary/donation) charges, in [percentage points](./#glossary/percentage-point) per year

**Compared:** each pool with its cumulative floor removed with the same pool keeping the current gate

**Same for both:** the shared September Bitcoin path and the pool’s own starting state

**Higher means:** a larger gain from removing the floor

- The profit floor protects the pool’s recorded value per share. A [stall](./#glossary/stall) is a large, lasting gap between the pool’s centre price and the market. Removing the floor cuts September stall duration by at least half in 5 of 5 pool/setup combinations. [WBTC](./#glossary/wbtc) falls from 30 days to 2.6 days.
- WBTC ends much closer to market. The end gap is 1.4%, against 16.5% with the current gate.
- The same Bitcoin price history gives opposite results across pools. Compared with the current gate, removing the floor changes growth in the [market value](./#glossary/market-value) of each share by +10.70 pp/yr on WBTC. On [cbBTC](./#glossary/cbbtc) the change is −4.37 pp/yr on the same Bitcoin history.

On the same September Bitcoin history, floor removal helps WBTC and hurts cbBTC compared with keeping the floor. The pools have different starting states. Runs cover 1 September 2026 to 1 October 2026, using [pings](./#glossary/ping) and simulated [financing](./#glossary/financing). All 16 input-error repeats keep those signs. 

Rebuilding the month’s market segments gives a second view. WBTC’s M-growth difference then has a 95% interval of −16.34 to +41.08 pp/yr. Error bars resample segments of the same month. They show 95% uncertainty intervals for the mean M-growth difference.

The market-history interval is wide because this month contains only about 4.3 effective windows.

| Pool | Market-valued LP growth (M), pp/yr | 95% M confidence interval, pp/yr | YB position at market prices, pp/yr | Outcome of the pool keeping the current gate | 
| --- | --- | --- | --- | --- |
| WBTC | +10.70 | −16.34 to +41.08 | +23.15 | Stays stalled | 
| [tBTC](./#glossary/tbtc) | +10.72 | −14.67 to +39.43 | +23.24 | Stays stalled | 
| cbBTC | −4.37 | −12.57 to +3.38 | −12.02 | Recovers when price reverses | 

During this month, [re-pegs](./#glossary/re-peg) reduce [virtual price](./#glossary/virtual-price) by about 0.7–0.9%. The remaining absolute floor requires virtual price to stay above 1, its starting accounting unit. This limit governs the internal index. Externally priced asset value can move differently.

### Why the reversal differs

The cbBTC pool with the current gate [re-centres](./#glossary/re-centre) on its own as prices fall back. Before that, the pool sells Bitcoin during the early price rise while its centre price remains out of date. It buys again near the middle-month low. It then sells into the next rally. 

Immediately moving the centre price with the market gives up this favourable sequence. The assets it holds therefore earn less when prices reverse.

On the shared Bitcoin path, WBTC and tBTC keep stale reference prices. cbBTC’s different starting state lets it recover when prices reverse. Keeping stale holdings helps cbBTC on this sequence. The tests found no stable advance signal for choosing that favourable sequence.

> **Common misunderstanding:** “Pools facing the same prices gain equally from removing the floor.”
>
> **What is true.**
>
> On the same September Bitcoin prices, removing the floor raised growth in WBTC's market value per [LP](./#glossary/lp) share by 10.70 pp/yr. It lowered cbBTC's by 4.37 pp/yr. The pools started in different states, and the starting state decided the sign.

**More detail**

The market-value intervals are wide because the month contains few independent market moves. A tested alternative resets the protected floor after a step would overdraw it. That alternative tracks the fully removed-floor result closely.

Return rates follow the [shared conventions](./#settings).

Stall and “both attached” labels use the [shared price-gap rule](./#settings).

[← previous](./#repeg/protection)[next $\to$](./#detachment/measure)

**Chart data $\cdot$ Removing the floor: differences from the current gate**

pp/yr, floor removed minus current gate
| Comparison | Market-valued LP growth (M) $\cdot$ pp/yr, floor removed minus current gate | YB position, external market prices $\cdot$ pp/yr, floor removed minus current gate | Market-valued LP growth (M) $\cdot$ Interval low $\cdot$ pp/yr, floor removed minus current gate | Market-valued LP growth (M) $\cdot$ Interval high $\cdot$ pp/yr, floor removed minus current gate | 
| --- | --- | --- | --- | --- |
| WBTC | +10.70 | +23.15 | −16.34 | +41.08 | 
| tBTC | +10.72 | +23.24 | −14.67 | +39.43 | 
| cbBTC | −4.37 | −12.02 | −12.57 | +3.38 |


# G. When price_scale detaches {#detachment}

**This chapter develops one point on each page.**

- [G1 Detachment is depth missing at the market](./#detachment/measure) — [Detachment](./#glossary/detachment) is depth missing at the market price.
- [G2 Donations, the gate and when volatility arrives](./#detachment/donations) — More [donations](./#glossary/donation) reduce serious detachment in these tests.
- [G3 The directional bet decides the live stall outcome](./#detachment/costs) — During live Bitcoin [stalls](./#glossary/stall), the pool usually finished ahead of holding its opening coins.
- [G4 Repairing a detached pool needs capital](./#detachment/repairs) — Repairing a detached pool often needs more accounting capital than the gate has available.
- [G5 Test orders get worse quotes during detachment](./#detachment/trader-cost) — During serious [episodes](./#glossary/episode), standardised test orders receive worse quotes than in an equally funded [centred pool](./#glossary/centred-pool).
- [G6 Staying attached does not reliably raise wealth](./#detachment/funded) — Staying attached does not reliably increase wealth in these tests.


# G1 Detachment is depth missing at the market {#detachment/measure}

**[Detachment](./#glossary/detachment) is depth missing at the market price.**

**Measure:** trading capacity near the market price, as a percentage of the [centred](./#glossary/centred-pool) reference pool’s capacity

**Compared:** the pool with an equally funded pool of the same curve shape centred on that price

**Same for both:** the pool’s funding, its curve shape and the market price at that moment

**Higher means:** more capacity for small trades at the market price

Trading depth is the amount available to trade near a price. More depth means a small trade moves the price less.

Lower retained depth means the same small order moves the price more. The live-pool chart shows this loss of trading capacity. More detail explains the [episode](./#glossary/episode) rule. It also explains how squared price moves measure market movement during episodes.

Serious detachment means less than 75.00% of the reference trading depth remains at the market price. At that boundary, a very small trade moves the price about 1.33 times as much as in the reference pool. A larger order also faces fees and further price movement along the curve.

The horizontal axis shows the log distance between [price_scale](./#glossary/price_scale) and the market price. The vertical axis shows retained depth. Markers locate the three tiers.

| Detachment tier | Depth retained below | Absolute log gap, about | Price impact of a tiny trade at the boundary, before fees | Hours of permitted steps to reach the 1.36% log-price band | 
| --- | --- | --- | --- | --- |
| Warning | 92.00% | 4.93% | 1.09 times | 8 hours | 
| Serious | 75.00% | 10.05% | 1.33 times | 18 hours | 
| Severe | 50.00% | 19.11% | 2.00 times | 36 hours | 

The same price gap removes more depth from a pool with more [concentrated liquidity](./#glossary/concentrated-liquidity). That is why the tiers use [depth retained](./#glossary/depth-retained), rather than the price gap alone. This curve uses the observed pools’ [amplification](./#glossary/amplification) setting of 5.

**More detail**

To calculate the log gap, divide the pool’s centre price, price_scale, by the external market price. Take the natural logarithm. Ignore the sign.

The tiers are [service standards](./#glossary/service-standard). The contract does not enforce them.

The walk times assume one [re-peg](./#glossary/re-peg) per hour. The maximum step is 0.50%. Every policy uses the same 1.36% log-price [fee band](./#glossary/fee-band). The walk times ignore delays from the gate, [reports](./#glossary/report) and funding.

Walking back from the severe boundary takes 36 hours even under these assumptions. That is longer than the 24-hour episode threshold.

### The live pools

Over 26 May 2026 to 1 October 2026 [UTC](./#glossary/utc), mean depth missing is smallest for [WETH](./#glossary/weth) and largest for [tBTC](./#glossary/tbtc). WETH retains nearly all reference depth on average. The Bitcoin pools lose much more. The table gives each pool’s mean depth missing.

Each point is the daily average retained depth. Shading uses the separate price-gap [stall](./#glossary/stall) rule. That rule flags a gap above 5% lasting at least 24 hours. It is not the serious-depth threshold.

Daily means smooth intraday extremes. The table gives the minimum block-level depth. Stalls still open stop at the study endpoint.

[WBTC](./#glossary/wbtc) and tBTC at times kept less than half the reference depth. [cbBTC](./#glossary/cbbtc) did not go below half.

| Pool | Mean depth missing, % | Minimum depth retained, % | Mean missing trading capacity, USD per basis point | Mean pool capital at market prices, million USD | 
| --- | --- | --- | --- | --- |
| WETH | 0.47 | 81.18 | 21.09 | 32.97 | 
| WBTC | 17.30 | 43.22 | 1,558.89 | 51.42 | 
| cbBTC | 8.42 | 53.00 | 1,076.14 | 80.82 | 
| tBTC | 19.47 | 44.00 | 1,061.04 | 35.58 | 

### How we count

**More detail: episodes and market movement**

An episode first requires 24 uninterrupted hours below the selected depth threshold. Qualifying periods then join when the recovery between them lasts less than 24 hours. Brief dips add to time below the threshold. They cannot combine into a qualifying period.

The [volatility clock](./#glossary/volatility-clock) adds squared log-price changes. It advances more during large moves. It therefore distinguishes a turbulent detached day from a calm one. Calendar time sets episode length and the timing of [donations](./#glossary/donation), reports and [financing](./#glossary/financing).

A setting passes “[almost never](./#glossary/almost-never)” only if both tests pass. The first test uses a one-sided 95% [Wilson upper bound](./#glossary/wilson-bound), an upper limit allowing for sampling uncertainty. The upper limit on the chance of a first serious episode by day 365 must be at most 5.00%. 

Test two: the mean share of the full 556-day path below serious depth must be at most 0.50%. First-episode counts use paths starting outside the tier. The time share includes brief dips. 

The chart’s [bootstrap](./#glossary/bootstrap) error bars use a different calculation. They do not determine qualification.

These probabilities describe rebuilt versions of one WETH price history. All paths start from the simulator’s template state. 

An episode still open at the endpoint has a known duration so far. Its eventual duration is unknown. Paths that start below the selected depth threshold are reported separately.

The [shared settings and conventions](./#settings) distinguish these depth, event and quote measures from return rates.

[Settings and conventions](./#settings) distinguishes depth episodes from the price-gap stall rule.

[← previous](./#repeg/removal)[next $\to$](./#detachment/donations)

**Chart data $\cdot$ Depth falls as price_scale moves away**

depth retained, % of centred depth
| Panel / curve | Coordinate $\cdot$ Absolute log price gap, % | depth retained, % of centred depth | 
| --- | --- | --- |
| Today’s amplification / Depth retained | 0.00 | 100.00 | 
| Today’s amplification / Depth retained | 0.10 | 100.00 | 
| Today’s amplification / Depth retained | 0.20 | 99.99 | 
| Today’s amplification / Depth retained | 0.30 | 99.97 | 
| Today’s amplification / Depth retained | 0.40 | 99.94 | 
| Today’s amplification / Depth retained | 0.50 | 99.91 | 
| Today’s amplification / Depth retained | 0.60 | 99.87 | 
| Today’s amplification / Depth retained | 0.70 | 99.82 | 
| Today’s amplification / Depth retained | 0.80 | 99.76 | 
| Today’s amplification / Depth retained | 0.90 | 99.70 | 
| Today’s amplification / Depth retained | 1.00 | 99.63 | 
| Today’s amplification / Depth retained | 1.10 | 99.55 | 
| Today’s amplification / Depth retained | 1.20 | 99.47 | 
| Today’s amplification / Depth retained | 1.30 | 99.38 | 
| Today’s amplification / Depth retained | 1.40 | 99.28 | 
| Today’s amplification / Depth retained | 1.50 | 99.18 | 
| Today’s amplification / Depth retained | 1.60 | 99.06 | 
| Today’s amplification / Depth retained | 1.70 | 98.95 | 
| Today’s amplification / Depth retained | 1.80 | 98.82 | 
| Today’s amplification / Depth retained | 1.90 | 98.69 | 
| Today’s amplification / Depth retained | 2.00 | 98.55 | 
| Today’s amplification / Depth retained | 2.10 | 98.40 | 
| Today’s amplification / Depth retained | 2.20 | 98.25 | 
| Today’s amplification / Depth retained | 2.30 | 98.09 | 
| Today’s amplification / Depth retained | 2.40 | 97.93 | 
| Today’s amplification / Depth retained | 2.51 | 97.76 | 
| Today’s amplification / Depth retained | 2.61 | 97.58 | 
| Today’s amplification / Depth retained | 2.71 | 97.40 | 
| Today’s amplification / Depth retained | 2.81 | 97.21 | 
| Today’s amplification / Depth retained | 2.91 | 97.01 | 
| Today’s amplification / Depth retained | 3.01 | 96.81 | 
| Today’s amplification / Depth retained | 3.11 | 96.61 | 
| Today’s amplification / Depth retained | 3.21 | 96.39 | 
| Today’s amplification / Depth retained | 3.31 | 96.18 | 
| Today’s amplification / Depth retained | 3.41 | 95.95 | 
| Today’s amplification / Depth retained | 3.51 | 95.73 | 
| Today’s amplification / Depth retained | 3.61 | 95.49 | 
| Today’s amplification / Depth retained | 3.71 | 95.26 | 
| Today’s amplification / Depth retained | 3.81 | 95.01 | 
| Today’s amplification / Depth retained | 3.91 | 94.77 | 
| Today’s amplification / Depth retained | 4.01 | 94.51 | 
| Today’s amplification / Depth retained | 4.11 | 94.26 | 
| Today’s amplification / Depth retained | 4.21 | 94.00 | 
| Today’s amplification / Depth retained | 4.31 | 93.73 | 
| Today’s amplification / Depth retained | 4.41 | 93.46 | 
| Today’s amplification / Depth retained | 4.51 | 93.19 | 
| Today’s amplification / Depth retained | 4.61 | 92.91 | 
| Today’s amplification / Depth retained | 4.71 | 92.63 | 
| Today’s amplification / Depth retained | 4.81 | 92.35 | 
| Today’s amplification / Depth retained | 4.91 | 92.06 | 
| Today’s amplification / Depth retained | 5.01 | 91.77 | 
| Today’s amplification / Depth retained | 5.11 | 91.47 | 
| Today’s amplification / Depth retained | 5.21 | 91.17 | 
| Today’s amplification / Depth retained | 5.31 | 90.87 | 
| Today’s amplification / Depth retained | 5.41 | 90.57 | 
| Today’s amplification / Depth retained | 5.51 | 90.26 | 
| Today’s amplification / Depth retained | 5.61 | 89.95 | 
| Today’s amplification / Depth retained | 5.71 | 89.64 | 
| Today’s amplification / Depth retained | 5.81 | 89.33 | 
| Today’s amplification / Depth retained | 5.91 | 89.01 | 
| Today’s amplification / Depth retained | 6.01 | 88.69 | 
| Today’s amplification / Depth retained | 6.11 | 88.37 | 
| Today’s amplification / Depth retained | 6.21 | 88.04 | 
| Today’s amplification / Depth retained | 6.31 | 87.72 | 
| Today’s amplification / Depth retained | 6.41 | 87.39 | 
| Today’s amplification / Depth retained | 6.51 | 87.06 | 
| Today’s amplification / Depth retained | 6.61 | 86.73 | 
| Today’s amplification / Depth retained | 6.71 | 86.40 | 
| Today’s amplification / Depth retained | 6.81 | 86.06 | 
| Today’s amplification / Depth retained | 6.91 | 85.73 | 
| Today’s amplification / Depth retained | 7.01 | 85.39 | 
| Today’s amplification / Depth retained | 7.11 | 85.05 | 
| Today’s amplification / Depth retained | 7.21 | 84.71 | 
| Today’s amplification / Depth retained | 7.31 | 84.37 | 
| Today’s amplification / Depth retained | 7.41 | 84.03 | 
| Today’s amplification / Depth retained | 7.52 | 83.69 | 
| Today’s amplification / Depth retained | 7.62 | 83.35 | 
| Today’s amplification / Depth retained | 7.72 | 83.01 | 
| Today’s amplification / Depth retained | 7.82 | 82.66 | 
| Today’s amplification / Depth retained | 7.92 | 82.32 | 
| Today’s amplification / Depth retained | 8.02 | 81.97 | 
| Today’s amplification / Depth retained | 8.12 | 81.63 | 
| Today’s amplification / Depth retained | 8.22 | 81.28 | 
| Today’s amplification / Depth retained | 8.32 | 80.94 | 
| Today’s amplification / Depth retained | 8.42 | 80.59 | 
| Today’s amplification / Depth retained | 8.52 | 80.24 | 
| Today’s amplification / Depth retained | 8.62 | 79.90 | 
| Today’s amplification / Depth retained | 8.72 | 79.55 | 
| Today’s amplification / Depth retained | 8.82 | 79.21 | 
| Today’s amplification / Depth retained | 8.92 | 78.86 | 
| Today’s amplification / Depth retained | 9.02 | 78.52 | 
| Today’s amplification / Depth retained | 9.12 | 78.17 | 
| Today’s amplification / Depth retained | 9.22 | 77.83 | 
| Today’s amplification / Depth retained | 9.32 | 77.48 | 
| Today’s amplification / Depth retained | 9.42 | 77.14 | 
| Today’s amplification / Depth retained | 9.52 | 76.80 | 
| Today’s amplification / Depth retained | 9.62 | 76.46 | 
| Today’s amplification / Depth retained | 9.72 | 76.11 | 
| Today’s amplification / Depth retained | 9.82 | 75.77 | 
| Today’s amplification / Depth retained | 9.92 | 75.43 | 
| Today’s amplification / Depth retained | 10.02 | 75.09 | 
| Today’s amplification / Depth retained | 10.12 | 74.75 | 
| Today’s amplification / Depth retained | 10.22 | 74.42 | 
| Today’s amplification / Depth retained | 10.32 | 74.08 | 
| Today’s amplification / Depth retained | 10.42 | 73.74 | 
| Today’s amplification / Depth retained | 10.52 | 73.41 | 
| Today’s amplification / Depth retained | 10.62 | 73.07 | 
| Today’s amplification / Depth retained | 10.72 | 72.74 | 
| Today’s amplification / Depth retained | 10.82 | 72.41 | 
| Today’s amplification / Depth retained | 10.92 | 72.08 | 
| Today’s amplification / Depth retained | 11.02 | 71.75 | 
| Today’s amplification / Depth retained | 11.12 | 71.42 | 
| Today’s amplification / Depth retained | 11.22 | 71.09 | 
| Today’s amplification / Depth retained | 11.32 | 70.77 | 
| Today’s amplification / Depth retained | 11.42 | 70.44 | 
| Today’s amplification / Depth retained | 11.52 | 70.12 | 
| Today’s amplification / Depth retained | 11.62 | 69.79 | 
| Today’s amplification / Depth retained | 11.72 | 69.47 | 
| Today’s amplification / Depth retained | 11.82 | 69.15 | 
| Today’s amplification / Depth retained | 11.92 | 68.83 | 
| Today’s amplification / Depth retained | 12.02 | 68.52 | 
| Today’s amplification / Depth retained | 12.12 | 68.20 | 
| Today’s amplification / Depth retained | 12.22 | 67.89 | 
| Today’s amplification / Depth retained | 12.32 | 67.57 | 
| Today’s amplification / Depth retained | 12.42 | 67.26 | 
| Today’s amplification / Depth retained | 12.53 | 66.95 | 
| Today’s amplification / Depth retained | 12.63 | 66.64 | 
| Today’s amplification / Depth retained | 12.73 | 66.34 | 
| Today’s amplification / Depth retained | 12.83 | 66.03 | 
| Today’s amplification / Depth retained | 12.93 | 65.73 | 
| Today’s amplification / Depth retained | 13.03 | 65.43 | 
| Today’s amplification / Depth retained | 13.13 | 65.12 | 
| Today’s amplification / Depth retained | 13.23 | 64.83 | 
| Today’s amplification / Depth retained | 13.33 | 64.53 | 
| Today’s amplification / Depth retained | 13.43 | 64.23 | 
| Today’s amplification / Depth retained | 13.53 | 63.94 | 
| Today’s amplification / Depth retained | 13.63 | 63.64 | 
| Today’s amplification / Depth retained | 13.73 | 63.35 | 
| Today’s amplification / Depth retained | 13.83 | 63.06 | 
| Today’s amplification / Depth retained | 13.93 | 62.77 | 
| Today’s amplification / Depth retained | 14.03 | 62.49 | 
| Today’s amplification / Depth retained | 14.13 | 62.20 | 
| Today’s amplification / Depth retained | 14.23 | 61.92 | 
| Today’s amplification / Depth retained | 14.33 | 61.64 | 
| Today’s amplification / Depth retained | 14.43 | 61.35 | 
| Today’s amplification / Depth retained | 14.53 | 61.08 | 
| Today’s amplification / Depth retained | 14.63 | 60.80 | 
| Today’s amplification / Depth retained | 14.73 | 60.52 | 
| Today’s amplification / Depth retained | 14.83 | 60.25 | 
| Today’s amplification / Depth retained | 14.93 | 59.98 | 
| Today’s amplification / Depth retained | 15.03 | 59.71 | 
| Today’s amplification / Depth retained | 15.13 | 59.44 | 
| Today’s amplification / Depth retained | 15.23 | 59.17 | 
| Today’s amplification / Depth retained | 15.33 | 58.90 | 
| Today’s amplification / Depth retained | 15.43 | 58.64 | 
| Today’s amplification / Depth retained | 15.53 | 58.38 | 
| Today’s amplification / Depth retained | 15.63 | 58.11 | 
| Today’s amplification / Depth retained | 15.73 | 57.85 | 
| Today’s amplification / Depth retained | 15.83 | 57.60 | 
| Today’s amplification / Depth retained | 15.93 | 57.34 | 
| Today’s amplification / Depth retained | 16.03 | 57.08 | 
| Today’s amplification / Depth retained | 16.13 | 56.83 | 
| Today’s amplification / Depth retained | 16.23 | 56.58 | 
| Today’s amplification / Depth retained | 16.33 | 56.33 | 
| Today’s amplification / Depth retained | 16.43 | 56.08 | 
| Today’s amplification / Depth retained | 16.53 | 55.83 | 
| Today’s amplification / Depth retained | 16.63 | 55.59 | 
| Today’s amplification / Depth retained | 16.73 | 55.34 | 
| Today’s amplification / Depth retained | 16.83 | 55.10 | 
| Today’s amplification / Depth retained | 16.93 | 54.86 | 
| Today’s amplification / Depth retained | 17.03 | 54.62 | 
| Today’s amplification / Depth retained | 17.13 | 54.38 | 
| Today’s amplification / Depth retained | 17.23 | 54.15 | 
| Today’s amplification / Depth retained | 17.33 | 53.91 | 
| Today’s amplification / Depth retained | 17.43 | 53.68 | 
| Today’s amplification / Depth retained | 17.54 | 53.45 | 
| Today’s amplification / Depth retained | 17.64 | 53.22 | 
| Today’s amplification / Depth retained | 17.74 | 52.99 | 
| Today’s amplification / Depth retained | 17.84 | 52.76 | 
| Today’s amplification / Depth retained | 17.94 | 52.53 | 
| Today’s amplification / Depth retained | 18.04 | 52.31 | 
| Today’s amplification / Depth retained | 18.14 | 52.09 | 
| Today’s amplification / Depth retained | 18.24 | 51.87 | 
| Today’s amplification / Depth retained | 18.34 | 51.65 | 
| Today’s amplification / Depth retained | 18.44 | 51.43 | 
| Today’s amplification / Depth retained | 18.54 | 51.21 | 
| Today’s amplification / Depth retained | 18.64 | 50.99 | 
| Today’s amplification / Depth retained | 18.74 | 50.78 | 
| Today’s amplification / Depth retained | 18.84 | 50.57 | 
| Today’s amplification / Depth retained | 18.94 | 50.35 | 
| Today’s amplification / Depth retained | 19.04 | 50.14 | 
| Today’s amplification / Depth retained | 19.14 | 49.94 | 
| Today’s amplification / Depth retained | 19.24 | 49.73 | 
| Today’s amplification / Depth retained | 19.34 | 49.52 | 
| Today’s amplification / Depth retained | 19.44 | 49.32 | 
| Today’s amplification / Depth retained | 19.54 | 49.11 | 
| Today’s amplification / Depth retained | 19.64 | 48.91 | 
| Today’s amplification / Depth retained | 19.74 | 48.71 | 
| Today’s amplification / Depth retained | 19.84 | 48.51 | 
| Today’s amplification / Depth retained | 19.94 | 48.31 | 
| Today’s amplification / Depth retained | 20.04 | 48.12 | 
| Today’s amplification / Depth retained | 20.14 | 47.92 | 
| Today’s amplification / Depth retained | 20.24 | 47.73 | 
| Today’s amplification / Depth retained | 20.34 | 47.53 | 
| Today’s amplification / Depth retained | 20.44 | 47.34 | 
| Today’s amplification / Depth retained | 20.54 | 47.15 | 
| Today’s amplification / Depth retained | 20.64 | 46.96 | 
| Today’s amplification / Depth retained | 20.74 | 46.77 | 
| Today’s amplification / Depth retained | 20.84 | 46.59 | 
| Today’s amplification / Depth retained | 20.94 | 46.40 | 
| Today’s amplification / Depth retained | 21.04 | 46.22 | 
| Today’s amplification / Depth retained | 21.14 | 46.03 | 
| Today’s amplification / Depth retained | 21.24 | 45.85 | 
| Today’s amplification / Depth retained | 21.34 | 45.67 | 
| Today’s amplification / Depth retained | 21.44 | 45.49 | 
| Today’s amplification / Depth retained | 21.54 | 45.31 | 
| Today’s amplification / Depth retained | 21.64 | 45.14 | 
| Today’s amplification / Depth retained | 21.74 | 44.96 | 
| Today’s amplification / Depth retained | 21.84 | 44.79 | 
| Today’s amplification / Depth retained | 21.94 | 44.61 | 
| Today’s amplification / Depth retained | 22.04 | 44.44 | 
| Today’s amplification / Depth retained | 22.14 | 44.27 | 
| Today’s amplification / Depth retained | 22.24 | 44.10 | 
| Today’s amplification / Depth retained | 22.34 | 43.93 | 
| Today’s amplification / Depth retained | 22.44 | 43.76 | 
| Today’s amplification / Depth retained | 22.55 | 43.60 | 
| Today’s amplification / Depth retained | 22.65 | 43.43 | 
| Today’s amplification / Depth retained | 22.75 | 43.26 | 
| Today’s amplification / Depth retained | 22.85 | 43.10 | 
| Today’s amplification / Depth retained | 22.95 | 42.94 | 
| Today’s amplification / Depth retained | 23.05 | 42.78 | 
| Today’s amplification / Depth retained | 23.15 | 42.62 | 
| Today’s amplification / Depth retained | 23.25 | 42.46 | 
| Today’s amplification / Depth retained | 23.35 | 42.30 | 
| Today’s amplification / Depth retained | 23.45 | 42.14 | 
| Today’s amplification / Depth retained | 23.55 | 41.99 | 
| Today’s amplification / Depth retained | 23.65 | 41.83 | 
| Today’s amplification / Depth retained | 23.75 | 41.68 | 
| Today’s amplification / Depth retained | 23.85 | 41.52 | 
| Today’s amplification / Depth retained | 23.95 | 41.37 | 
| Today’s amplification / Depth retained | 24.05 | 41.22 | 
| Today’s amplification / Depth retained | 24.15 | 41.07 | 
| Today’s amplification / Depth retained | 24.25 | 40.92 | 
| Today’s amplification / Depth retained | 24.35 | 40.77 | 
| Today’s amplification / Depth retained | 24.45 | 40.62 | 
| Today’s amplification / Depth retained | 24.55 | 40.48 | 
| Today’s amplification / Depth retained | 24.65 | 40.33 | 
| Today’s amplification / Depth retained | 24.75 | 40.19 | 
| Today’s amplification / Depth retained | 24.85 | 40.04 | 
| Today’s amplification / Depth retained | 24.95 | 39.90 | 
| Today’s amplification / Depth retained | 25.05 | 39.76 | 
| Today’s amplification / Depth retained | 25.15 | 39.62 | 
| Today’s amplification / Depth retained | 25.25 | 39.48 | 
| Today’s amplification / Depth retained | 25.35 | 39.34 | 
| Today’s amplification / Depth retained | 25.45 | 39.20 | 
| Today’s amplification / Depth retained | 25.55 | 39.06 | 
| Today’s amplification / Depth retained | 25.65 | 38.93 | 
| Today’s amplification / Depth retained | 25.75 | 38.79 | 
| Today’s amplification / Depth retained | 25.85 | 38.66 | 
| Today’s amplification / Depth retained | 25.95 | 38.52 | 
| Today’s amplification / Depth retained | 26.05 | 38.39 | 
| Today’s amplification / Depth retained | 26.15 | 38.26 | 
| Today’s amplification / Depth retained | 26.25 | 38.12 | 
| Today’s amplification / Depth retained | 26.35 | 37.99 | 
| Today’s amplification / Depth retained | 26.45 | 37.86 | 
| Today’s amplification / Depth retained | 26.55 | 37.73 | 
| Today’s amplification / Depth retained | 26.65 | 37.61 | 
| Today’s amplification / Depth retained | 26.75 | 37.48 | 
| Today’s amplification / Depth retained | 26.85 | 37.35 | 
| Today’s amplification / Depth retained | 26.95 | 37.23 | 
| Today’s amplification / Depth retained | 27.05 | 37.10 | 
| Today’s amplification / Depth retained | 27.15 | 36.98 | 
| Today’s amplification / Depth retained | 27.25 | 36.85 | 
| Today’s amplification / Depth retained | 27.35 | 36.73 | 
| Today’s amplification / Depth retained | 27.45 | 36.61 | 
| Today’s amplification / Depth retained | 27.56 | 36.49 | 
| Today’s amplification / Depth retained | 27.66 | 36.37 | 
| Today’s amplification / Depth retained | 27.76 | 36.25 | 
| Today’s amplification / Depth retained | 27.86 | 36.13 | 
| Today’s amplification / Depth retained | 27.96 | 36.01 | 
| Today’s amplification / Depth retained | 28.06 | 35.89 | 
| Today’s amplification / Depth retained | 28.16 | 35.78 | 
| Today’s amplification / Depth retained | 28.26 | 35.66 | 
| Today’s amplification / Depth retained | 28.36 | 35.55 | 
| Today’s amplification / Depth retained | 28.46 | 35.43 | 
| Today’s amplification / Depth retained | 28.56 | 35.32 | 
| Today’s amplification / Depth retained | 28.66 | 35.20 | 
| Today’s amplification / Depth retained | 28.76 | 35.09 | 
| Today’s amplification / Depth retained | 28.86 | 34.98 | 
| Today’s amplification / Depth retained | 28.96 | 34.87 | 
| Today’s amplification / Depth retained | 29.06 | 34.76 | 
| Today’s amplification / Depth retained | 29.16 | 34.65 | 
| Today’s amplification / Depth retained | 29.26 | 34.54 | 
| Today’s amplification / Depth retained | 29.36 | 34.43 | 
| Today’s amplification / Depth retained | 29.46 | 34.32 | 
| Today’s amplification / Depth retained | 29.56 | 34.22 | 
| Today’s amplification / Depth retained | 29.66 | 34.11 | 
| Today’s amplification / Depth retained | 29.76 | 34.00 | 
| Today’s amplification / Depth retained | 29.86 | 33.90 | 
| Today’s amplification / Depth retained | 29.96 | 33.79 | 
| Warning tier boundary | 4.93 | 92.00 | 
| Serious tier boundary | 10.05 | 75.00 | 
| Severe tier boundary | 19.11 | 50.00 | 

**Chart data $\cdot$ Daily depth retained in the live pools**

% of centred depth
| Panel / curve | Coordinate $\cdot$ UTC date | % of centred depth | Stall-window end, UTC | 
| --- | --- | --- | --- |
| WETH / WETH | 2026-05-26 00:00:00+00:00 | 99.70 | — | 
| WETH / WETH | 2026-05-27 00:00:00+00:00 | 99.81 | — | 
| WETH / WETH | 2026-05-28 00:00:00+00:00 | 99.05 | — | 
| WETH / WETH | 2026-05-29 00:00:00+00:00 | 99.77 | — | 
| WETH / WETH | 2026-05-30 00:00:00+00:00 | 99.98 | — | 
| WETH / WETH | 2026-05-31 00:00:00+00:00 | 99.84 | — | 
| WETH / WETH | 2026-06-01 00:00:00+00:00 | 99.50 | — | 
| WETH / WETH | 2026-06-02 00:00:00+00:00 | 99.75 | — | 
| WETH / WETH | 2026-06-03 00:00:00+00:00 | 99.35 | — | 
| WETH / WETH | 2026-06-04 00:00:00+00:00 | 99.43 | — | 
| WETH / WETH | 2026-06-05 00:00:00+00:00 | 98.22 | — | 
| WETH / WETH | 2026-06-06 00:00:00+00:00 | 99.57 | — | 
| WETH / WETH | 2026-06-07 00:00:00+00:00 | 99.14 | — | 
| WETH / WETH | 2026-06-08 00:00:00+00:00 | 99.32 | — | 
| WETH / WETH | 2026-06-09 00:00:00+00:00 | 99.64 | — | 
| WETH / WETH | 2026-06-10 00:00:00+00:00 | 99.70 | — | 
| WETH / WETH | 2026-06-11 00:00:00+00:00 | 99.46 | — | 
| WETH / WETH | 2026-06-12 00:00:00+00:00 | 99.80 | — | 
| WETH / WETH | 2026-06-13 00:00:00+00:00 | 99.93 | — | 
| WETH / WETH | 2026-06-14 00:00:00+00:00 | 99.69 | — | 
| WETH / WETH | 2026-06-15 00:00:00+00:00 | 98.87 | — | 
| WETH / WETH | 2026-06-16 00:00:00+00:00 | 99.44 | — | 
| WETH / WETH | 2026-06-17 00:00:00+00:00 | 99.62 | — | 
| WETH / WETH | 2026-06-18 00:00:00+00:00 | 99.31 | — | 
| WETH / WETH | 2026-06-19 00:00:00+00:00 | 99.72 | — | 
| WETH / WETH | 2026-06-20 00:00:00+00:00 | 99.14 | — | 
| WETH / WETH | 2026-06-21 00:00:00+00:00 | 99.51 | — | 
| WETH / WETH | 2026-06-22 00:00:00+00:00 | 99.72 | — | 
| WETH / WETH | 2026-06-23 00:00:00+00:00 | 98.63 | — | 
| WETH / WETH | 2026-06-24 00:00:00+00:00 | 99.10 | — | 
| WETH / WETH | 2026-06-25 00:00:00+00:00 | 98.08 | — | 
| WETH / WETH | 2026-06-26 00:00:00+00:00 | 98.06 | — | 
| WETH / WETH | 2026-06-27 00:00:00+00:00 | 99.72 | — | 
| WETH / WETH | 2026-06-28 00:00:00+00:00 | 99.49 | — | 
| WETH / WETH | 2026-06-29 00:00:00+00:00 | 99.45 | — | 
| WETH / WETH | 2026-06-30 00:00:00+00:00 | 99.66 | — | 
| WETH / WETH | 2026-07-01 00:00:00+00:00 | 99.21 | — | 
| WETH / WETH | 2026-07-02 00:00:00+00:00 | 99.62 | — | 
| WETH / WETH | 2026-07-03 00:00:00+00:00 | 99.52 | — | 
| WETH / WETH | 2026-07-04 00:00:00+00:00 | 99.65 | — | 
| WETH / WETH | 2026-07-05 00:00:00+00:00 | 99.78 | — | 
| WETH / WETH | 2026-07-06 00:00:00+00:00 | 99.63 | — | 
| WETH / WETH | 2026-07-07 00:00:00+00:00 | 99.41 | — | 
| WETH / WETH | 2026-07-08 00:00:00+00:00 | 99.56 | — | 
| WETH / WETH | 2026-07-09 00:00:00+00:00 | 99.84 | — | 
| WETH / WETH | 2026-07-10 00:00:00+00:00 | 99.54 | — | 
| WETH / WETH | 2026-07-11 00:00:00+00:00 | 99.81 | — | 
| WETH / WETH | 2026-07-12 00:00:00+00:00 | 99.87 | — | 
| WETH / WETH | 2026-07-13 00:00:00+00:00 | 99.17 | — | 
| WETH / WETH | 2026-07-14 00:00:00+00:00 | 99.38 | — | 
| WETH / WETH | 2026-07-15 00:00:00+00:00 | 99.40 | — | 
| WETH / WETH | 2026-07-16 00:00:00+00:00 | 99.18 | — | 
| WETH / WETH | 2026-07-17 00:00:00+00:00 | 99.41 | — | 
| WETH / WETH | 2026-07-18 00:00:00+00:00 | 99.28 | — | 
| WETH / WETH | 2026-07-19 00:00:00+00:00 | 98.91 | — | 
| WETH / WETH | 2026-07-20 00:00:00+00:00 | 99.52 | — | 
| WETH / WETH | 2026-07-21 00:00:00+00:00 | 99.09 | — | 
| WETH / WETH | 2026-07-22 00:00:00+00:00 | 99.59 | — | 
| WETH / WETH | 2026-07-23 00:00:00+00:00 | 99.56 | — | 
| WETH / WETH | 2026-07-24 00:00:00+00:00 | 99.54 | — | 
| WETH / WETH | 2026-07-25 00:00:00+00:00 | 99.68 | — | 
| WETH / WETH | 2026-07-26 00:00:00+00:00 | 99.57 | — | 
| WETH / WETH | 2026-07-27 00:00:00+00:00 | 99.60 | — | 
| WETH / WETH | 2026-07-28 00:00:00+00:00 | 99.20 | — | 
| WETH / WETH | 2026-07-29 00:00:00+00:00 | 99.68 | — | 
| WETH / WETH | 2026-07-30 00:00:00+00:00 | 99.78 | — | 
| WETH / WETH | 2026-07-31 00:00:00+00:00 | 99.55 | — | 
| WETH / WETH | 2026-08-01 00:00:00+00:00 | 99.52 | — | 
| WETH / WETH | 2026-08-02 00:00:00+00:00 | 99.56 | — | 
| WETH / WETH | 2026-08-03 00:00:00+00:00 | 99.79 | — | 
| WETH / WETH | 2026-08-04 00:00:00+00:00 | 99.69 | — | 
| WETH / WETH | 2026-08-05 00:00:00+00:00 | 99.35 | — | 
| WETH / WETH | 2026-08-06 00:00:00+00:00 | 99.33 | — | 
| WETH / WETH | 2026-08-07 00:00:00+00:00 | 99.83 | — | 
| WETH / WETH | 2026-08-08 00:00:00+00:00 | 99.97 | — | 
| WETH / WETH | 2026-08-09 00:00:00+00:00 | 99.97 | — | 
| WETH / WETH | 2026-08-10 00:00:00+00:00 | 99.49 | — | 
| WETH / WETH | 2026-08-11 00:00:00+00:00 | 99.39 | — | 
| WETH / WETH | 2026-08-12 00:00:00+00:00 | 99.81 | — | 
| WETH / WETH | 2026-08-13 00:00:00+00:00 | 99.84 | — | 
| WETH / WETH | 2026-08-14 00:00:00+00:00 | 99.61 | — | 
| WETH / WETH | 2026-08-15 00:00:00+00:00 | 99.83 | — | 
| WETH / WETH | 2026-08-16 00:00:00+00:00 | 99.88 | — | 
| WETH / WETH | 2026-08-17 00:00:00+00:00 | 99.68 | — | 
| WETH / WETH | 2026-08-18 00:00:00+00:00 | 99.70 | — | 
| WETH / WETH | 2026-08-19 00:00:00+00:00 | 98.73 | — | 
| WETH / WETH | 2026-08-20 00:00:00+00:00 | 99.58 | — | 
| WETH / WETH | 2026-08-21 00:00:00+00:00 | 99.41 | — | 
| WETH / WETH | 2026-08-22 00:00:00+00:00 | 99.06 | — | 
| WETH / WETH | 2026-08-23 00:00:00+00:00 | 99.56 | — | 
| WETH / WETH | 2026-08-24 00:00:00+00:00 | 99.63 | — | 
| WETH / WETH | 2026-08-25 00:00:00+00:00 | 99.75 | — | 
| WETH / WETH | 2026-08-26 00:00:00+00:00 | 99.66 | — | 
| WETH / WETH | 2026-08-27 00:00:00+00:00 | 99.78 | — | 
| WETH / WETH | 2026-08-28 00:00:00+00:00 | 99.71 | — | 
| WETH / WETH | 2026-08-29 00:00:00+00:00 | 99.68 | — | 
| WETH / WETH | 2026-08-30 00:00:00+00:00 | 99.42 | — | 
| WETH / WETH | 2026-08-31 00:00:00+00:00 | 99.61 | — | 
| WETH / WETH | 2026-09-01 00:00:00+00:00 | 99.66 | — | 
| WETH / WETH | 2026-09-02 00:00:00+00:00 | 99.80 | — | 
| WETH / WETH | 2026-09-03 00:00:00+00:00 | 99.41 | — | 
| WETH / WETH | 2026-09-04 00:00:00+00:00 | 99.60 | — | 
| WETH / WETH | 2026-09-05 00:00:00+00:00 | 99.44 | — | 
| WETH / WETH | 2026-09-06 00:00:00+00:00 | 99.51 | — | 
| WETH / WETH | 2026-09-07 00:00:00+00:00 | 99.78 | — | 
| WETH / WETH | 2026-09-08 00:00:00+00:00 | 99.78 | — | 
| WETH / WETH | 2026-09-09 00:00:00+00:00 | 99.72 | — | 
| WETH / WETH | 2026-09-10 00:00:00+00:00 | 99.83 | — | 
| WETH / WETH | 2026-09-11 00:00:00+00:00 | 99.30 | — | 
| WETH / WETH | 2026-09-12 00:00:00+00:00 | 99.76 | — | 
| WETH / WETH | 2026-09-13 00:00:00+00:00 | 99.75 | — | 
| WETH / WETH | 2026-09-14 00:00:00+00:00 | 99.44 | — | 
| WETH / WETH | 2026-09-15 00:00:00+00:00 | 99.63 | — | 
| WETH / WETH | 2026-09-16 00:00:00+00:00 | 99.76 | — | 
| WETH / WETH | 2026-09-17 00:00:00+00:00 | 99.77 | — | 
| WETH / WETH | 2026-09-18 00:00:00+00:00 | 99.50 | — | 
| WETH / WETH | 2026-09-19 00:00:00+00:00 | 99.80 | — | 
| WETH / WETH | 2026-09-20 00:00:00+00:00 | 99.53 | — | 
| WETH / WETH | 2026-09-21 00:00:00+00:00 | 99.67 | — | 
| WETH / WETH | 2026-09-22 00:00:00+00:00 | 99.61 | — | 
| WETH / WETH | 2026-09-23 00:00:00+00:00 | 99.60 | — | 
| WETH / WETH | 2026-09-24 00:00:00+00:00 | 99.66 | — | 
| WETH / WETH | 2026-09-25 00:00:00+00:00 | 99.71 | — | 
| WETH / WETH | 2026-09-26 00:00:00+00:00 | 99.93 | — | 
| WETH / WETH | 2026-09-27 00:00:00+00:00 | 99.93 | — | 
| WETH / WETH | 2026-09-28 00:00:00+00:00 | 99.69 | — | 
| WETH / WETH | 2026-09-29 00:00:00+00:00 | 99.55 | — | 
| WETH / WETH | 2026-09-30 00:00:00+00:00 | 99.63 | — | 
| WBTC / WBTC | 2026-05-26 00:00:00+00:00 | 99.61 | — | 
| WBTC / WBTC | 2026-05-27 00:00:00+00:00 | 99.59 | — | 
| WBTC / WBTC | 2026-05-28 00:00:00+00:00 | 99.43 | — | 
| WBTC / WBTC | 2026-05-29 00:00:00+00:00 | 99.84 | — | 
| WBTC / WBTC | 2026-05-30 00:00:00+00:00 | 99.96 | — | 
| WBTC / WBTC | 2026-05-31 00:00:00+00:00 | 99.97 | — | 
| WBTC / WBTC | 2026-06-01 00:00:00+00:00 | 99.23 | — | 
| WBTC / WBTC | 2026-06-02 00:00:00+00:00 | 92.95 | — | 
| WBTC / WBTC | 2026-06-03 00:00:00+00:00 | 84.65 | — | 
| WBTC / WBTC | 2026-06-04 00:00:00+00:00 | 73.09 | — | 
| WBTC / WBTC | 2026-06-05 00:00:00+00:00 | 66.14 | — | 
| WBTC / WBTC | 2026-06-06 00:00:00+00:00 | 62.51 | — | 
| WBTC / WBTC | 2026-06-07 00:00:00+00:00 | 68.33 | — | 
| WBTC / WBTC | 2026-06-08 00:00:00+00:00 | 77.21 | — | 
| WBTC / WBTC | 2026-06-09 00:00:00+00:00 | 72.13 | — | 
| WBTC / WBTC | 2026-06-10 00:00:00+00:00 | 68.09 | — | 
| WBTC / WBTC | 2026-06-11 00:00:00+00:00 | 75.03 | — | 
| WBTC / WBTC | 2026-06-12 00:00:00+00:00 | 79.97 | — | 
| WBTC / WBTC | 2026-06-13 00:00:00+00:00 | 82.11 | — | 
| WBTC / WBTC | 2026-06-14 00:00:00+00:00 | 84.58 | — | 
| WBTC / WBTC | 2026-06-15 00:00:00+00:00 | 95.15 | — | 
| WBTC / WBTC | 2026-06-16 00:00:00+00:00 | 96.38 | — | 
| WBTC / WBTC | 2026-06-17 00:00:00+00:00 | 94.02 | — | 
| WBTC / WBTC | 2026-06-18 00:00:00+00:00 | 88.23 | — | 
| WBTC / WBTC | 2026-06-19 00:00:00+00:00 | 85.10 | — | 
| WBTC / WBTC | 2026-06-20 00:00:00+00:00 | 89.40 | — | 
| WBTC / WBTC | 2026-06-21 00:00:00+00:00 | 91.27 | — | 
| WBTC / WBTC | 2026-06-22 00:00:00+00:00 | 94.18 | — | 
| WBTC / WBTC | 2026-06-23 00:00:00+00:00 | 89.34 | — | 
| WBTC / WBTC | 2026-06-24 00:00:00+00:00 | 84.91 | — | 
| WBTC / WBTC | 2026-06-25 00:00:00+00:00 | 81.52 | — | 
| WBTC / WBTC | 2026-06-26 00:00:00+00:00 | 78.12 | — | 
| WBTC / WBTC | 2026-06-27 00:00:00+00:00 | 81.70 | — | 
| WBTC / WBTC | 2026-06-28 00:00:00+00:00 | 80.59 | — | 
| WBTC / WBTC | 2026-06-29 00:00:00+00:00 | 80.68 | — | 
| WBTC / WBTC | 2026-06-30 00:00:00+00:00 | 75.73 | — | 
| WBTC / WBTC | 2026-07-01 00:00:00+00:00 | 78.13 | — | 
| WBTC / WBTC | 2026-07-02 00:00:00+00:00 | 89.09 | — | 
| WBTC / WBTC | 2026-07-03 00:00:00+00:00 | 94.31 | — | 
| WBTC / WBTC | 2026-07-04 00:00:00+00:00 | 98.21 | — | 
| WBTC / WBTC | 2026-07-05 00:00:00+00:00 | 99.87 | — | 
| WBTC / WBTC | 2026-07-06 00:00:00+00:00 | 99.31 | — | 
| WBTC / WBTC | 2026-07-07 00:00:00+00:00 | 99.61 | — | 
| WBTC / WBTC | 2026-07-08 00:00:00+00:00 | 99.48 | — | 
| WBTC / WBTC | 2026-07-09 00:00:00+00:00 | 99.74 | — | 
| WBTC / WBTC | 2026-07-10 00:00:00+00:00 | 99.72 | — | 
| WBTC / WBTC | 2026-07-11 00:00:00+00:00 | 99.78 | — | 
| WBTC / WBTC | 2026-07-12 00:00:00+00:00 | 99.94 | — | 
| WBTC / WBTC | 2026-07-13 00:00:00+00:00 | 99.17 | — | 
| WBTC / WBTC | 2026-07-14 00:00:00+00:00 | 98.70 | — | 
| WBTC / WBTC | 2026-07-15 00:00:00+00:00 | 99.05 | — | 
| WBTC / WBTC | 2026-07-16 00:00:00+00:00 | 99.58 | — | 
| WBTC / WBTC | 2026-07-17 00:00:00+00:00 | 99.11 | — | 
| WBTC / WBTC | 2026-07-18 00:00:00+00:00 | 99.23 | — | 
| WBTC / WBTC | 2026-07-19 00:00:00+00:00 | 99.19 | — | 
| WBTC / WBTC | 2026-07-20 00:00:00+00:00 | 99.58 | — | 
| WBTC / WBTC | 2026-07-21 00:00:00+00:00 | 99.35 | — | 
| WBTC / WBTC | 2026-07-22 00:00:00+00:00 | 99.32 | — | 
| WBTC / WBTC | 2026-07-23 00:00:00+00:00 | 99.20 | — | 
| WBTC / WBTC | 2026-07-24 00:00:00+00:00 | 99.68 | — | 
| WBTC / WBTC | 2026-07-25 00:00:00+00:00 | 99.85 | — | 
| WBTC / WBTC | 2026-07-26 00:00:00+00:00 | 99.24 | — | 
| WBTC / WBTC | 2026-07-27 00:00:00+00:00 | 99.28 | — | 
| WBTC / WBTC | 2026-07-28 00:00:00+00:00 | 99.64 | — | 
| WBTC / WBTC | 2026-07-29 00:00:00+00:00 | 99.72 | — | 
| WBTC / WBTC | 2026-07-30 00:00:00+00:00 | 99.68 | — | 
| WBTC / WBTC | 2026-07-31 00:00:00+00:00 | 99.45 | — | 
| WBTC / WBTC | 2026-08-01 00:00:00+00:00 | 99.58 | — | 
| WBTC / WBTC | 2026-08-02 00:00:00+00:00 | 99.30 | — | 
| WBTC / WBTC | 2026-08-03 00:00:00+00:00 | 99.64 | — | 
| WBTC / WBTC | 2026-08-04 00:00:00+00:00 | 99.66 | — | 
| WBTC / WBTC | 2026-08-05 00:00:00+00:00 | 99.69 | — | 
| WBTC / WBTC | 2026-08-06 00:00:00+00:00 | 99.96 | — | 
| WBTC / WBTC | 2026-08-07 00:00:00+00:00 | 99.90 | — | 
| WBTC / WBTC | 2026-08-08 00:00:00+00:00 | 99.85 | — | 
| WBTC / WBTC | 2026-08-09 00:00:00+00:00 | 99.80 | — | 
| WBTC / WBTC | 2026-08-10 00:00:00+00:00 | 99.76 | — | 
| WBTC / WBTC | 2026-08-11 00:00:00+00:00 | 99.67 | — | 
| WBTC / WBTC | 2026-08-12 00:00:00+00:00 | 99.80 | — | 
| WBTC / WBTC | 2026-08-13 00:00:00+00:00 | 99.62 | — | 
| WBTC / WBTC | 2026-08-14 00:00:00+00:00 | 99.68 | — | 
| WBTC / WBTC | 2026-08-15 00:00:00+00:00 | 99.95 | — | 
| WBTC / WBTC | 2026-08-16 00:00:00+00:00 | 99.99 | — | 
| WBTC / WBTC | 2026-08-17 00:00:00+00:00 | 99.60 | — | 
| WBTC / WBTC | 2026-08-18 00:00:00+00:00 | 99.76 | — | 
| WBTC / WBTC | 2026-08-19 00:00:00+00:00 | 97.44 | — | 
| WBTC / WBTC | 2026-08-20 00:00:00+00:00 | 85.74 | — | 
| WBTC / WBTC | 2026-08-21 00:00:00+00:00 | 66.62 | — | 
| WBTC / WBTC | 2026-08-22 00:00:00+00:00 | 64.55 | — | 
| WBTC / WBTC | 2026-08-23 00:00:00+00:00 | 65.91 | — | 
| WBTC / WBTC | 2026-08-24 00:00:00+00:00 | 62.05 | — | 
| WBTC / WBTC | 2026-08-25 00:00:00+00:00 | 58.25 | — | 
| WBTC / WBTC | 2026-08-26 00:00:00+00:00 | 61.13 | — | 
| WBTC / WBTC | 2026-08-27 00:00:00+00:00 | 57.86 | — | 
| WBTC / WBTC | 2026-08-28 00:00:00+00:00 | 60.25 | — | 
| WBTC / WBTC | 2026-08-29 00:00:00+00:00 | 64.43 | — | 
| WBTC / WBTC | 2026-08-30 00:00:00+00:00 | 62.19 | — | 
| WBTC / WBTC | 2026-08-31 00:00:00+00:00 | 62.64 | — | 
| WBTC / WBTC | 2026-09-01 00:00:00+00:00 | 64.03 | — | 
| WBTC / WBTC | 2026-09-02 00:00:00+00:00 | 67.49 | — | 
| WBTC / WBTC | 2026-09-03 00:00:00+00:00 | 60.89 | — | 
| WBTC / WBTC | 2026-09-04 00:00:00+00:00 | 57.13 | — | 
| WBTC / WBTC | 2026-09-05 00:00:00+00:00 | 58.83 | — | 
| WBTC / WBTC | 2026-09-06 00:00:00+00:00 | 58.33 | — | 
| WBTC / WBTC | 2026-09-07 00:00:00+00:00 | 59.92 | — | 
| WBTC / WBTC | 2026-09-08 00:00:00+00:00 | 63.09 | — | 
| WBTC / WBTC | 2026-09-09 00:00:00+00:00 | 62.43 | — | 
| WBTC / WBTC | 2026-09-10 00:00:00+00:00 | 66.97 | — | 
| WBTC / WBTC | 2026-09-11 00:00:00+00:00 | 68.70 | — | 
| WBTC / WBTC | 2026-09-12 00:00:00+00:00 | 69.19 | — | 
| WBTC / WBTC | 2026-09-13 00:00:00+00:00 | 70.28 | — | 
| WBTC / WBTC | 2026-09-14 00:00:00+00:00 | 66.54 | — | 
| WBTC / WBTC | 2026-09-15 00:00:00+00:00 | 72.81 | — | 
| WBTC / WBTC | 2026-09-16 00:00:00+00:00 | 77.83 | — | 
| WBTC / WBTC | 2026-09-17 00:00:00+00:00 | 74.67 | — | 
| WBTC / WBTC | 2026-09-18 00:00:00+00:00 | 65.57 | — | 
| WBTC / WBTC | 2026-09-19 00:00:00+00:00 | 57.90 | — | 
| WBTC / WBTC | 2026-09-20 00:00:00+00:00 | 59.58 | — | 
| WBTC / WBTC | 2026-09-21 00:00:00+00:00 | 50.47 | — | 
| WBTC / WBTC | 2026-09-22 00:00:00+00:00 | 46.18 | — | 
| WBTC / WBTC | 2026-09-23 00:00:00+00:00 | 47.46 | — | 
| WBTC / WBTC | 2026-09-24 00:00:00+00:00 | 50.67 | — | 
| WBTC / WBTC | 2026-09-25 00:00:00+00:00 | 50.49 | — | 
| WBTC / WBTC | 2026-09-26 00:00:00+00:00 | 50.82 | — | 
| WBTC / WBTC | 2026-09-27 00:00:00+00:00 | 49.51 | — | 
| WBTC / WBTC | 2026-09-28 00:00:00+00:00 | 52.78 | — | 
| WBTC / WBTC | 2026-09-29 00:00:00+00:00 | 52.33 | — | 
| WBTC / WBTC | 2026-09-30 00:00:00+00:00 | 52.13 | — | 
| cbBTC / cbBTC | 2026-05-26 00:00:00+00:00 | 99.72 | — | 
| cbBTC / cbBTC | 2026-05-27 00:00:00+00:00 | 99.54 | — | 
| cbBTC / cbBTC | 2026-05-28 00:00:00+00:00 | 99.55 | — | 
| cbBTC / cbBTC | 2026-05-29 00:00:00+00:00 | 99.88 | — | 
| cbBTC / cbBTC | 2026-05-30 00:00:00+00:00 | 99.97 | — | 
| cbBTC / cbBTC | 2026-05-31 00:00:00+00:00 | 99.97 | — | 
| cbBTC / cbBTC | 2026-06-01 00:00:00+00:00 | 99.20 | — | 
| cbBTC / cbBTC | 2026-06-02 00:00:00+00:00 | 92.62 | — | 
| cbBTC / cbBTC | 2026-06-03 00:00:00+00:00 | 84.17 | — | 
| cbBTC / cbBTC | 2026-06-04 00:00:00+00:00 | 71.31 | — | 
| cbBTC / cbBTC | 2026-06-05 00:00:00+00:00 | 63.95 | — | 
| cbBTC / cbBTC | 2026-06-06 00:00:00+00:00 | 59.72 | — | 
| cbBTC / cbBTC | 2026-06-07 00:00:00+00:00 | 66.16 | — | 
| cbBTC / cbBTC | 2026-06-08 00:00:00+00:00 | 73.38 | — | 
| cbBTC / cbBTC | 2026-06-09 00:00:00+00:00 | 68.38 | — | 
| cbBTC / cbBTC | 2026-06-10 00:00:00+00:00 | 64.54 | — | 
| cbBTC / cbBTC | 2026-06-11 00:00:00+00:00 | 71.99 | — | 
| cbBTC / cbBTC | 2026-06-12 00:00:00+00:00 | 76.05 | — | 
| cbBTC / cbBTC | 2026-06-13 00:00:00+00:00 | 78.17 | — | 
| cbBTC / cbBTC | 2026-06-14 00:00:00+00:00 | 80.70 | — | 
| cbBTC / cbBTC | 2026-06-15 00:00:00+00:00 | 91.74 | — | 
| cbBTC / cbBTC | 2026-06-16 00:00:00+00:00 | 92.20 | — | 
| cbBTC / cbBTC | 2026-06-17 00:00:00+00:00 | 89.31 | — | 
| cbBTC / cbBTC | 2026-06-18 00:00:00+00:00 | 82.71 | — | 
| cbBTC / cbBTC | 2026-06-19 00:00:00+00:00 | 79.45 | — | 
| cbBTC / cbBTC | 2026-06-20 00:00:00+00:00 | 83.95 | — | 
| cbBTC / cbBTC | 2026-06-21 00:00:00+00:00 | 86.02 | — | 
| cbBTC / cbBTC | 2026-06-22 00:00:00+00:00 | 88.00 | — | 
| cbBTC / cbBTC | 2026-06-23 00:00:00+00:00 | 80.97 | — | 
| cbBTC / cbBTC | 2026-06-24 00:00:00+00:00 | 76.33 | — | 
| cbBTC / cbBTC | 2026-06-25 00:00:00+00:00 | 71.31 | — | 
| cbBTC / cbBTC | 2026-06-26 00:00:00+00:00 | 68.72 | — | 
| cbBTC / cbBTC | 2026-06-27 00:00:00+00:00 | 72.14 | — | 
| cbBTC / cbBTC | 2026-06-28 00:00:00+00:00 | 69.99 | — | 
| cbBTC / cbBTC | 2026-06-29 00:00:00+00:00 | 70.04 | — | 
| cbBTC / cbBTC | 2026-06-30 00:00:00+00:00 | 65.55 | — | 
| cbBTC / cbBTC | 2026-07-01 00:00:00+00:00 | 67.22 | — | 
| cbBTC / cbBTC | 2026-07-02 00:00:00+00:00 | 77.71 | — | 
| cbBTC / cbBTC | 2026-07-03 00:00:00+00:00 | 82.86 | — | 
| cbBTC / cbBTC | 2026-07-04 00:00:00+00:00 | 88.76 | — | 
| cbBTC / cbBTC | 2026-07-05 00:00:00+00:00 | 89.24 | — | 
| cbBTC / cbBTC | 2026-07-06 00:00:00+00:00 | 92.82 | — | 
| cbBTC / cbBTC | 2026-07-07 00:00:00+00:00 | 96.12 | — | 
| cbBTC / cbBTC | 2026-07-08 00:00:00+00:00 | 92.57 | — | 
| cbBTC / cbBTC | 2026-07-09 00:00:00+00:00 | 94.50 | — | 
| cbBTC / cbBTC | 2026-07-10 00:00:00+00:00 | 99.33 | — | 
| cbBTC / cbBTC | 2026-07-11 00:00:00+00:00 | 99.93 | — | 
| cbBTC / cbBTC | 2026-07-12 00:00:00+00:00 | 99.98 | — | 
| cbBTC / cbBTC | 2026-07-13 00:00:00+00:00 | 99.24 | — | 
| cbBTC / cbBTC | 2026-07-14 00:00:00+00:00 | 99.55 | — | 
| cbBTC / cbBTC | 2026-07-15 00:00:00+00:00 | 99.54 | — | 
| cbBTC / cbBTC | 2026-07-16 00:00:00+00:00 | 99.61 | — | 
| cbBTC / cbBTC | 2026-07-17 00:00:00+00:00 | 99.20 | — | 
| cbBTC / cbBTC | 2026-07-18 00:00:00+00:00 | 99.33 | — | 
| cbBTC / cbBTC | 2026-07-19 00:00:00+00:00 | 99.74 | — | 
| cbBTC / cbBTC | 2026-07-20 00:00:00+00:00 | 99.73 | — | 
| cbBTC / cbBTC | 2026-07-21 00:00:00+00:00 | 99.27 | — | 
| cbBTC / cbBTC | 2026-07-22 00:00:00+00:00 | 99.33 | — | 
| cbBTC / cbBTC | 2026-07-23 00:00:00+00:00 | 99.21 | — | 
| cbBTC / cbBTC | 2026-07-24 00:00:00+00:00 | 99.69 | — | 
| cbBTC / cbBTC | 2026-07-25 00:00:00+00:00 | 99.90 | — | 
| cbBTC / cbBTC | 2026-07-26 00:00:00+00:00 | 99.83 | — | 
| cbBTC / cbBTC | 2026-07-27 00:00:00+00:00 | 99.42 | — | 
| cbBTC / cbBTC | 2026-07-28 00:00:00+00:00 | 99.34 | — | 
| cbBTC / cbBTC | 2026-07-29 00:00:00+00:00 | 99.84 | — | 
| cbBTC / cbBTC | 2026-07-30 00:00:00+00:00 | 99.59 | — | 
| cbBTC / cbBTC | 2026-07-31 00:00:00+00:00 | 99.40 | — | 
| cbBTC / cbBTC | 2026-08-01 00:00:00+00:00 | 99.37 | — | 
| cbBTC / cbBTC | 2026-08-02 00:00:00+00:00 | 99.56 | — | 
| cbBTC / cbBTC | 2026-08-03 00:00:00+00:00 | 99.65 | — | 
| cbBTC / cbBTC | 2026-08-04 00:00:00+00:00 | 99.56 | — | 
| cbBTC / cbBTC | 2026-08-05 00:00:00+00:00 | 99.83 | — | 
| cbBTC / cbBTC | 2026-08-06 00:00:00+00:00 | 99.81 | — | 
| cbBTC / cbBTC | 2026-08-07 00:00:00+00:00 | 99.79 | — | 
| cbBTC / cbBTC | 2026-08-08 00:00:00+00:00 | 99.99 | — | 
| cbBTC / cbBTC | 2026-08-09 00:00:00+00:00 | 99.96 | — | 
| cbBTC / cbBTC | 2026-08-10 00:00:00+00:00 | 99.70 | — | 
| cbBTC / cbBTC | 2026-08-11 00:00:00+00:00 | 99.48 | — | 
| cbBTC / cbBTC | 2026-08-12 00:00:00+00:00 | 99.61 | — | 
| cbBTC / cbBTC | 2026-08-13 00:00:00+00:00 | 99.68 | — | 
| cbBTC / cbBTC | 2026-08-14 00:00:00+00:00 | 99.90 | — | 
| cbBTC / cbBTC | 2026-08-15 00:00:00+00:00 | 99.97 | — | 
| cbBTC / cbBTC | 2026-08-16 00:00:00+00:00 | 99.94 | — | 
| cbBTC / cbBTC | 2026-08-17 00:00:00+00:00 | 99.72 | — | 
| cbBTC / cbBTC | 2026-08-18 00:00:00+00:00 | 99.32 | — | 
| cbBTC / cbBTC | 2026-08-19 00:00:00+00:00 | 99.31 | — | 
| cbBTC / cbBTC | 2026-08-20 00:00:00+00:00 | 98.81 | — | 
| cbBTC / cbBTC | 2026-08-21 00:00:00+00:00 | 87.93 | — | 
| cbBTC / cbBTC | 2026-08-22 00:00:00+00:00 | 86.26 | — | 
| cbBTC / cbBTC | 2026-08-23 00:00:00+00:00 | 87.75 | — | 
| cbBTC / cbBTC | 2026-08-24 00:00:00+00:00 | 83.80 | — | 
| cbBTC / cbBTC | 2026-08-25 00:00:00+00:00 | 79.69 | — | 
| cbBTC / cbBTC | 2026-08-26 00:00:00+00:00 | 84.37 | — | 
| cbBTC / cbBTC | 2026-08-27 00:00:00+00:00 | 80.15 | — | 
| cbBTC / cbBTC | 2026-08-28 00:00:00+00:00 | 83.15 | — | 
| cbBTC / cbBTC | 2026-08-29 00:00:00+00:00 | 89.93 | — | 
| cbBTC / cbBTC | 2026-08-30 00:00:00+00:00 | 88.11 | — | 
| cbBTC / cbBTC | 2026-08-31 00:00:00+00:00 | 88.56 | — | 
| cbBTC / cbBTC | 2026-09-01 00:00:00+00:00 | 90.03 | — | 
| cbBTC / cbBTC | 2026-09-02 00:00:00+00:00 | 93.53 | — | 
| cbBTC / cbBTC | 2026-09-03 00:00:00+00:00 | 86.57 | — | 
| cbBTC / cbBTC | 2026-09-04 00:00:00+00:00 | 83.06 | — | 
| cbBTC / cbBTC | 2026-09-05 00:00:00+00:00 | 85.96 | — | 
| cbBTC / cbBTC | 2026-09-06 00:00:00+00:00 | 85.43 | — | 
| cbBTC / cbBTC | 2026-09-07 00:00:00+00:00 | 88.92 | — | 
| cbBTC / cbBTC | 2026-09-08 00:00:00+00:00 | 97.11 | — | 
| cbBTC / cbBTC | 2026-09-09 00:00:00+00:00 | 98.11 | — | 
| cbBTC / cbBTC | 2026-09-10 00:00:00+00:00 | 99.79 | — | 
| cbBTC / cbBTC | 2026-09-11 00:00:00+00:00 | 99.14 | — | 
| cbBTC / cbBTC | 2026-09-12 00:00:00+00:00 | 99.77 | — | 
| cbBTC / cbBTC | 2026-09-13 00:00:00+00:00 | 99.47 | — | 
| cbBTC / cbBTC | 2026-09-14 00:00:00+00:00 | 99.65 | — | 
| cbBTC / cbBTC | 2026-09-15 00:00:00+00:00 | 99.30 | — | 
| cbBTC / cbBTC | 2026-09-16 00:00:00+00:00 | 99.94 | — | 
| cbBTC / cbBTC | 2026-09-17 00:00:00+00:00 | 99.65 | — | 
| cbBTC / cbBTC | 2026-09-18 00:00:00+00:00 | 99.68 | — | 
| cbBTC / cbBTC | 2026-09-19 00:00:00+00:00 | 99.31 | — | 
| cbBTC / cbBTC | 2026-09-20 00:00:00+00:00 | 99.70 | — | 
| cbBTC / cbBTC | 2026-09-21 00:00:00+00:00 | 99.54 | — | 
| cbBTC / cbBTC | 2026-09-22 00:00:00+00:00 | 99.69 | — | 
| cbBTC / cbBTC | 2026-09-23 00:00:00+00:00 | 99.46 | — | 
| cbBTC / cbBTC | 2026-09-24 00:00:00+00:00 | 99.58 | — | 
| cbBTC / cbBTC | 2026-09-25 00:00:00+00:00 | 99.82 | — | 
| cbBTC / cbBTC | 2026-09-26 00:00:00+00:00 | 99.52 | — | 
| cbBTC / cbBTC | 2026-09-27 00:00:00+00:00 | 99.88 | — | 
| cbBTC / cbBTC | 2026-09-28 00:00:00+00:00 | 99.39 | — | 
| cbBTC / cbBTC | 2026-09-29 00:00:00+00:00 | 99.88 | — | 
| cbBTC / cbBTC | 2026-09-30 00:00:00+00:00 | 99.76 | — | 
| tBTC / tBTC | 2026-05-26 00:00:00+00:00 | 99.68 | — | 
| tBTC / tBTC | 2026-05-27 00:00:00+00:00 | 99.45 | — | 
| tBTC / tBTC | 2026-05-28 00:00:00+00:00 | 99.43 | — | 
| tBTC / tBTC | 2026-05-29 00:00:00+00:00 | 99.74 | — | 
| tBTC / tBTC | 2026-05-30 00:00:00+00:00 | 99.91 | — | 
| tBTC / tBTC | 2026-05-31 00:00:00+00:00 | 99.97 | — | 
| tBTC / tBTC | 2026-06-01 00:00:00+00:00 | 98.89 | — | 
| tBTC / tBTC | 2026-06-02 00:00:00+00:00 | 91.84 | — | 
| tBTC / tBTC | 2026-06-03 00:00:00+00:00 | 82.10 | — | 
| tBTC / tBTC | 2026-06-04 00:00:00+00:00 | 70.51 | — | 
| tBTC / tBTC | 2026-06-05 00:00:00+00:00 | 63.36 | — | 
| tBTC / tBTC | 2026-06-06 00:00:00+00:00 | 59.14 | — | 
| tBTC / tBTC | 2026-06-07 00:00:00+00:00 | 64.49 | — | 
| tBTC / tBTC | 2026-06-08 00:00:00+00:00 | 72.60 | — | 
| tBTC / tBTC | 2026-06-09 00:00:00+00:00 | 67.55 | — | 
| tBTC / tBTC | 2026-06-10 00:00:00+00:00 | 63.63 | — | 
| tBTC / tBTC | 2026-06-11 00:00:00+00:00 | 69.72 | — | 
| tBTC / tBTC | 2026-06-12 00:00:00+00:00 | 74.46 | — | 
| tBTC / tBTC | 2026-06-13 00:00:00+00:00 | 77.28 | — | 
| tBTC / tBTC | 2026-06-14 00:00:00+00:00 | 79.68 | — | 
| tBTC / tBTC | 2026-06-15 00:00:00+00:00 | 90.83 | — | 
| tBTC / tBTC | 2026-06-16 00:00:00+00:00 | 91.50 | — | 
| tBTC / tBTC | 2026-06-17 00:00:00+00:00 | 87.75 | — | 
| tBTC / tBTC | 2026-06-18 00:00:00+00:00 | 81.25 | — | 
| tBTC / tBTC | 2026-06-19 00:00:00+00:00 | 76.91 | — | 
| tBTC / tBTC | 2026-06-20 00:00:00+00:00 | 81.40 | — | 
| tBTC / tBTC | 2026-06-21 00:00:00+00:00 | 83.49 | — | 
| tBTC / tBTC | 2026-06-22 00:00:00+00:00 | 86.43 | — | 
| tBTC / tBTC | 2026-06-23 00:00:00+00:00 | 79.72 | — | 
| tBTC / tBTC | 2026-06-24 00:00:00+00:00 | 74.60 | — | 
| tBTC / tBTC | 2026-06-25 00:00:00+00:00 | 69.33 | — | 
| tBTC / tBTC | 2026-06-26 00:00:00+00:00 | 65.39 | — | 
| tBTC / tBTC | 2026-06-27 00:00:00+00:00 | 68.80 | — | 
| tBTC / tBTC | 2026-06-28 00:00:00+00:00 | 67.62 | — | 
| tBTC / tBTC | 2026-06-29 00:00:00+00:00 | 67.68 | — | 
| tBTC / tBTC | 2026-06-30 00:00:00+00:00 | 63.35 | — | 
| tBTC / tBTC | 2026-07-01 00:00:00+00:00 | 64.96 | — | 
| tBTC / tBTC | 2026-07-02 00:00:00+00:00 | 75.19 | — | 
| tBTC / tBTC | 2026-07-03 00:00:00+00:00 | 80.03 | — | 
| tBTC / tBTC | 2026-07-04 00:00:00+00:00 | 85.04 | — | 
| tBTC / tBTC | 2026-07-05 00:00:00+00:00 | 86.67 | — | 
| tBTC / tBTC | 2026-07-06 00:00:00+00:00 | 89.18 | — | 
| tBTC / tBTC | 2026-07-07 00:00:00+00:00 | 93.05 | — | 
| tBTC / tBTC | 2026-07-08 00:00:00+00:00 | 88.37 | — | 
| tBTC / tBTC | 2026-07-09 00:00:00+00:00 | 91.17 | — | 
| tBTC / tBTC | 2026-07-10 00:00:00+00:00 | 96.77 | — | 
| tBTC / tBTC | 2026-07-11 00:00:00+00:00 | 97.82 | — | 
| tBTC / tBTC | 2026-07-12 00:00:00+00:00 | 97.25 | — | 
| tBTC / tBTC | 2026-07-13 00:00:00+00:00 | 93.39 | — | 
| tBTC / tBTC | 2026-07-14 00:00:00+00:00 | 96.02 | — | 
| tBTC / tBTC | 2026-07-15 00:00:00+00:00 | 99.40 | — | 
| tBTC / tBTC | 2026-07-16 00:00:00+00:00 | 99.46 | — | 
| tBTC / tBTC | 2026-07-17 00:00:00+00:00 | 99.11 | — | 
| tBTC / tBTC | 2026-07-18 00:00:00+00:00 | 99.33 | — | 
| tBTC / tBTC | 2026-07-19 00:00:00+00:00 | 99.28 | — | 
| tBTC / tBTC | 2026-07-20 00:00:00+00:00 | 99.60 | — | 
| tBTC / tBTC | 2026-07-21 00:00:00+00:00 | 99.37 | — | 
| tBTC / tBTC | 2026-07-22 00:00:00+00:00 | 99.59 | — | 
| tBTC / tBTC | 2026-07-23 00:00:00+00:00 | 99.23 | — | 
| tBTC / tBTC | 2026-07-24 00:00:00+00:00 | 99.43 | — | 
| tBTC / tBTC | 2026-07-25 00:00:00+00:00 | 99.36 | — | 
| tBTC / tBTC | 2026-07-26 00:00:00+00:00 | 99.19 | — | 
| tBTC / tBTC | 2026-07-27 00:00:00+00:00 | 99.42 | — | 
| tBTC / tBTC | 2026-07-28 00:00:00+00:00 | 99.44 | — | 
| tBTC / tBTC | 2026-07-29 00:00:00+00:00 | 99.65 | — | 
| tBTC / tBTC | 2026-07-30 00:00:00+00:00 | 99.58 | — | 
| tBTC / tBTC | 2026-07-31 00:00:00+00:00 | 99.46 | — | 
| tBTC / tBTC | 2026-08-01 00:00:00+00:00 | 99.55 | — | 
| tBTC / tBTC | 2026-08-02 00:00:00+00:00 | 99.13 | — | 
| tBTC / tBTC | 2026-08-03 00:00:00+00:00 | 99.55 | — | 
| tBTC / tBTC | 2026-08-04 00:00:00+00:00 | 99.58 | — | 
| tBTC / tBTC | 2026-08-05 00:00:00+00:00 | 99.68 | — | 
| tBTC / tBTC | 2026-08-06 00:00:00+00:00 | 99.92 | — | 
| tBTC / tBTC | 2026-08-07 00:00:00+00:00 | 99.90 | — | 
| tBTC / tBTC | 2026-08-08 00:00:00+00:00 | 99.95 | — | 
| tBTC / tBTC | 2026-08-09 00:00:00+00:00 | 99.93 | — | 
| tBTC / tBTC | 2026-08-10 00:00:00+00:00 | 99.76 | — | 
| tBTC / tBTC | 2026-08-11 00:00:00+00:00 | 99.48 | — | 
| tBTC / tBTC | 2026-08-12 00:00:00+00:00 | 99.58 | — | 
| tBTC / tBTC | 2026-08-13 00:00:00+00:00 | 99.64 | — | 
| tBTC / tBTC | 2026-08-14 00:00:00+00:00 | 99.89 | — | 
| tBTC / tBTC | 2026-08-15 00:00:00+00:00 | 99.29 | — | 
| tBTC / tBTC | 2026-08-16 00:00:00+00:00 | 99.39 | — | 
| tBTC / tBTC | 2026-08-17 00:00:00+00:00 | 99.14 | — | 
| tBTC / tBTC | 2026-08-18 00:00:00+00:00 | 99.64 | — | 
| tBTC / tBTC | 2026-08-19 00:00:00+00:00 | 98.71 | — | 
| tBTC / tBTC | 2026-08-20 00:00:00+00:00 | 88.17 | — | 
| tBTC / tBTC | 2026-08-21 00:00:00+00:00 | 67.82 | — | 
| tBTC / tBTC | 2026-08-22 00:00:00+00:00 | 65.05 | — | 
| tBTC / tBTC | 2026-08-23 00:00:00+00:00 | 66.37 | — | 
| tBTC / tBTC | 2026-08-24 00:00:00+00:00 | 62.70 | — | 
| tBTC / tBTC | 2026-08-25 00:00:00+00:00 | 59.04 | — | 
| tBTC / tBTC | 2026-08-26 00:00:00+00:00 | 61.91 | — | 
| tBTC / tBTC | 2026-08-27 00:00:00+00:00 | 58.61 | — | 
| tBTC / tBTC | 2026-08-28 00:00:00+00:00 | 60.73 | — | 
| tBTC / tBTC | 2026-08-29 00:00:00+00:00 | 65.33 | — | 
| tBTC / tBTC | 2026-08-30 00:00:00+00:00 | 63.52 | — | 
| tBTC / tBTC | 2026-08-31 00:00:00+00:00 | 63.97 | — | 
| tBTC / tBTC | 2026-09-01 00:00:00+00:00 | 65.15 | — | 
| tBTC / tBTC | 2026-09-02 00:00:00+00:00 | 68.87 | — | 
| tBTC / tBTC | 2026-09-03 00:00:00+00:00 | 61.97 | — | 
| tBTC / tBTC | 2026-09-04 00:00:00+00:00 | 57.90 | — | 
| tBTC / tBTC | 2026-09-05 00:00:00+00:00 | 59.69 | — | 
| tBTC / tBTC | 2026-09-06 00:00:00+00:00 | 59.22 | — | 
| tBTC / tBTC | 2026-09-07 00:00:00+00:00 | 60.98 | — | 
| tBTC / tBTC | 2026-09-08 00:00:00+00:00 | 64.17 | — | 
| tBTC / tBTC | 2026-09-09 00:00:00+00:00 | 63.69 | — | 
| tBTC / tBTC | 2026-09-10 00:00:00+00:00 | 68.36 | — | 
| tBTC / tBTC | 2026-09-11 00:00:00+00:00 | 69.93 | — | 
| tBTC / tBTC | 2026-09-12 00:00:00+00:00 | 70.60 | — | 
| tBTC / tBTC | 2026-09-13 00:00:00+00:00 | 71.45 | — | 
| tBTC / tBTC | 2026-09-14 00:00:00+00:00 | 67.85 | — | 
| tBTC / tBTC | 2026-09-15 00:00:00+00:00 | 73.90 | — | 
| tBTC / tBTC | 2026-09-16 00:00:00+00:00 | 78.91 | — | 
| tBTC / tBTC | 2026-09-17 00:00:00+00:00 | 76.16 | — | 
| tBTC / tBTC | 2026-09-18 00:00:00+00:00 | 66.85 | — | 
| tBTC / tBTC | 2026-09-19 00:00:00+00:00 | 58.89 | — | 
| tBTC / tBTC | 2026-09-20 00:00:00+00:00 | 60.85 | — | 
| tBTC / tBTC | 2026-09-21 00:00:00+00:00 | 51.48 | — | 
| tBTC / tBTC | 2026-09-22 00:00:00+00:00 | 47.06 | — | 
| tBTC / tBTC | 2026-09-23 00:00:00+00:00 | 48.42 | — | 
| tBTC / tBTC | 2026-09-24 00:00:00+00:00 | 51.78 | — | 
| tBTC / tBTC | 2026-09-25 00:00:00+00:00 | 51.57 | — | 
| tBTC / tBTC | 2026-09-26 00:00:00+00:00 | 51.90 | — | 
| tBTC / tBTC | 2026-09-27 00:00:00+00:00 | 50.54 | — | 
| tBTC / tBTC | 2026-09-28 00:00:00+00:00 | 53.87 | — | 
| tBTC / tBTC | 2026-09-29 00:00:00+00:00 | 53.44 | — | 
| tBTC / tBTC | 2026-09-30 00:00:00+00:00 | 53.10 | — | 
| WBTC stall window | 2026-06-02T14:20:11+00:00 | — | 2026-06-14T23:16:11+00:00 | 
| WBTC stall window | 2026-06-18T03:01:35+00:00 | — | 2026-06-20T22:28:35+00:00 | 
| WBTC stall window | 2026-06-23T05:18:47+00:00 | — | 2026-07-02T13:19:23+00:00 | 
| WBTC stall window | 2026-08-20T07:54:11+00:00 | — | 2026-10-01T00:00:00+00:00 | 
| cbBTC stall window | 2026-06-02T14:02:59+00:00 | — | 2026-06-15T12:41:47+00:00 | 
| cbBTC stall window | 2026-06-17T18:57:47+00:00 | — | 2026-06-22T13:44:11+00:00 | 
| cbBTC stall window | 2026-06-22T15:43:35+00:00 | — | 2026-07-04T21:32:47+00:00 | 
| cbBTC stall window | 2026-07-04T21:33:11+00:00 | — | 2026-07-05T22:20:47+00:00 | 
| cbBTC stall window | 2026-08-21T06:48:23+00:00 | — | 2026-08-23T05:14:35+00:00 | 
| cbBTC stall window | 2026-08-23T08:09:47+00:00 | — | 2026-08-28T16:24:11+00:00 | 
| cbBTC stall window | 2026-08-29T13:11:23+00:00 | — | 2026-08-30T23:36:11+00:00 | 
| cbBTC stall window | 2026-08-31T05:04:47+00:00 | — | 2026-09-01T13:36:47+00:00 | 
| cbBTC stall window | 2026-09-03T11:18:35+00:00 | — | 2026-09-07T15:27:35+00:00 | 
| tBTC stall window | 2026-06-02T13:49:11+00:00 | — | 2026-06-15T12:51:47+00:00 | 
| tBTC stall window | 2026-06-17T16:30:47+00:00 | — | 2026-06-22T13:50:47+00:00 | 
| tBTC stall window | 2026-06-22T14:00:47+00:00 | — | 2026-07-05T23:15:11+00:00 | 
| tBTC stall window | 2026-07-08T01:36:35+00:00 | — | 2026-07-09T07:00:47+00:00 | 
| tBTC stall window | 2026-08-20T08:09:23+00:00 | — | 2026-10-01T00:00:00+00:00 |


# G2 Donations, the gate and when volatility arrives {#detachment/donations}

**More [donations](./#glossary/donation) reduce serious [detachment](./#glossary/detachment) in these tests.**

**Measure:** first serious [episodes](./#glossary/episode) by day 365, in percent of paths starting outside the serious tier

**Compared:** [volatility](./#glossary/volatility)-scaled histories with plain histories, using the same proposal settings

**Same for both:** the donation rate and the price-average speed

**Higher means:** more paths develop a serious episode

The dotted line on the chart is 5.00%.

Both versions use a [resettable floor](./#glossary/resettable-floor). This rule lowers the protected accounting threshold after a permitted move below it. Volatility scaling resizes sampled price moves to match volatility on their new dates.

**Measure:** the same first-episode share, in percent

**Compared:** the deployed gate with the resettable-floor proposal

**Same for both:** the rebuilt [WETH](./#glossary/weth) histories and donation rates up to 6% a year

**Higher means:** more paths have a serious episode

In this scan the deployed gate stays above the rarity limits at every tested rate.

Donations supply capital from outside the pool. Serious detachment means too little trading depth remains at the market price. An episode is a sustained period below a depth threshold. The profit gate limits which centre-price moves the pool can make.

Whether serious detachment becomes rare depends on this gate. The timing of market moves matters too.

The scan changes annual donations. The other named settings stay fixed.

Under the deployed gate, no tested rate passes both rarity limits. The proposal with a resettable floor passes at some rates on plain rebuilt histories. That result disappears when sampled moves are scaled to the volatility of their new dates.

Under the deployed gate, no tested donation rate through 6% a year passes both “[almost never](./#glossary/almost-never)” limits. With the proposal and resettable floor on plain rebuilt histories, the first passing rate is about 1.20% with faster price averages. With the original averages it is about 1.60%.

Each panel compares plain and volatility-scaled histories at its named averaging speed. Both curves use the same proposal and resettable floor. 

Open markers pass both rarity tests. One test allows for uncertainty in the event count. The other limits time spent below the depth threshold. 

Error bars resample whole histories. No deployed-gate setting passes both tests through 6% annual donations.

**More detail: all policy, gate and averaging settings**

Full plain-history scan: current and proposed price rules under both gates and both averaging speeds. The companion row zooms in on the rarity threshold. The table gives onset counts, history counts, time below depth and upper confidence limits.

Full scan across both history constructions. Each speed has a plain and a volatility-scaled panel. Companion panels sit near the qualifying line. The table records every tested gate and rule, including settings that fail the rarity limits.

Donations create [headroom](./#glossary/headroom) for a [re-peg](./#glossary/re-peg) to pass the profit gate. The deployed gate keeps its protected floor after a re-peg. Later moves then need fresh profit or funding to rebuild that headroom.

The first passing rates come from the tested grid. The minimum donation rate needed remains uncertain. Some resamples have no passing rate within the scan. 

All curves fix reserved profit at 42.91% and use 180-day blocks. Half-life means the time for a price’s weight to halve. Faster price averages use halved half-lives. The current rule keeps its own averaging settings unchanged.

| Proposal with resettable floor, at the stated averaging speed | First passing donation rate, %/yr | Boundary uncertainty, %/yr | Resamples with no passing rate through 6%, % | 
| --- | --- | --- | --- |
| Original [EMA](./#glossary/ema) half-lives | 1.60 | 0.60 or beyond the scan | 25.55% | 
| Halved EMA half-lives | 1.20 | 0.60 or beyond the scan | 5.50% | 

**More detail**

Chart error bars estimate uncertainty in event frequency. The table interval instead estimates uncertainty in the first donation rate passing both rarity rules. Both use 2,000 resamples of whole rebuilt histories. 

“Beyond the scan” means no rate through 6% passed in those resamples. It is not a measured rate beyond 6%. The resettable floor allows the protected accounting threshold to fall after an allowed move.

### Where the volatility falls matters

Take the proposal with resettable floor, faster price averages and 1.20% donations. First serious onset by day 365 rises from 2.73% on plain histories to 6.64% on volatility-scaled histories. Mean time below serious depth over the 556 days rises from 0.25% to 1.91%.

Both constructions reuse one original WETH price history.

Volatility scaling stretches or shrinks each sampled price move. The scale is the volatility of the move’s new date compared with its source date. Each move keeps its direction but changes size. 

The scaling changes when large fluctuations arrive. It also changes the cumulative direction of prices.

**More detail**

At 1.20% annual donations, the proposal with resettable floor and faster price averages is compared across 256 paired histories. The plain first-episode probability interval is 0.78% to 5.08%. The scaled interval is 3.52% to 9.77%.

 Scaled histories also exceed the allowed time below serious depth. Both use 180-day blocks.

The [shared settings and conventions](./#settings) distinguish these depth, event and quote measures from return rates.

The [settings table](./#settings) defines the current-rule and proposal bundles. Each result states its donation rate.

The [settings page](./#settings) defines the scanned bundles and rate conventions. These histories simulate [arbitrage](./#glossary/arbitrage) and the debt-financed YB holder. The [customer-response page](./#simulation/limits) explains the separate demand question.

[← previous](./#detachment/measure)[next $\to$](./#detachment/costs)

**Chart data $\cdot$ Serious detachment against annual donations**

% of paths starting outside the serious tier with a first episode by day 365
| Panel / curve | Coordinate $\cdot$ Donation rate, % of pool value per year | % of paths starting outside the serious tier with a first episode by day 365 | Interval low | Interval high | Passes both rarity tests | Paths starting outside the tier | Mean time below tier over 556 days, % | Upper confidence limit for first onset, % | Paths with first onset by day 365 | 
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 60.76 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 59.99 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 58.00 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 56.11 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 50.32 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 45.74 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 4.00 | 86.00 | 79.00 | 92.00 | 0 | 100 | 27.75 | 90.76 | 86 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 5.00 | 68.00 | 59.00 | 77.00 | 0 | 100 | 8.81 | 75.11 | 68 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 6.00 | 60.00 | 51.00 | 70.00 | 0 | 100 | 5.48 | 67.69 | 60 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 0.60 | 10.16 | 6.64 | 14.06 | 0 | 256 | 0.58 | 13.69 | 26 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 1.20 | 9.38 | 6.24 | 12.89 | 0 | 256 | 0.55 | 12.81 | 24 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 1.60 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.48 | 12.37 | 23 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 2.00 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.47 | 12.37 | 23 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 2.50 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.46 | 12.37 | 23 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 3.00 | 7.42 | 4.30 | 10.94 | 0 | 256 | 0.40 | 10.58 | 19 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 4.00 | 5.47 | 2.73 | 8.20 | 0 | 256 | 0.26 | 8.31 | 14 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 5.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.25 | 7.84 | 13 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 6.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.23 | 7.84 | 13 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 0.60 | 98.00 | 95.00 | 100.00 | 0 | 100 | 52.76 | 99.34 | 98 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 1.20 | 53.00 | 43.00 | 63.00 | 0 | 100 | 13.49 | 61.02 | 53 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 1.60 | 32.00 | 23.00 | 41.00 | 0 | 100 | 10.90 | 40.06 | 32 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 2.00 | 27.00 | 19.00 | 36.00 | 0 | 100 | 10.20 | 34.84 | 27 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 2.50 | 23.00 | 15.00 | 32.00 | 0 | 100 | 8.44 | 30.58 | 23 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 3.00 | 21.00 | 14.00 | 29.02 | 0 | 100 | 7.09 | 28.42 | 21 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 4.00 | 17.00 | 10.00 | 25.00 | 0 | 100 | 5.21 | 24.03 | 17 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 5.00 | 15.00 | 9.00 | 22.00 | 0 | 100 | 4.83 | 21.79 | 15 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 6.00 | 13.00 | 7.00 | 20.00 | 0 | 100 | 4.41 | 19.52 | 13 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 0.60 | 3.12 | 1.17 | 5.47 | 0 | 256 | 0.27 | 5.46 | 8 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 1.20 | 3.12 | 1.17 | 5.47 | 0 | 256 | 0.24 | 5.46 | 8 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 1.60 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 2.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.23 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 2.50 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.23 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 3.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.22 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 4.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.21 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 5.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.17 | 4.47 | 6 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 6.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.17 | 4.47 | 6 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 60.76 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 59.99 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 58.00 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 56.11 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 50.32 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 45.74 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 4.00 | 86.00 | 79.00 | 92.00 | 0 | 100 | 27.75 | 90.76 | 86 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 5.00 | 68.00 | 59.00 | 77.00 | 0 | 100 | 8.81 | 75.11 | 68 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 6.00 | 60.00 | 51.00 | 70.00 | 0 | 100 | 5.48 | 67.69 | 60 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 0.60 | 10.16 | 6.64 | 14.06 | 0 | 256 | 0.58 | 13.69 | 26 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 1.20 | 9.38 | 6.24 | 12.89 | 0 | 256 | 0.55 | 12.81 | 24 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 1.60 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.48 | 12.37 | 23 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 2.00 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.47 | 12.37 | 23 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 2.50 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.46 | 12.37 | 23 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 3.00 | 7.42 | 4.30 | 10.94 | 0 | 256 | 0.40 | 10.58 | 19 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 4.00 | 5.47 | 2.73 | 8.20 | 0 | 256 | 0.26 | 8.31 | 14 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 5.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.25 | 7.84 | 13 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 6.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.23 | 7.84 | 13 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 0.60 | 90.00 | 84.00 | 95.00 | 0 | 100 | 49.41 | 93.93 | 90 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 1.20 | 77.00 | 68.00 | 85.00 | 0 | 100 | 28.99 | 83.16 | 77 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 1.60 | 31.00 | 22.00 | 40.00 | 0 | 100 | 8.43 | 39.02 | 31 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 2.00 | 26.00 | 18.00 | 35.00 | 0 | 100 | 7.15 | 33.78 | 26 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 2.50 | 21.00 | 13.98 | 29.00 | 0 | 100 | 5.57 | 28.42 | 21 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 3.00 | 18.00 | 11.00 | 26.00 | 0 | 100 | 5.29 | 25.14 | 18 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 4.00 | 13.00 | 7.00 | 20.00 | 0 | 100 | 4.55 | 19.52 | 13 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 5.00 | 11.00 | 5.00 | 18.00 | 0 | 100 | 4.16 | 17.21 | 11 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 6.00 | 11.00 | 5.00 | 17.00 | 0 | 100 | 3.72 | 17.21 | 11 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 0.60 | 3.91 | 1.56 | 6.25 | 0 | 256 | 0.28 | 6.43 | 10 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 1.20 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.25 | 4.97 | 7 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 1.60 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 2.00 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 2.50 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.20 | 4.47 | 6 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 3.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.20 | 4.47 | 6 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 4.00 | 1.95 | 0.39 | 3.91 | 1 | 256 | 0.16 | 3.96 | 5 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 5.00 | 1.56 | 0.39 | 3.12 | 1 | 256 | 0.13 | 3.43 | 4 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 6.00 | 1.56 | 0.39 | 3.12 | 1 | 256 | 0.13 | 3.43 | 4 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 60.76 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 59.99 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 58.00 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 56.11 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 50.32 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 45.74 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 4.00 | 86.00 | 79.00 | 92.00 | 0 | 100 | 27.75 | 90.76 | 86 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 5.00 | 68.00 | 59.00 | 77.00 | 0 | 100 | 8.81 | 75.11 | 68 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 6.00 | 60.00 | 51.00 | 70.00 | 0 | 100 | 5.48 | 67.69 | 60 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 0.60 | 10.16 | 6.64 | 14.06 | 0 | 256 | 0.58 | 13.69 | 26 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 1.20 | 9.38 | 6.24 | 12.89 | 0 | 256 | 0.55 | 12.81 | 24 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 1.60 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.48 | 12.37 | 23 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 2.00 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.47 | 12.37 | 23 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 2.50 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.46 | 12.37 | 23 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 3.00 | 7.42 | 4.30 | 10.94 | 0 | 256 | 0.40 | 10.58 | 19 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 4.00 | 5.47 | 2.73 | 8.20 | 0 | 256 | 0.26 | 8.31 | 14 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 5.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.25 | 7.84 | 13 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 6.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.23 | 7.84 | 13 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 0.60 | 98.00 | 95.00 | 100.00 | 0 | 100 | 52.76 | 99.34 | 98 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 1.20 | 53.00 | 43.00 | 63.00 | 0 | 100 | 13.49 | 61.02 | 53 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 1.60 | 32.00 | 23.00 | 41.00 | 0 | 100 | 10.90 | 40.06 | 32 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 2.00 | 27.00 | 19.00 | 36.00 | 0 | 100 | 10.20 | 34.84 | 27 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 2.50 | 23.00 | 15.00 | 32.00 | 0 | 100 | 8.44 | 30.58 | 23 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 3.00 | 21.00 | 14.00 | 29.02 | 0 | 100 | 7.09 | 28.42 | 21 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 4.00 | 17.00 | 10.00 | 25.00 | 0 | 100 | 5.21 | 24.03 | 17 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 5.00 | 15.00 | 9.00 | 22.00 | 0 | 100 | 4.83 | 21.79 | 15 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 6.00 | 13.00 | 7.00 | 20.00 | 0 | 100 | 4.41 | 19.52 | 13 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 0.60 | 3.12 | 1.17 | 5.47 | 0 | 256 | 0.27 | 5.46 | 8 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 1.20 | 3.12 | 1.17 | 5.47 | 0 | 256 | 0.24 | 5.46 | 8 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 1.60 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 2.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.23 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 2.50 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.23 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 3.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.22 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 4.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.21 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 5.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.17 | 4.47 | 6 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 6.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.17 | 4.47 | 6 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 60.76 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 59.99 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 58.00 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 56.11 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 50.32 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 45.74 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 4.00 | 86.00 | 79.00 | 92.00 | 0 | 100 | 27.75 | 90.76 | 86 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 5.00 | 68.00 | 59.00 | 77.00 | 0 | 100 | 8.81 | 75.11 | 68 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 6.00 | 60.00 | 51.00 | 70.00 | 0 | 100 | 5.48 | 67.69 | 60 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 0.60 | 10.16 | 6.64 | 14.06 | 0 | 256 | 0.58 | 13.69 | 26 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 1.20 | 9.38 | 6.24 | 12.89 | 0 | 256 | 0.55 | 12.81 | 24 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 1.60 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.48 | 12.37 | 23 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 2.00 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.47 | 12.37 | 23 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 2.50 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.46 | 12.37 | 23 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 3.00 | 7.42 | 4.30 | 10.94 | 0 | 256 | 0.40 | 10.58 | 19 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 4.00 | 5.47 | 2.73 | 8.20 | 0 | 256 | 0.26 | 8.31 | 14 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 5.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.25 | 7.84 | 13 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 6.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.23 | 7.84 | 13 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 0.60 | 90.00 | 84.00 | 95.00 | 0 | 100 | 49.41 | 93.93 | 90 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 1.20 | 77.00 | 68.00 | 85.00 | 0 | 100 | 28.99 | 83.16 | 77 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 1.60 | 31.00 | 22.00 | 40.00 | 0 | 100 | 8.43 | 39.02 | 31 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 2.00 | 26.00 | 18.00 | 35.00 | 0 | 100 | 7.15 | 33.78 | 26 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 2.50 | 21.00 | 13.98 | 29.00 | 0 | 100 | 5.57 | 28.42 | 21 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 3.00 | 18.00 | 11.00 | 26.00 | 0 | 100 | 5.29 | 25.14 | 18 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 4.00 | 13.00 | 7.00 | 20.00 | 0 | 100 | 4.55 | 19.52 | 13 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 5.00 | 11.00 | 5.00 | 18.00 | 0 | 100 | 4.16 | 17.21 | 11 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 6.00 | 11.00 | 5.00 | 17.00 | 0 | 100 | 3.72 | 17.21 | 11 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 0.60 | 3.91 | 1.56 | 6.25 | 0 | 256 | 0.28 | 6.43 | 10 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 1.20 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.25 | 4.97 | 7 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 1.60 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 2.00 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 2.50 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.20 | 4.47 | 6 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 3.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.20 | 4.47 | 6 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 4.00 | 1.95 | 0.39 | 3.91 | 1 | 256 | 0.16 | 3.96 | 5 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 5.00 | 1.56 | 0.39 | 3.12 | 1 | 256 | 0.13 | 3.43 | 4 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 6.00 | 1.56 | 0.39 | 3.12 | 1 | 256 | 0.13 | 3.43 | 4 | 
| Reference line | — | 5.00 | — | — | — | — | — | — | — | 

**Chart data $\cdot$ Serious detachment against annual donations**

% of paths starting outside the serious tier with a first episode by day 365
| Panel / curve | Coordinate $\cdot$ Donation rate, % of pool value per year | % of paths starting outside the serious tier with a first episode by day 365 | Interval low | Interval high | Passes both rarity tests | Paths starting outside the tier | Mean time below tier over 556 days, % | Upper confidence limit for first onset, % | Paths with first onset by day 365 | 
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 60.76 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 59.99 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 58.00 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 56.11 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 50.32 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 45.74 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 4.00 | 86.00 | 79.00 | 92.00 | 0 | 100 | 27.75 | 90.76 | 86 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 5.00 | 68.00 | 59.00 | 77.00 | 0 | 100 | 8.81 | 75.11 | 68 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 6.00 | 60.00 | 51.00 | 70.00 | 0 | 100 | 5.48 | 67.69 | 60 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 0.60 | 10.16 | 6.64 | 14.06 | 0 | 256 | 0.58 | 13.69 | 26 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 1.20 | 9.38 | 6.24 | 12.89 | 0 | 256 | 0.55 | 12.81 | 24 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 1.60 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.48 | 12.37 | 23 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 2.00 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.47 | 12.37 | 23 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 2.50 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.46 | 12.37 | 23 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 3.00 | 7.42 | 4.30 | 10.94 | 0 | 256 | 0.40 | 10.58 | 19 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 4.00 | 5.47 | 2.73 | 8.20 | 0 | 256 | 0.26 | 8.31 | 14 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 5.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.25 | 7.84 | 13 | 
| Plain $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 6.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.23 | 7.84 | 13 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 0.60 | 98.00 | 95.00 | 100.00 | 0 | 100 | 52.76 | 99.34 | 98 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 1.20 | 53.00 | 43.00 | 63.00 | 0 | 100 | 13.49 | 61.02 | 53 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 1.60 | 32.00 | 23.00 | 41.00 | 0 | 100 | 10.90 | 40.06 | 32 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 2.00 | 27.00 | 19.00 | 36.00 | 0 | 100 | 10.20 | 34.84 | 27 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 2.50 | 23.00 | 15.00 | 32.00 | 0 | 100 | 8.44 | 30.58 | 23 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 3.00 | 21.00 | 14.00 | 29.02 | 0 | 100 | 7.09 | 28.42 | 21 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 4.00 | 17.00 | 10.00 | 25.00 | 0 | 100 | 5.21 | 24.03 | 17 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 5.00 | 15.00 | 9.00 | 22.00 | 0 | 100 | 4.83 | 21.79 | 15 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 6.00 | 13.00 | 7.00 | 20.00 | 0 | 100 | 4.41 | 19.52 | 13 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 0.60 | 3.12 | 1.17 | 5.47 | 0 | 256 | 0.27 | 5.46 | 8 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 1.20 | 3.12 | 1.17 | 5.47 | 0 | 256 | 0.24 | 5.46 | 8 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 1.60 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 2.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.23 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 2.50 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.23 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 3.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.22 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 4.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.21 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 5.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.17 | 4.47 | 6 | 
| Plain $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 6.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.17 | 4.47 | 6 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 60.76 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 59.99 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 58.00 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 56.11 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 50.32 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 45.74 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 4.00 | 86.00 | 79.00 | 92.00 | 0 | 100 | 27.75 | 90.76 | 86 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 5.00 | 68.00 | 59.00 | 77.00 | 0 | 100 | 8.81 | 75.11 | 68 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 6.00 | 60.00 | 51.00 | 70.00 | 0 | 100 | 5.48 | 67.69 | 60 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 0.60 | 10.16 | 6.64 | 14.06 | 0 | 256 | 0.58 | 13.69 | 26 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 1.20 | 9.38 | 6.24 | 12.89 | 0 | 256 | 0.55 | 12.81 | 24 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 1.60 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.48 | 12.37 | 23 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 2.00 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.47 | 12.37 | 23 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 2.50 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.46 | 12.37 | 23 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 3.00 | 7.42 | 4.30 | 10.94 | 0 | 256 | 0.40 | 10.58 | 19 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 4.00 | 5.47 | 2.73 | 8.20 | 0 | 256 | 0.26 | 8.31 | 14 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 5.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.25 | 7.84 | 13 | 
| Plain $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 6.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.23 | 7.84 | 13 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 0.60 | 90.00 | 84.00 | 95.00 | 0 | 100 | 49.41 | 93.93 | 90 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 1.20 | 77.00 | 68.00 | 85.00 | 0 | 100 | 28.99 | 83.16 | 77 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 1.60 | 31.00 | 22.00 | 40.00 | 0 | 100 | 8.43 | 39.02 | 31 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 2.00 | 26.00 | 18.00 | 35.00 | 0 | 100 | 7.15 | 33.78 | 26 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 2.50 | 21.00 | 13.98 | 29.00 | 0 | 100 | 5.57 | 28.42 | 21 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 3.00 | 18.00 | 11.00 | 26.00 | 0 | 100 | 5.29 | 25.14 | 18 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 4.00 | 13.00 | 7.00 | 20.00 | 0 | 100 | 4.55 | 19.52 | 13 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 5.00 | 11.00 | 5.00 | 18.00 | 0 | 100 | 4.16 | 17.21 | 11 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 6.00 | 11.00 | 5.00 | 17.00 | 0 | 100 | 3.72 | 17.21 | 11 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 0.60 | 3.91 | 1.56 | 6.25 | 0 | 256 | 0.28 | 6.43 | 10 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 1.20 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.25 | 4.97 | 7 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 1.60 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 2.00 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 2.50 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.20 | 4.47 | 6 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 3.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.20 | 4.47 | 6 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 4.00 | 1.95 | 0.39 | 3.91 | 1 | 256 | 0.16 | 3.96 | 5 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 5.00 | 1.56 | 0.39 | 3.12 | 1 | 256 | 0.13 | 3.43 | 4 | 
| Plain $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 6.00 | 1.56 | 0.39 | 3.12 | 1 | 256 | 0.13 | 3.43 | 4 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 71.40 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 70.21 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 69.23 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 68.15 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 67.22 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 64.45 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 4.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 59.71 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 5.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 56.94 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ deployed gate | 6.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 51.44 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 0.60 | 9.00 | 4.00 | 15.00 | 0 | 100 | 2.37 | 14.85 | 9 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 1.20 | 9.00 | 4.00 | 15.00 | 0 | 100 | 2.35 | 14.85 | 9 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 1.60 | 12.00 | 6.00 | 19.00 | 0 | 100 | 2.59 | 18.37 | 12 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 2.00 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.29 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 2.50 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.27 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 3.00 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.25 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 4.00 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.18 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 5.00 | 9.00 | 4.00 | 15.00 | 0 | 100 | 2.09 | 14.85 | 9 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Current policy $\cdot$ resettable floor | 6.00 | 8.00 | 3.00 | 14.00 | 0 | 100 | 1.72 | 13.65 | 8 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 71.40 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 68.17 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 65.14 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 62.38 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 57.68 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 54.58 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 4.00 | 98.00 | 95.00 | 100.00 | 0 | 100 | 48.89 | 99.34 | 98 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 5.00 | 94.00 | 89.00 | 98.00 | 0 | 100 | 36.29 | 96.87 | 94 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ deployed gate | 6.00 | 80.00 | 72.00 | 87.00 | 0 | 100 | 27.97 | 85.75 | 80 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 0.60 | 9.77 | 6.25 | 13.67 | 0 | 256 | 2.31 | 13.25 | 25 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 1.20 | 9.77 | 6.25 | 13.67 | 0 | 256 | 2.30 | 13.25 | 25 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 1.60 | 8.98 | 5.47 | 12.50 | 0 | 256 | 2.28 | 12.37 | 23 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 2.00 | 8.20 | 5.08 | 11.72 | 0 | 256 | 1.46 | 11.48 | 21 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 2.50 | 7.42 | 4.30 | 10.94 | 0 | 256 | 1.35 | 10.58 | 19 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 3.00 | 7.03 | 3.91 | 10.16 | 0 | 256 | 1.28 | 10.13 | 18 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 4.00 | 5.86 | 3.12 | 8.98 | 0 | 256 | 1.26 | 8.77 | 15 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 5.00 | 5.86 | 3.12 | 8.98 | 0 | 256 | 1.25 | 8.77 | 15 | 
| Volatility-scaled $\cdot$ original EMA half-lives / Proposed policy $\cdot$ resettable floor | 6.00 | 5.47 | 2.73 | 8.59 | 0 | 256 | 1.10 | 8.31 | 14 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 71.40 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 70.21 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 69.23 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 68.15 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 67.22 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 64.45 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 4.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 59.71 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 5.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 56.94 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ deployed gate | 6.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 51.44 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 0.60 | 9.00 | 4.00 | 15.00 | 0 | 100 | 2.37 | 14.85 | 9 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 1.20 | 9.00 | 4.00 | 15.00 | 0 | 100 | 2.35 | 14.85 | 9 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 1.60 | 12.00 | 6.00 | 19.00 | 0 | 100 | 2.59 | 18.37 | 12 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 2.00 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.29 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 2.50 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.27 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 3.00 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.25 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 4.00 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.18 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 5.00 | 9.00 | 4.00 | 15.00 | 0 | 100 | 2.09 | 14.85 | 9 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Current policy $\cdot$ resettable floor | 6.00 | 8.00 | 3.00 | 14.00 | 0 | 100 | 1.72 | 13.65 | 8 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 71.91 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 66.34 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 63.41 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 61.61 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 58.24 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 52.27 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 4.00 | 97.00 | 93.00 | 100.00 | 0 | 100 | 43.10 | 98.79 | 97 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 5.00 | 89.00 | 82.00 | 94.00 | 0 | 100 | 35.05 | 93.15 | 89 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ deployed gate | 6.00 | 75.00 | 67.00 | 83.00 | 0 | 100 | 21.65 | 81.40 | 75 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 0.60 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.95 | 9.68 | 17 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 1.20 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.91 | 9.68 | 17 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 1.60 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.90 | 9.68 | 17 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 2.00 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.90 | 9.68 | 17 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 2.50 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.86 | 9.68 | 17 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 3.00 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.85 | 9.68 | 17 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 4.00 | 5.47 | 2.73 | 8.59 | 0 | 256 | 1.08 | 8.31 | 14 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 5.00 | 4.69 | 2.34 | 7.42 | 0 | 256 | 1.06 | 7.37 | 12 | 
| Volatility-scaled $\cdot$ halved EMA half-lives / Proposed policy $\cdot$ resettable floor | 6.00 | 4.69 | 2.34 | 7.42 | 0 | 256 | 1.06 | 7.37 | 12 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 60.76 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 59.99 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 58.00 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 56.11 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 50.32 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 45.74 | 100.00 | 100 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 4.00 | 86.00 | 79.00 | 92.00 | 0 | 100 | 27.75 | 90.76 | 86 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 5.00 | 68.00 | 59.00 | 77.00 | 0 | 100 | 8.81 | 75.11 | 68 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 6.00 | 60.00 | 51.00 | 70.00 | 0 | 100 | 5.48 | 67.69 | 60 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 0.60 | 10.16 | 6.64 | 14.06 | 0 | 256 | 0.58 | 13.69 | 26 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 1.20 | 9.38 | 6.24 | 12.89 | 0 | 256 | 0.55 | 12.81 | 24 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 1.60 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.48 | 12.37 | 23 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 2.00 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.47 | 12.37 | 23 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 2.50 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.46 | 12.37 | 23 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 3.00 | 7.42 | 4.30 | 10.94 | 0 | 256 | 0.40 | 10.58 | 19 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 4.00 | 5.47 | 2.73 | 8.20 | 0 | 256 | 0.26 | 8.31 | 14 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 5.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.25 | 7.84 | 13 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 6.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.23 | 7.84 | 13 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 0.60 | 98.00 | 95.00 | 100.00 | 0 | 100 | 52.76 | 99.34 | 98 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 1.20 | 53.00 | 43.00 | 63.00 | 0 | 100 | 13.49 | 61.02 | 53 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 1.60 | 32.00 | 23.00 | 41.00 | 0 | 100 | 10.90 | 40.06 | 32 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 2.00 | 27.00 | 19.00 | 36.00 | 0 | 100 | 10.20 | 34.84 | 27 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 2.50 | 23.00 | 15.00 | 32.00 | 0 | 100 | 8.44 | 30.58 | 23 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 3.00 | 21.00 | 14.00 | 29.02 | 0 | 100 | 7.09 | 28.42 | 21 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 4.00 | 17.00 | 10.00 | 25.00 | 0 | 100 | 5.21 | 24.03 | 17 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 5.00 | 15.00 | 9.00 | 22.00 | 0 | 100 | 4.83 | 21.79 | 15 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 6.00 | 13.00 | 7.00 | 20.00 | 0 | 100 | 4.41 | 19.52 | 13 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 0.60 | 3.12 | 1.17 | 5.47 | 0 | 256 | 0.27 | 5.46 | 8 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 1.20 | 3.12 | 1.17 | 5.47 | 0 | 256 | 0.24 | 5.46 | 8 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 1.60 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 2.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.23 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 2.50 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.23 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 3.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.22 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 4.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.21 | 4.97 | 7 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 5.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.17 | 4.47 | 6 | 
| Plain $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 6.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.17 | 4.47 | 6 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 60.76 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 59.99 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 58.00 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 56.11 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 50.32 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 45.74 | 100.00 | 100 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 4.00 | 86.00 | 79.00 | 92.00 | 0 | 100 | 27.75 | 90.76 | 86 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 5.00 | 68.00 | 59.00 | 77.00 | 0 | 100 | 8.81 | 75.11 | 68 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 6.00 | 60.00 | 51.00 | 70.00 | 0 | 100 | 5.48 | 67.69 | 60 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 0.60 | 10.16 | 6.64 | 14.06 | 0 | 256 | 0.58 | 13.69 | 26 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 1.20 | 9.38 | 6.24 | 12.89 | 0 | 256 | 0.55 | 12.81 | 24 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 1.60 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.48 | 12.37 | 23 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 2.00 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.47 | 12.37 | 23 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 2.50 | 8.98 | 5.47 | 12.50 | 0 | 256 | 0.46 | 12.37 | 23 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 3.00 | 7.42 | 4.30 | 10.94 | 0 | 256 | 0.40 | 10.58 | 19 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 4.00 | 5.47 | 2.73 | 8.20 | 0 | 256 | 0.26 | 8.31 | 14 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 5.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.25 | 7.84 | 13 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 6.00 | 5.08 | 2.73 | 7.81 | 0 | 256 | 0.23 | 7.84 | 13 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 0.60 | 90.00 | 84.00 | 95.00 | 0 | 100 | 49.41 | 93.93 | 90 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 1.20 | 77.00 | 68.00 | 85.00 | 0 | 100 | 28.99 | 83.16 | 77 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 1.60 | 31.00 | 22.00 | 40.00 | 0 | 100 | 8.43 | 39.02 | 31 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 2.00 | 26.00 | 18.00 | 35.00 | 0 | 100 | 7.15 | 33.78 | 26 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 2.50 | 21.00 | 13.98 | 29.00 | 0 | 100 | 5.57 | 28.42 | 21 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 3.00 | 18.00 | 11.00 | 26.00 | 0 | 100 | 5.29 | 25.14 | 18 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 4.00 | 13.00 | 7.00 | 20.00 | 0 | 100 | 4.55 | 19.52 | 13 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 5.00 | 11.00 | 5.00 | 18.00 | 0 | 100 | 4.16 | 17.21 | 11 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 6.00 | 11.00 | 5.00 | 17.00 | 0 | 100 | 3.72 | 17.21 | 11 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 0.60 | 3.91 | 1.56 | 6.25 | 0 | 256 | 0.28 | 6.43 | 10 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 1.20 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.25 | 4.97 | 7 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 1.60 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 2.00 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 2.50 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.20 | 4.47 | 6 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 3.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.20 | 4.47 | 6 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 4.00 | 1.95 | 0.39 | 3.91 | 1 | 256 | 0.16 | 3.96 | 5 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 5.00 | 1.56 | 0.39 | 3.12 | 1 | 256 | 0.13 | 3.43 | 4 | 
| Plain $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 6.00 | 1.56 | 0.39 | 3.12 | 1 | 256 | 0.13 | 3.43 | 4 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 71.40 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 70.21 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 69.23 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 68.15 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 67.22 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 64.45 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 4.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 59.71 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 5.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 56.94 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 6.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 51.44 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 0.60 | 9.00 | 4.00 | 15.00 | 0 | 100 | 2.37 | 14.85 | 9 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 1.20 | 9.00 | 4.00 | 15.00 | 0 | 100 | 2.35 | 14.85 | 9 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 1.60 | 12.00 | 6.00 | 19.00 | 0 | 100 | 2.59 | 18.37 | 12 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 2.00 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.29 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 2.50 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.27 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 3.00 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.25 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 4.00 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.18 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 5.00 | 9.00 | 4.00 | 15.00 | 0 | 100 | 2.09 | 14.85 | 9 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 6.00 | 8.00 | 3.00 | 14.00 | 0 | 100 | 1.72 | 13.65 | 8 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 71.40 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 68.17 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 65.14 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 62.38 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 57.68 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 54.58 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 4.00 | 98.00 | 95.00 | 100.00 | 0 | 100 | 48.89 | 99.34 | 98 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 5.00 | 94.00 | 89.00 | 98.00 | 0 | 100 | 36.29 | 96.87 | 94 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 6.00 | 80.00 | 72.00 | 87.00 | 0 | 100 | 27.97 | 85.75 | 80 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 0.60 | 9.77 | 6.25 | 13.67 | 0 | 256 | 2.31 | 13.25 | 25 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 1.20 | 9.77 | 6.25 | 13.67 | 0 | 256 | 2.30 | 13.25 | 25 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 1.60 | 8.98 | 5.47 | 12.50 | 0 | 256 | 2.28 | 12.37 | 23 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 2.00 | 8.20 | 5.08 | 11.72 | 0 | 256 | 1.46 | 11.48 | 21 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 2.50 | 7.42 | 4.30 | 10.94 | 0 | 256 | 1.35 | 10.58 | 19 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 3.00 | 7.03 | 3.91 | 10.16 | 0 | 256 | 1.28 | 10.13 | 18 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 4.00 | 5.86 | 3.12 | 8.98 | 0 | 256 | 1.26 | 8.77 | 15 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 5.00 | 5.86 | 3.12 | 8.98 | 0 | 256 | 1.25 | 8.77 | 15 | 
| Volatility-scaled $\cdot$ original EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 6.00 | 5.47 | 2.73 | 8.59 | 0 | 256 | 1.10 | 8.31 | 14 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 71.40 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 70.21 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 69.23 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 68.15 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 67.22 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 64.45 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 4.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 59.71 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 5.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 56.94 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ deployed gate | 6.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 51.44 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 0.60 | 9.00 | 4.00 | 15.00 | 0 | 100 | 2.37 | 14.85 | 9 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 1.20 | 9.00 | 4.00 | 15.00 | 0 | 100 | 2.35 | 14.85 | 9 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 1.60 | 12.00 | 6.00 | 19.00 | 0 | 100 | 2.59 | 18.37 | 12 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 2.00 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.29 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 2.50 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.27 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 3.00 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.25 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 4.00 | 10.00 | 5.00 | 16.00 | 0 | 100 | 2.18 | 16.04 | 10 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 5.00 | 9.00 | 4.00 | 15.00 | 0 | 100 | 2.09 | 14.85 | 9 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Current policy $\cdot$ resettable floor | 6.00 | 8.00 | 3.00 | 14.00 | 0 | 100 | 1.72 | 13.65 | 8 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 0.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 71.91 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 1.20 | 100.00 | 100.00 | 100.00 | 0 | 100 | 66.34 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 1.60 | 100.00 | 100.00 | 100.00 | 0 | 100 | 63.41 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 2.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 61.61 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 2.50 | 100.00 | 100.00 | 100.00 | 0 | 100 | 58.24 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 3.00 | 100.00 | 100.00 | 100.00 | 0 | 100 | 52.27 | 100.00 | 100 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 4.00 | 97.00 | 93.00 | 100.00 | 0 | 100 | 43.10 | 98.79 | 97 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 5.00 | 89.00 | 82.00 | 94.00 | 0 | 100 | 35.05 | 93.15 | 89 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ deployed gate | 6.00 | 75.00 | 67.00 | 83.00 | 0 | 100 | 21.65 | 81.40 | 75 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 0.60 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.95 | 9.68 | 17 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 1.20 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.91 | 9.68 | 17 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 1.60 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.90 | 9.68 | 17 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 2.00 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.90 | 9.68 | 17 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 2.50 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.86 | 9.68 | 17 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 3.00 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.85 | 9.68 | 17 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 4.00 | 5.47 | 2.73 | 8.59 | 0 | 256 | 1.08 | 8.31 | 14 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 5.00 | 4.69 | 2.34 | 7.42 | 0 | 256 | 1.06 | 7.37 | 12 | 
| Volatility-scaled $\cdot$ halved EMA half-lives $\cdot$ near the qualifying line / Proposed policy $\cdot$ resettable floor | 6.00 | 4.69 | 2.34 | 7.42 | 0 | 256 | 1.06 | 7.37 | 12 | 
| Reference line | — | 5.00 | — | — | — | — | — | — | — | 

**Chart data $\cdot$ The proposal with resettable floor: plain against scaled histories**

% of paths starting outside the serious tier with a first episode by day 365
| Panel / curve | Coordinate $\cdot$ Donation rate, % of pool value per year | % of paths starting outside the serious tier with a first episode by day 365 | Interval low | Interval high | Passes both rarity tests | Paths starting outside the tier | Mean time below tier over 556 days, % | Upper confidence limit for first onset, % | Paths with first onset by day 365 | 
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Original EMA half-lives / Plain | 0.60 | 3.12 | 1.17 | 5.47 | 0 | 256 | 0.27 | 5.46 | 8 | 
| Original EMA half-lives / Plain | 1.20 | 3.12 | 1.17 | 5.47 | 0 | 256 | 0.24 | 5.46 | 8 | 
| Original EMA half-lives / Plain | 1.60 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Original EMA half-lives / Plain | 2.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.23 | 4.97 | 7 | 
| Original EMA half-lives / Plain | 2.50 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.23 | 4.97 | 7 | 
| Original EMA half-lives / Plain | 3.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.22 | 4.97 | 7 | 
| Original EMA half-lives / Plain | 4.00 | 2.73 | 1.17 | 5.08 | 1 | 256 | 0.21 | 4.97 | 7 | 
| Original EMA half-lives / Plain | 5.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.17 | 4.47 | 6 | 
| Original EMA half-lives / Plain | 6.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.17 | 4.47 | 6 | 
| Halved EMA half-lives / Plain | 0.60 | 3.91 | 1.56 | 6.25 | 0 | 256 | 0.28 | 6.43 | 10 | 
| Halved EMA half-lives / Plain | 1.20 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.25 | 4.97 | 7 | 
| Halved EMA half-lives / Plain | 1.60 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Halved EMA half-lives / Plain | 2.00 | 2.73 | 0.78 | 5.08 | 1 | 256 | 0.24 | 4.97 | 7 | 
| Halved EMA half-lives / Plain | 2.50 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.20 | 4.47 | 6 | 
| Halved EMA half-lives / Plain | 3.00 | 2.34 | 0.78 | 4.30 | 1 | 256 | 0.20 | 4.47 | 6 | 
| Halved EMA half-lives / Plain | 4.00 | 1.95 | 0.39 | 3.91 | 1 | 256 | 0.16 | 3.96 | 5 | 
| Halved EMA half-lives / Plain | 5.00 | 1.56 | 0.39 | 3.12 | 1 | 256 | 0.13 | 3.43 | 4 | 
| Halved EMA half-lives / Plain | 6.00 | 1.56 | 0.39 | 3.12 | 1 | 256 | 0.13 | 3.43 | 4 | 
| Original EMA half-lives / Volatility-scaled | 0.60 | 9.77 | 6.25 | 13.67 | 0 | 256 | 2.31 | 13.25 | 25 | 
| Original EMA half-lives / Volatility-scaled | 1.20 | 9.77 | 6.25 | 13.67 | 0 | 256 | 2.30 | 13.25 | 25 | 
| Original EMA half-lives / Volatility-scaled | 1.60 | 8.98 | 5.47 | 12.50 | 0 | 256 | 2.28 | 12.37 | 23 | 
| Original EMA half-lives / Volatility-scaled | 2.00 | 8.20 | 5.08 | 11.72 | 0 | 256 | 1.46 | 11.48 | 21 | 
| Original EMA half-lives / Volatility-scaled | 2.50 | 7.42 | 4.30 | 10.94 | 0 | 256 | 1.35 | 10.58 | 19 | 
| Original EMA half-lives / Volatility-scaled | 3.00 | 7.03 | 3.91 | 10.16 | 0 | 256 | 1.28 | 10.13 | 18 | 
| Original EMA half-lives / Volatility-scaled | 4.00 | 5.86 | 3.12 | 8.98 | 0 | 256 | 1.26 | 8.77 | 15 | 
| Original EMA half-lives / Volatility-scaled | 5.00 | 5.86 | 3.12 | 8.98 | 0 | 256 | 1.25 | 8.77 | 15 | 
| Original EMA half-lives / Volatility-scaled | 6.00 | 5.47 | 2.73 | 8.59 | 0 | 256 | 1.10 | 8.31 | 14 | 
| Halved EMA half-lives / Volatility-scaled | 0.60 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.95 | 9.68 | 17 | 
| Halved EMA half-lives / Volatility-scaled | 1.20 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.91 | 9.68 | 17 | 
| Halved EMA half-lives / Volatility-scaled | 1.60 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.90 | 9.68 | 17 | 
| Halved EMA half-lives / Volatility-scaled | 2.00 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.90 | 9.68 | 17 | 
| Halved EMA half-lives / Volatility-scaled | 2.50 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.86 | 9.68 | 17 | 
| Halved EMA half-lives / Volatility-scaled | 3.00 | 6.64 | 3.52 | 9.77 | 0 | 256 | 1.85 | 9.68 | 17 | 
| Halved EMA half-lives / Volatility-scaled | 4.00 | 5.47 | 2.73 | 8.59 | 0 | 256 | 1.08 | 8.31 | 14 | 
| Halved EMA half-lives / Volatility-scaled | 5.00 | 4.69 | 2.34 | 7.42 | 0 | 256 | 1.06 | 7.37 | 12 | 
| Halved EMA half-lives / Volatility-scaled | 6.00 | 4.69 | 2.34 | 7.42 | 0 | 256 | 1.06 | 7.37 | 12 | 
| Reference line | — | 5.00 | — | — | — | — | — | — | — |


# G3 The directional bet decides the live stall outcome {#detachment/costs}

**During live Bitcoin [stalls](./#glossary/stall), the pool usually finished ahead of holding its opening coins.**

**Measure:** ending investment value, in USD per million of opening wealth, pool minus holding

**Compared:** investing in the live pool with holding that stall’s opening coins

**Same for both:** each Bitcoin stall, counted until recovery or the study endpoint

**Higher means:** the pool finishes further ahead of holding

A stall is a gap above 5% between [price_scale](./#glossary/price_scale) and the market, lasting at least 24 hours.

The distribution covers every observed stall. It includes stalls still open at the study endpoint. These comparisons include trades, fees and changes in the number of shares.

The pool’s holdings determine which price moves help or hurt. The harvesting and curvature comparisons below ask separate questions on the same live price path. The repair page shows the capital needed to restore the pool’s centre price.

Across 18 live Bitcoin stalls, the pool usually ends ahead of holding its opening coins. It ends ahead in 14 stalls. It ends behind in 3 stalls. It is tied in 1 stall. Each comparison uses the same end price, including the study endpoint for open stalls.

Each point is the pool’s investment value minus the value of holding that stall’s opening coins. The unit is dollars per million of starting wealth. Higher points favour the pool. 

Hollow diamonds stop at the study endpoint while the stall remains open. Other points stop at recovery.

### [Missed harvesting](./#glossary/missed-harvesting)

**Measure:** harvesting lost by drifting from equal asset values, in [percentage points](./#glossary/percentage-point) of pool value

**Compared:** a pool holding equal value in cash and [WBTC](./#glossary/wbtc) with the mix WBTC actually held

**Same for both:** the same live prices over 128 days, with the mix measured before each price move

**Higher means:** more harvesting was forgone as the pool drifted from equal asset values

Very small: the equal-value term is larger by only 0.038 percentage points of pool value over the 128 days. The pool’s drift away from equal value gave up almost no harvesting.

> **Common misunderstanding:** “A detached pool loses mainly because it stops harvesting [volatility](./#glossary/volatility).”
>
> **What is true.**
>
> On live WBTC prices, the [missed harvesting](./#glossary/missed-harvesting) totals only 0.038 percentage points over 128 days. The market's direction decides each stall. In 14 of 18 live Bitcoin stalls, the pool ended ahead of holding its opening coins.

### [Curvature-exposure gap](./#glossary/curvature-exposure-gap)

**Measure:** estimated loss difference before fees over 128 days, in percentage points of pool value

**Compared:** the pool [centred](./#glossary/centred-pool) on the market with the actual [off-centre](./#glossary/off-centre) WBTC pool

**Same for both:** pool value, curve shape and live WBTC prices from 26 May 2026 to 1 October 2026

**Higher means:** the actual pool had less trading depth at the market price while prices moved

The centred pool’s estimate is larger by 1.08 percentage points of pool value over the 128 days. The estimate assumes that arbitrageurs correct every price move at once. It also assumes they pay no fees. 

The estimate measures potential losses to arbitrageurs, not a payment made by either pool. The [repair page](./#detachment/repairs) measures funding needs. The [attachment page](./#detachment/funded) tests returns after funded maintenance.

[← previous](./#detachment/donations)[next $\to$](./#detachment/repairs)

**Chart data $\cdot$ All Bitcoin stall outcomes against holding**

USD per million of opening wealth
| Panel / curve | Coordinate $\cdot$ Stall start, UTC | USD per million of opening wealth | Still open at the endpoint | 
| --- | --- | --- | --- |
| Every observed Bitcoin stall / WBTC | 2026-06-02T14:20:11+00:00 | +3,550.25 | 0 | 
| Every observed Bitcoin stall / WBTC | 2026-06-18T03:01:35+00:00 | +582.73 | 0 | 
| Every observed Bitcoin stall / WBTC | 2026-06-23T05:18:47+00:00 | +2,387.10 | 0 | 
| Every observed Bitcoin stall / WBTC | 2026-08-20T07:54:11+00:00 | −11,234.05 | 1 | 
| Every observed Bitcoin stall / [cbBTC](./#glossary/cbbtc) | 2026-06-02T14:02:59+00:00 | +2,895.80 | 0 | 
| Every observed Bitcoin stall / cbBTC | 2026-06-17T18:57:47+00:00 | +919.88 | 0 | 
| Every observed Bitcoin stall / cbBTC | 2026-06-22T15:43:35+00:00 | +2,977.75 | 0 | 
| Every observed Bitcoin stall / cbBTC | 2026-07-04T21:33:11+00:00 | 0.00 | 0 | 
| Every observed Bitcoin stall / cbBTC | 2026-08-21T06:48:23+00:00 | +851.48 | 0 | 
| Every observed Bitcoin stall / cbBTC | 2026-08-23T08:09:47+00:00 | +1,629.91 | 0 | 
| Every observed Bitcoin stall / cbBTC | 2026-08-29T13:11:23+00:00 | −39.79 | 0 | 
| Every observed Bitcoin stall / cbBTC | 2026-08-31T05:04:47+00:00 | +25.79 | 0 | 
| Every observed Bitcoin stall / cbBTC | 2026-09-03T11:18:35+00:00 | +2,056.45 | 0 | 
| Every observed Bitcoin stall / [tBTC](./#glossary/tbtc) | 2026-06-02T13:49:11+00:00 | +2,958.32 | 0 | 
| Every observed Bitcoin stall / tBTC | 2026-06-17T16:30:47+00:00 | +1,040.75 | 0 | 
| Every observed Bitcoin stall / tBTC | 2026-06-22T14:00:47+00:00 | +2,887.79 | 0 | 
| Every observed Bitcoin stall / tBTC | 2026-07-08T01:36:35+00:00 | +293.20 | 0 | 
| Every observed Bitcoin stall / tBTC | 2026-08-20T08:09:23+00:00 | −11,335.62 | 1 | 
| Reference line | — | 0 | — |


# G4 Repairing a detached pool needs capital {#detachment/repairs}

**Repairing a detached pool often needs more accounting capital than the gate has available.**

**Measure:** extra reserves needed for full re-centring to pass the gate, as a percentage of pool [market value](./#glossary/market-value)

**Compared:** the pool’s original reserves with the same pool after a proportional top-up

**Same for both:** shares, unlocked shares and the protected floor, all held fixed

**Higher means:** more additional capital is needed

Full re-centring moves the pool’s centre price to the market price. The gate is the accounting check that permits centre-price moves. The top-up adds both reserve assets in their existing proportions.

Among these [stalls](./#glossary/stall), [WBTC](./#glossary/wbtc)’s August–October stall needs the largest reserve top-up. At that peak, the extra reserves needed for full re-centring equal 3.87% of pool market value. That is $2.71 million. The corresponding peaks are 3.75% for [tBTC](./#glossary/tbtc) and 2.51% for [cbBTC](./#glossary/cbbtc)’s June stall.

| Pool and stall | Reserve top-up needed, % of pool value | Reserve top-up needed, million USD | 
| --- | --- | --- |
| WBTC, August–October | 3.87 | 2.71 | 
| tBTC, August–October | 3.75 | 1.42 | 
| cbBTC, June | 2.51 | 1.99 | 

It is a funding need with the floor and shares held fixed, not money the pool spends.

The repair calculation adds reserves while keeping [LP](./#glossary/lp) supply, the protected floor and unlocked shares fixed. An [executable donation](./#glossary/executable-donation) instead follows the contract’s minting and lock rules. The [funded-attachment test](./#detachment/funded) measures wealth after repeated maintenance. It includes the external funding costs.

The live-peak and simulated-[episode](./#glossary/episode) calculations find the reserve top-up needed for full re-centring. Shares and the floor stay fixed in them. A separate test asks whether the next controller step would pass if an update were supplied. The executable-[donation](./#glossary/donation) test then applies the actual minting, lock and share-cap rules.

**Measure:** serious-episode time in which the budget would refuse a supplied update, in percent of episode time

**Compared:** the current rule at the lower donation rate with the same rule at the higher rate

**Same for both:** the same plain [WETH](./#glossary/weth) histories

**Higher means:** the budget blocks repairs for more of the episode

On plain WETH histories with the current rule and deployed gate, an update at an episode state is usually not enough. The budget still rejects the next controller step through 99.87% of serious-episode time at 1.20% annual donations. At 6.00% donations the share is 99.71%.

> **Common misunderstanding:** “Faster tracking would fix [detachment](./#glossary/detachment).”
>
> **What is true.**
>
> Under the deployed gate, the budget blocks repairs, not the speed. During serious detachment, the budget would refuse the next step through 99.87% of the time at 1.20% donations. Faster tracking cannot move the centre while the budget refuses.

Each point averages the extra reserve capital needed for full re-centring to pass the stated gate. The unit is a percentage of pool value at that moment. 

The average weights merged serious episodes by their duration, including brief recoveries. Only histories with episodes contribute. Intervals resample whole histories. Plain and [volatility](./#glossary/volatility)-scaled histories are shown separately.

The current price rule with shared [financing](./#glossary/financing) settings and the deployed gate is tested on plain WETH histories. Full re-centring requires an average reserve top-up of 15.51% of pool value at 1.20% annual donations. At 6.00% donations the average is 10.35%. 

The average covers episode time. The protected floor, LP supply and unlocked shares stay fixed.

**Measure:** the share of episode peaks where no permitted donation funds full re-centring, in percent of tested peaks

**Compared:** the current rule at the lower donation rate with the same rule at the higher rate

**Same for both:** the same 7-day wait, with prices unchanged and no operations

**Higher means:** more peaks where the share cap blocks the repair

The executable-donation test mints and locks shares within the contract’s cap. It waits 7 days with prices unchanged and no operations. It then tests the full re-centring budget. 

No permitted deposit passes at 24.70% of episode peaks with 1.20% annual donations. With 6.00% donations the share is 4.55%. A passing deposit funds the target. The controller’s step limit still governs an actual move.

> **Common misunderstanding:** “A large enough donation can always fund a repair.”
>
> **What is true.**
>
> Donations are capped, and the cap can bind. At 1.20% yearly donations, no permitted donation passes the gate at 24.70% of serious-episode peaks. At 6.00% the share is 4.55%.

**More detail**

In the low-donation current-rule run, 99.40% of serious-episode blocks have no actual pool operation. Separately, the budget test supplies an update opportunity at each state and asks whether the next step would pass. A block can satisfy both descriptions.

Repair averages use merged episode time. Uncertainty intervals resample the 100 rebuilt histories.

The [shared settings and conventions](./#settings) distinguish these depth, event and quote measures from return rates.

The [settings table](./#settings) defines the current-rule and proposal bundles. Each result states its donation rate.

The simulated actors are arbitrageurs and the debt-financed YB holder. Customer demand requires a separate [response model](./#simulation/limits). The [settings page](./#settings) defines the bundles.

[← previous](./#detachment/costs)[next $\to$](./#detachment/trader-cost)

**Chart data $\cdot$ Capital needed for full re-centring during serious episodes**

pp of contemporaneous pool value
| Panel / curve | Coordinate $\cdot$ Donation rate, % of pool value per year | pp of contemporaneous pool value | Interval low | Interval high | Rebuilt histories | Histories with serious episodes | 
| --- | --- | --- | --- | --- | --- | --- |
| Plain histories / Current rule $\cdot$ deployed gate | 1.20 | 15.51 | 13.58 | 17.63 | 100 | 100 | 
| Plain histories / Current rule $\cdot$ deployed gate | 2.50 | 11.57 | 9.76 | 13.72 | 100 | 100 | 
| Plain histories / Current rule $\cdot$ deployed gate | 4.00 | 11.13 | 8.27 | 14.39 | 100 | 90 | 
| Plain histories / Current rule $\cdot$ deployed gate | 6.00 | 10.35 | 4.09 | 17.61 | 100 | 71 | 
| Plain histories / Proposed policy $\cdot$ [resettable floor](./#glossary/resettable-floor) $\cdot$ halved [EMAs](./#glossary/ema) | 1.20 | 2.96 | 2.75 | 3.12 | 100 | 4 | 
| Plain histories / Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs | 2.50 | 2.78 | 2.51 | 3.06 | 100 | 3 | 
| Plain histories / Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs | 4.00 | 2.86 | 2.73 | 2.98 | 100 | 2 | 
| Plain histories / Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs | 6.00 | 2.65 | 2.56 | 2.74 | 100 | 2 | 
| Volatility-scaled histories / Current rule $\cdot$ deployed gate | 1.20 | 17.15 | 14.96 | 19.55 | 100 | 100 | 
| Volatility-scaled histories / Current rule $\cdot$ deployed gate | 2.50 | 16.47 | 14.31 | 18.79 | 100 | 100 | 
| Volatility-scaled histories / Current rule $\cdot$ deployed gate | 4.00 | 16.21 | 13.94 | 18.69 | 100 | 100 | 
| Volatility-scaled histories / Current rule $\cdot$ deployed gate | 6.00 | 15.67 | 13.20 | 18.18 | 100 | 100 | 
| Volatility-scaled histories / Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs | 1.20 | 23.47 | 4.64 | 36.64 | 100 | 7 | 
| Volatility-scaled histories / Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs | 2.50 | 22.65 | 4.01 | 35.23 | 100 | 7 | 
| Volatility-scaled histories / Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs | 4.00 | 31.95 | 1.61 | 35.51 | 100 | 5 | 
| Volatility-scaled histories / Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs | 6.00 | 31.01 | 1.51 | 33.65 | 100 | 4 |


# G5 Test orders get worse quotes during detachment {#detachment/trader-cost}

**During serious [episodes](./#glossary/episode), standardised test orders receive worse quotes than in an equally funded [centred pool](./#glossary/centred-pool).**

**Measure:** the extra cost of the same standard order, in [basis points](./#glossary/basis-point) of order value

**Compared:** the observed pool with an equally funded pool centred at the market price

**Same for both:** curve shape, fee rule, time and [report](./#glossary/report) information

**Higher means:** a worse quote in the observed pool

A centred pool places its trading capacity around the market price. A basis point is one hundredth of a [percentage point](./#glossary/percentage-point). Serious episodes are sustained periods with too little depth at the market price.

During current-rule serious episodes, orders worth 0.50% of pool value cost more than in the centred reference pool. Buying [ETH](./#glossary/eth) costs an average 192.15 bp more. Selling ETH costs 210.14 bp more. These plain [WETH](./#glossary/weth) histories use 1.20% annual [donations](./#glossary/donation).

Exact quoted costs, fees included, for standardised orders worth 0.50% of pool value at that time. The reference is an equally funded centred pool at the same hourly states. 

Current rule, 1.20% annual donations, plain histories. 100 histories have serious episodes. 

Error bars show uncertainty from resampling whole histories. Positive values mean worse actual quotes.

The proposal’s own serious episodes come from runs with the [resettable floor](./#glossary/resettable-floor), faster price averages and 2.50% annual donations. In those episodes, extra cost against the centred reference averages 12.80 bp to buy ETH. The extra cost to sell ETH averages 16.89 bp. 

Only 3 histories contribute. Those episodes differ from the current-rule sample.

These are quoted costs for test orders, not realised customer costs. Predicting how many trades occur or go elsewhere needs a demand model. [What cannot yet be measured](./#simulation/limits) explains that limitation.

**More detail**

Both quotes use the exact fee rule and equal market-valued capital. The centred reference keeps the same accepted report, report age and price averages as the tested state. Orders are quoted hourly during merged serious episodes. The average includes negative differences, which mean the actual pool offers a better quote.

The [shared settings and conventions](./#settings) distinguish these depth, event and quote measures from return rates.

The [settings table](./#settings) defines the current-rule and proposal bundles. Each result states its donation rate.

The [settings page](./#settings) defines this current-rule bundle. The [customer-response page](./#simulation/limits) explains why quoted costs alone do not measure lost trades. Only arbitrageurs and the debt-financed YB holder are simulated.

[← previous](./#detachment/repairs)[next $\to$](./#detachment/funded)

**Chart data $\cdot$ Current-rule test orders during serious episodes**

basis points per order, compared with an equally funded centred pool
| Comparison | Buy ETH $\cdot$ basis points per order, compared with an equally funded centred pool | Sell ETH $\cdot$ basis points per order, compared with an equally funded centred pool | Buy ETH $\cdot$ Interval low $\cdot$ basis points per order, compared with an equally funded centred pool | Buy ETH $\cdot$ Interval high $\cdot$ basis points per order, compared with an equally funded centred pool | Sell ETH $\cdot$ Interval low $\cdot$ basis points per order, compared with an equally funded centred pool | Sell ETH $\cdot$ Interval high $\cdot$ basis points per order, compared with an equally funded centred pool | 
| --- | --- | --- | --- | --- | --- | --- |
| Current rule $\cdot$ 1.20%/yr | 192.15 | 210.14 | 187.16 | 196.99 | 203.49 | 216.53 |


# G6 Staying attached does not reliably raise wealth {#detachment/funded}

**Staying attached does not reliably increase wealth in these tests.**

**Measure:** growth differences for the three measures below, in [percentage points](./#glossary/percentage-point) per year

**Compared:** each lower-[detachment](./#glossary/detachment) package with the current-rule control

**Same for both:** the same rebuilt [WETH](./#glossary/weth) histories

**Higher means:** the package grows faster than the control

The tests measure returns in three ways:

- YB-position growth measures the holder’s [ETH](./#glossary/eth) wealth after debt.
- [M](./#glossary/m) growth compares each share with a fee-free reference pool.
- [LP/xyk](./#glossary/lp-xyk) subtracts the [donation](./#glossary/donation) charge from M growth.

The control pays 5% annual donations. The packages pay 1.20% or 1.60%.

A pool stays attached when its centre price stays near the market price. The first comparison tests packages that reduce detachment against a stated current-rule control on the same rebuilt histories. The packages have lower mean growth.

The second comparison forces each pool to the market centre. It counts the funding, withdrawals and execution charges. Forced maintenance has mixed outcomes under the current rule. It has a negative mean under the proposal.

> **Common misunderstanding:** “Keeping the pool attached always makes [LPs](./#glossary/lp) and holders richer.”
>
> **What is true.**
>
> In these tests, staying attached did not reliably raise wealth. The settings that keep detachment rare grew the holder's position more slowly than the control. The growth differences are −4.03 and −4.30 pp/yr. Forcing attachment, with its funding counted, gave mixed results across histories.

Against the current-rule control on 100 shared histories, both settings lower YB-position ETH growth. The faster-average setting changes it by −4.03 pp/yr. The original-average setting changes it by −4.30 pp/yr. 

Their M-growth differences are −4.61 and −4.36 pp/yr. Each rate covers the full 556-day path.

The whole packages differ in policy, gate, donation rate and price-average speed. The control uses current price rules, the deployed gate and 5% annual donations. Both sides use 42.91% reserved profit and a 1.50% [LevAMM](./#glossary/levamm) fee. [Settings](./#settings) names these bundles.

| Setting | Paired histories | YB position in ETH, log pp/yr | M, log pp/yr | LP/xyk, log pp/yr | 
| --- | --- | --- | --- | --- |
| 1.20% donations, Halved [EMA](./#glossary/ema) half-lives | 100 | −4.03 [−5.66, −1.76] | −4.61 [−5.43, −3.51] | −0.99 [−1.76, +0.07] | 
| 1.60% donations, Original EMA half-lives | 100 | −4.30 [−5.93, −2.03] | −4.36 [−5.17, −3.25] | −1.12 [−1.89, −0.06] | 

The table separates pairs where neither pool has a serious [episode](./#glossary/episode) from pairs where at least one does. Either the control or the proposal can put a pair in the second group. These groups are selected from the realised outcomes. Brackets show 95% intervals from resampling paired histories.

| Setting | Serious episodes over the full path | Paired histories | YB position in ETH, log pp/yr | M, log pp/yr | LP/xyk, log pp/yr | 
| --- | --- | --- | --- | --- | --- |
| 1.20% donations, Halved EMA half-lives | Both arms stay out of serious episodes | 19 | −4.69 [−5.59, −3.85] | −5.39 [−5.66, −5.13] | −1.65 [−1.93, −1.38] | 
| 1.20% donations, Halved EMA half-lives | Either arm has a serious episode | 81 | −3.87 [−5.98, −1.04] | −4.43 [−5.49, −3.09] | −0.83 [−1.83, +0.47] | 
| 1.60% donations, Original EMA half-lives | Both arms stay out of serious episodes | 19 | −4.72 [−5.81, −3.71] | −5.03 [−5.39, −4.69] | −1.69 [−2.06, −1.35] | 
| 1.60% donations, Original EMA half-lives | Either arm has a serious episode | 81 | −4.20 [−6.30, −1.38] | −4.20 [−5.24, −2.85] | −0.98 [−1.97, +0.32] | 

Funding before counting returned value is averaged over all 256 histories per setting. Donation charges use yearly [log growth](./#glossary/log-growth) in the value of each pool share as their scale. Interest uses initial YB equity. 

The growth comparisons above use only histories shared with the control. These funding averages are a separate summary.

| Setting | Gross donated-share charge, log pp/yr of LP/xyk | Gross interest, % of initial YB equity per year | 
| --- | --- | --- |
| 1.20% donations, halved EMA half-lives | 1.16 | 2.28 | 
| 1.60% donations, original EMA half-lives | 1.54 | 3.04 | 

The funding measures have different denominators. They are never added together. [Burns](./#glossary/burn) and other returned value are already reflected in the [YB position](./#glossary/yb-position). Interest alone is not the holder’s loss.

The [resettable floor](./#glossary/resettable-floor) relaxes cumulative [book-value](./#glossary/book-value) protection. Better tracking does not by itself imply greater market-valued wealth.

**More detail**

The earlier example used 2.50% donations, faster price averages and a control reserving 45% of profit. Using the [price-gap stall rule](./#settings), the YB-growth difference was −3.69 pp/yr in 5 pairs without a [stall](./#glossary/stall). Across the 95 pairs with a stall, it was −3.87 pp/yr. These are separate settings from the serious-depth comparison above.

### Forcing the pool to stay attached does not reliably pay

**Measure:** maintained-minus-unmaintained LP/xyk, in pp/yr, after the funding account and execution charges

**Compared:** a pool forced to stay at the market centre with the same pool left unmaintained

**Same for both:** the price rule, 32 plain WETH histories per rule, 2.50% annual donations

**Higher means:** maintenance gives a larger growth advantage over leaving the pool unmaintained

On 32 shared plain WETH histories, funded attachment changes current-rule LP/xyk by +1.71 pp/yr on average. It lowers LP/xyk in 22 histories. Under the proposal the mean is −2.02 pp/yr. Where neither pool has a price-gap stall, it is −2.12 pp/yr.

Every paired history appears once under each rule. Colour records whether the actual pool stalled. The maintained pool has no such stall. 

The vertical axis shows the return difference after accounting for funding, withdrawals and [execution costs](./#glossary/execution-cost). The horizontal coordinate identifies the rebuilt history. Positive values favour funded attachment. Each panel uses its own vertical scale.

This is one declared maintenance rule on 32 paired plain histories per rule, at 2.50% annual donations. The current rule uses the deployed gate. The proposal uses the resettable floor and halved EMA half-lives. Every difference compares the [funded attached pool](./#glossary/funded-attached-pool) with its corresponding actual arm.

| Rule and attachment group | Histories | LP/xyk difference, log pp/yr | 95% interval | Positive | Negative | 
| --- | --- | --- | --- | --- | --- |
| Current rule, all | 32 | +1.71 | −1.22 to +4.92 | 10 | 22 | 
| Proposed policy, all | 32 | −2.02 | −3.31 to −0.89 | 12 | 20 | 
| Proposed policy, both attached | 31 | −2.12 | −3.37 to −0.98 | 11 | 20 | 

At each supplied opportunity, the maintained pool moves its centre to market. The capital measured by its reserve curve stays fixed. The number of pool shares also stays fixed.

 A funding account records reserve additions and execution costs as positive. It records withdrawals as negative. Subtract this balance from terminal market wealth before calculating LP/xyk. 

All 32 current-rule histories return net funds. All 32 proposal histories require net funding.

**More detail**

The execution charge is 5 [basis points](./#glossary/basis-point) of the change in ETH holdings, ignoring its sign, valued at the market price. The charge applies whether maintenance adds or withdraws reserve value. Cash in the funding account earns no interest. 

Both pools receive the same [re-peg](./#glossary/re-peg) opportunities and accepted [reports](./#glossary/report). Trading and YB activity can respond to their different states. Growth covers 556 days. 

“Attached” follows the [price-gap stall rule](./#settings). All 32 current-rule controls stall. Among proposal pairs, 31 avoid a stall. 

One control holder ends with shares worth no more than its debt. The pool’s LP/xyk remains defined and included.

The [settings table](./#settings) defines the current-rule and proposal bundles. Each result states its donation rate.

[Settings and conventions](./#settings) defines the return rates and the price-gap stall rule used for the maintained-pool groups. The simulated actors are arbitrageurs and the debt-financed YB holder. Customer demand requires a separate [response model](./#simulation/limits).

[← previous](./#detachment/trader-cost)[next $\to$](./#bets/mechanism)

**Chart data $\cdot$ Every paired outcome after the funding account**

LP/xyk difference, log pp/yr
| Panel / curve | Coordinate $\cdot$ Rebuilt history index | LP/xyk difference, log pp/yr | 
| --- | --- | --- |
| Current rule $\cdot$ deployed gate / Actual pool stalls | 0 | −0.92 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 1 | +0.66 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 2 | −0.02 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 3 | +31.24 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 4 | −4.13 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 5 | −1.89 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 6 | +20.22 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 7 | −3.62 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 8 | −2.20 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 9 | −3.57 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 10 | +1.56 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 11 | −4.04 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 12 | −1.53 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 13 | −3.89 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 14 | −4.10 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 15 | +11.46 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 16 | −2.88 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 17 | −2.81 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 18 | −3.90 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 19 | −3.31 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 20 | −4.61 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 21 | +16.15 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 22 | +12.61 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 23 | −3.00 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 24 | −4.20 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 25 | +16.23 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 26 | +2.29 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 27 | +16.08 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 28 | −5.57 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 29 | −5.29 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 30 | −4.65 | 
| Current rule $\cdot$ deployed gate / Actual pool stalls | 31 | −3.70 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 0 | −10.65 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 1 | +1.20 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 2 | −6.90 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 3 | +1.46 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 4 | −2.90 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 5 | −5.51 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 6 | +0.45 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 7 | −0.64 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 8 | −7.22 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 9 | +0.61 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 10 | +1.36 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 11 | −2.11 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 12 | −5.32 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 13 | +0.35 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 14 | +0.92 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 15 | +0.93 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 16 | −2.89 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 17 | −0.47 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 18 | −3.02 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 19 | −2.83 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 20 | −2.73 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 22 | +2.12 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 23 | −2.45 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 24 | −2.67 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 25 | +1.81 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 26 | +1.05 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 27 | −11.81 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 28 | −1.21 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 29 | −0.88 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 30 | −2.28 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Both pools stay attached | 31 | −3.57 | 
| Proposed policy $\cdot$ resettable floor $\cdot$ halved EMAs / Actual pool stalls | 21 | +1.20 | 
| Reference line | — | 0 |


# H. Choosing parameters means choosing bets {#bets}

A parameter choice decides how the pool behaves after a large price move. Each choice is a bet on what prices do next. This chapter names each bet, shows what our tests found, and describes what a convincing selection would show.

- [H1 A re-peg setting is a bet on whether a move lasts](./#bets/mechanism) — Every [re-peg](./#glossary/re-peg) setting is a bet on whether a price move lasts.
- [H2 What each setting bets on](./#bets/settings) — Each setting tilts the pool toward one of the two bets.
- [H3 Returns on the team’s tested grid](./#bets/direction) — On the team’s tested grid, higher past holder returns mostly came from one market term.
- [H4 The gate on histories with no built-in direction](./#bets/drift-free) — The drift-free tests show no clear average dollar advantage from resetting the floor.
- [H5 Switching the gate during a stall](./#bets/switch) — Switching floors during a [stall](./#glossary/stall) is a bet on the next move, not a free repair.
- [H6 When the resettable floor runs out of budget](./#bets/rearm) — In these tests, the [resettable floor](./#glossary/resettable-floor) ran short of budget mainly in pools that just started.
- [H7 Who carries each bet](./#bets/who) — [LPs](./#glossary/lp) and the YB holder carry the bet. Traders pay during stalls.
- [H8 What a convincing selection shows](./#bets/selection) — A convincing parameter choice names its promise and tests both price directions.
- [H9 Profiles of the tested settings](./#bets/profiles) — Each tested setting has a profile: its bet, its premium and its service.


# H1 A re-peg setting is a bet on whether a move lasts {#bets/mechanism}

**Every [re-peg](./#glossary/re-peg) setting is a bet on whether a price move lasts.**

The pool trades against each price move. When [ETH](./#glossary/eth) rises, [arbitrage](./#glossary/arbitrage) traders buy ETH from the pool. So the pool holds less ETH just as ETH becomes worth more. Far from its centre price, the pool holds too little of the asset that rose.

**Measure:** The payoff of re-pegging or [stalling](./#glossary/stall), shown schematically.

**Compared:** Moving the centre price with keeping the old centre price.

**Same for both:** The price rise before the choices separate.

**Higher means:** The named choice tends to finish ahead after the next move.

- **Re-peg.** The pool moves its centre price toward the market, step by step. Its later quotes then follow the new price. The move itself sells no coins. This tends to pay if the price keeps going.

  > **Common misunderstanding:** “A re-peg sells the pool's coins at the market price.”
  >
  > **What is true.**
  >
  > Changing the centre price does not itself transfer coins. It changes the pool’s future quotes and its accounting value. Donated shares can also be burned during the same update.

- **Stall.** The pool keeps its old centre price. It keeps trading around that old price. This tends to pay if the price comes back.

Every setting in this chapter changes how often, how fast or at what cost the pool re-pegs. So every setting chooses between these two bets.

After a price rise, the pool holds less ETH. A lasting move favours re-pegging. A return favours stalling.

Each branch shows which choice a price pattern tends to favour.

**More detail: the portfolio choice**

Portfolio theory studies a similar choice. Rebalancing to fixed weights gains when prices reverse. Portfolio insurance gains when moves continue, by selling as prices fall (Perold and Sharpe). A re-peg has a similar payoff without selling: it only moves the centre price.

> **Common misunderstanding:** “Some re-peg rule wins whatever prices do next.”
>
> **What is true.**
>
> Resetting can help when a move continues. Keeping the old centre can help when prices return. The full sequence of prices decides which finishes ahead.

Our [drift-free tests](./#bets/drift-free) found no clear average dollar advantage for either floor.

[← previous](./#detachment/funded)[next $\to$](./#bets/settings)


# H2 What each setting bets on {#bets/settings}

**Each setting tilts the pool toward one of the two bets.**

**Measure:** The market conditions under which each setting pays.

**Compared:** Settings that favour [re-pegging](./#glossary/re-peg) with settings that favour [stalling](./#glossary/stall).

**Same for both:** The choice after a market price move.

**Higher means:** The named setting benefits more from the stated market condition.

| Setting | What it does | It pays when | It loses when | 
| --- | --- | --- | --- |
| Profit floor (deployed gate) | Refuses a re-peg unless recorded profit can pay for it | The price comes back | The move lasts. The stall then tends to persist. | 
| [Resettable floor](./#glossary/resettable-floor) | Can allow moves the deployed floor refuses. Lowers the protected floor after spending. | The move lasts | The price snaps back after a re-peg | 
| Higher [reserved profit fraction](./#glossary/reserved-profit-fraction) | Locks part of each profit gain away from re-pegs | The price comes back | The move lasts | 
| Higher [donation](./#glossary/donation) rate | Buys re-peg budget; the YB holder pays interest for it | Repairs are needed | Few repairs are needed, or the repaired move reverses | 
| Faster tracking | Moves the centre price sooner | The new price lasts | The price snaps back, or a [report](./#glossary/report) is wrong | 
| Higher capture fee | Charges customers more when quotes are far from the market | Customers keep trading at wide quotes | Customers leave | 

Both floors refuse a move once the budget is spent.

On the four live pools, [arbitrage fees](./#glossary/arbitrage-fees) repaid 95.8% to 97.9% of what [arbitrage](./#glossary/arbitrage) took. See [how fees repay the trading loss](./#harvesting/fees).

The YB pools charge no admin fee, so the reserved fraction pays nobody outside the pool. A higher fraction protects more of each new profit and leaves less budget for re-pegs.

> **Common misunderstanding:** “The reserved profit fraction is income for the [DAO](./#glossary/dao).”
>
> **What is true.**
>
> The YB pools charge no admin fee, so the reserved fraction pays nobody outside the pool. A higher fraction protects more of each new profit and leaves less budget for re-pegs.

Under the deployed gate, tracking speed matters little. A supplied re-peg would almost always fail the budget test during serious [detachment](./#glossary/detachment). The [repair tests](./#detachment/repairs) measure that refusal. The resettable floor [can still run out of budget](./#bets/rearm).

[← previous](./#bets/mechanism)[next $\to$](./#bets/direction)


# H3 Returns on the team’s tested grid {#bets/direction}

**On the team’s tested grid, higher past holder returns mostly came from one market term.**

> **Common misunderstanding:** “The setting that earned most on past prices is the best setting.”
>
> **What is true.**
>
> On the team’s tested grid, the holder’s growth moved almost exactly with one market term. It is the change in the [ETH](./#glossary/eth) value of the holder’s leftover [crvUSD](./#glossary/crvusd), after debt.

**Measure:** Correlation between the holder’s ETH growth and that market term. 

**Compared:** The holder’s ETH growth with the market term, across 25,601 settings of the team’s grid.

**Same for both:** The original 556-day ETH history.

**Higher means:** The holder’s growth follows the market’s direction more closely.

Almost exact agreement: the correlation is 0.983. Most of the differences between these settings come from this term. Choosing by holder growth picks the loosest tracking the grid’s worst-week gap limit allows. This ranking alone does not show better trading.

Two more signs point the same way:

- The same September Bitcoin prices gave opposite answers on two pools. Removing the floor raises yearly growth in each [LP](./#glossary/lp) share’s [market value](./#glossary/market-value) by +10.70 pp/yr on [WBTC](./#glossary/wbtc). On [cbBTC](./#glossary/cbbtc), the change is −4.37 pp/yr. See the [September gate tests](./#repeg/removal).
- Both families of rebuilt histories rise on average. Plain histories rise +24.68 log pp/yr; [volatility](./#glossary/volatility)-scaled histories rise +42.46 log pp/yr. So averages over them include a rising market.

  > **Common misunderstanding:** “Rebuilt price histories have no built-in direction.”
  >
  > **What is true.**
  >
  > Rebuilt histories reuse the original moves, and the original history rose. On average, plain rebuilt histories rise by +24.68 log pp/yr. Volatility-scaled ones rise by +42.46 log pp/yr.

Each family contains 256 rebuilt histories. The [rate conventions](./#settings) explain [log growth](./#glossary/log-growth).

[← previous](./#bets/settings)[next $\to$](./#bets/drift-free)


# H4 The gate on histories with no built-in direction {#bets/drift-free}

**The drift-free tests show no clear average dollar advantage from resetting the floor.**

Both families of rebuilt histories rise on average, as [the previous page](./#bets/direction) shows. So we rebuilt each history once more. We keep the timing and pattern of each hour’s moves. A fair coin chooses each hour’s direction. A small correction keeps the average of the possible next prices equal to today's price at each hour boundary.

**Measure:** Growth in the dollar value of one [LP](./#glossary/lp) share, % per year.

**Compared:** The [resettable floor](./#glossary/resettable-floor) with the deployed floor.

**Same for both:** 256 [drift-free histories](./#glossary/drift-free-history), with the same settings otherwise.

**Higher means:** The resettable floor did better.

Small differences: −0.32% to 0.49% per year, across both fee rules and both history families. Every 95% interval for these dollar differences includes zero. On rising histories, the same comparison ranged from −2.13% to 16.37% per year.

Each point averages within-history differences between the two floors. Bars show 95% intervals for that average.

Purple diamonds use rising histories. Blue circles use fair hourly directions. The vertical line marks zero difference.

[M](./#glossary/m) compares share value with a fee-free constant-product reference. In M, the four point estimates run from 0.25 to 1.20 log [percentage points](./#glossary/percentage-point) per year. Three of the four 95% intervals include zero. Only the [volatility](./#glossary/volatility)-scaled proposal pair stays positive throughout its interval, from 0.10 to 2.45. On these four comparisons the resettable floor was behind on 163 to 191 of 256 histories. The average mixes the coins the pool holds, harvesting, trading losses and [financing](./#glossary/financing).

**[Detachment](./#glossary/detachment) became more common without the rise, not less.** The proposal with the deployed floor had a first serious [episode](./#glossary/episode) in 97.66% of 256 drift-free histories. These episodes occurred during their first year. On their 256 rising parents, the share was 55.08%. The [profiles page](./#bets/profiles) gives 53.00% for the first 100 rising parents of this same setting. This is a smaller sample, with the same financing bundle.

The rising histories had hidden most of the falls.

> **Common misunderstanding:** “The pool detaches because prices rose.”
>
> **What is true.**
>
> The deployed floor [stalls](./#glossary/stall) after large falls as well as large rises. For the proposal with that floor, a first serious episode was more common without the rise. It occurred in 97.66% of 256 drift-free histories, against 55.08% of their rising parents. Under the current rule, the share stayed near 100%.

Both low-detachment settings meet the “[almost never](./#glossary/almost-never)” standard on plain drift-free histories. Neither meets it on volatility-scaled ones. On plain drift-free histories, both lower the holder’s dollar growth against the current-rule control. The difference is about −2.11% of starting dollar equity per year.

The proposal settings donate 1.20% and 1.60% per year. The current-rule control donates 5%. Their [ETH](./#glossary/eth) arithmetic means are positive, but both intervals include zero. Only 26 and 27 of 256 paths have positive ETH differences.

| Low-detachment setting | Dollar holder-growth difference, % starting dollar equity/year | 95% interval | ETH arithmetic difference, % starting ETH equity/year | 95% interval | Paired histories | 
| --- | --- | --- | --- | --- | --- |
| Halved [EMA](./#glossary/ema) half-lives | −2.11 | −3.58 to −0.41 | +6.65 | −2.01 to 21.26 | 256 | 
| Original EMA half-lives | −2.11 | −3.57 to −0.38 | +6.60 | −2.07 to 21.14 | 256 | 

The chart compares gates that share a [donation](./#glossary/donation) rate. The holder rows above do not.

**More detail: construction and measurement**

We keep the timing and pattern of each hour’s moves. A fair coin chooses each hour’s direction. A small correction keeps the average of the possible next prices equal to today's price at each hour boundary.

Within an hour, the price sequence can reveal that hour’s direction.

Hourly volatility stays close to the source history. Monthly ratios range from 0.9993 to 1.0017. Dollar figures divide each change by initial value and elapsed years.

In 6 of 256 plain drift-free histories, the control holder ends with negative wealth. Full-sample holder [log growth](./#glossary/log-growth) is undefined. An additional comparison excludes those terminal cases. Dollar figures keep every history.

In the first year, the centre is above market at onset in 128 drift-free histories, against 19 rising ones. Below-market counts are 122 and 122.

The tests use [arbitrage](./#glossary/arbitrage)-only trading with hourly update opportunities. The [settings table](./#settings) defines the bundles.

[← previous](./#bets/direction)[next $\to$](./#bets/switch)

**Chart data $\cdot$ Gate payoff: rising versus drift-free histories**

Resettable floor minus deployed floor, % of initial LP-share value per year
| Gate comparison | History construction | Mean Resettable floor minus deployed floor, % of initial LP-share value per year | 95% interval | Paired histories | 
| --- | --- | --- | --- | --- |
| Current fee rule $\cdot$ plain | Fair hourly directions | +0.26 | −0.88 to 1.58 | 256 | 
| Current fee rule $\cdot$ plain | Rising histories | +13.16 | 10.55 to 16.19 | 256 | 
| Proposal $\cdot$ plain | Fair hourly directions | −0.21 | −1.21 to 0.93 | 256 | 
| Proposal $\cdot$ plain | Rising histories | −2.13 | −3.65 to −0.40 | 256 | 
| Current fee rule $\cdot$ scaled | Fair hourly directions | −0.32 | −1.68 to 1.25 | 256 | 
| Current fee rule $\cdot$ scaled | Rising histories | +13.53 | 10.24 to 17.06 | 256 | 
| Proposal $\cdot$ scaled | Fair hourly directions | +0.49 | −0.74 to 2.10 | 256 | 
| Proposal $\cdot$ scaled | Rising histories | +16.37 | 12.90 to 19.91 | 256 |


# H5 Switching the gate during a stall {#bets/switch}

**Switching floors during a [stall](./#glossary/stall) is a bet on the next move, not a free repair.**

We copied each simulated pool when a serious [detachment](./#glossary/detachment) became known. One copy kept the deployed floor. The other switched to the [resettable floor](./#glossary/resettable-floor). Both copies then faced the same prices.

[M](./#glossary/m) compares share value with a fee-free constant-product reference.

**Measure:** Change in M over the next 30 days, log [percentage points](./#glossary/percentage-point).

**Compared:** Switching to the resettable floor with keeping the deployed floor.

**Same for both:** The pool’s state at the switch and every later price.

**Higher means:** Switching did better.

A continuing rise generally favours switching when the centre starts below the market. A continuing fall generally favours switching when it starts above. The order of moves also matters.

The chart shows 51 stalls with the centre below market and 49 above. Each dot uses the same 30 days for the price move and M difference.

Dashed lines fit these same outcomes separately by side. The horizontal line marks zero payoff. The other history families remain in the data table.

The link is positive on one side of the market and negative on the other. Its strength ranges from 0.27 to 0.76 across 6 history families.

Average dollar results were close to zero: +0.11% and +0.15% per year. These compare the switch with keeping the floor, from the switch to each history’s endpoint. Both intervals include zero.

Switching ends the serious [episode](./#glossary/episode) within 7 days in 72.00% to 88.00% of eligible stalls. At that same day, the deployed floor is still inside the episode on 50.00% to 89.00% of those stalls.

Average test-order quotes are 7.97 to 16.49 [basis points](./#glossary/basis-point) cheaper across these families. Each test order is worth 0.50% of the pool’s value at that time.

**More detail: timing and the earlier comparison**

On plain histories, the same-state switch over 30 days was about −0.31 log percentage points (58 histories). Starting both floors at the beginning raised the resettable floor’s result by 0.34 log percentage points. The two pools had already drifted apart before the stall.

The annual figures use each [LP](./#glossary/lp) share’s dollar value at the switch. Each history’s difference is divided by its own remaining years.

| Fair-direction history family | Annual mean difference, % switch LP-share dollar value/year | 95% interval | Paired histories | 
| --- | --- | --- | --- |
| Plain | +0.11 | −1.72 to 2.16 | 100 | 
| [Volatility](./#glossary/volatility)-scaled | +0.15 | −1.53 to 2.14 | 100 | 

These proposal-rule pairs use the same [financing](./#glossary/financing) as the [paired gate tests](./#bets/drift-free). Trades come from [arbitrage](./#glossary/arbitrage) and the simulated YB holder.

[← previous](./#bets/drift-free)[next $\to$](./#bets/rearm)

**Chart data $\cdot$ Switch payoff: the next price move $\cdot$ 30 days**

switch minus kept-floor M, log percentage points
| Panel / curve | Coordinate $\cdot$ ETH price move, log percentage points | switch minus kept-floor M, log percentage points | 
| --- | --- | --- |
| Plain histories with fair hourly signs / Centre below market | −4.585404 | 0.035311 | 
| Plain histories with fair hourly signs / Centre below market | 13.980335 | 1.573958 | 
| Plain histories with fair hourly signs / Centre below market | −3.182842 | −0.803713 | 
| Plain histories with fair hourly signs / Centre below market | 3.328740 | −1.698674 | 
| Plain histories with fair hourly signs / Centre below market | 17.945753 | 1.885516 | 
| Plain histories with fair hourly signs / Centre below market | −10.404096 | −0.774798 | 
| Plain histories with fair hourly signs / Centre below market | −2.745351 | −1.032092 | 
| Plain histories with fair hourly signs / Centre below market | −3.317043 | −1.409402 | 
| Plain histories with fair hourly signs / Centre below market | 5.100106 | 0.366251 | 
| Plain histories with fair hourly signs / Centre below market | 27.001265 | 4.975926 | 
| Plain histories with fair hourly signs / Centre below market | 14.975477 | 2.186075 | 
| Plain histories with fair hourly signs / Centre below market | 4.704547 | −0.010642 | 
| Plain histories with fair hourly signs / Centre below market | −5.772023 | −1.129005 | 
| Plain histories with fair hourly signs / Centre below market | 14.921973 | 2.188300 | 
| Plain histories with fair hourly signs / Centre below market | −13.391193 | −0.423670 | 
| Plain histories with fair hourly signs / Centre below market | 21.074371 | −0.730862 | 
| Plain histories with fair hourly signs / Centre below market | 6.986357 | 0.582323 | 
| Plain histories with fair hourly signs / Centre below market | −20.793936 | −1.655467 | 
| Plain histories with fair hourly signs / Centre below market | −1.052838 | −0.712243 | 
| Plain histories with fair hourly signs / Centre below market | −3.765798 | −0.145836 | 
| Plain histories with fair hourly signs / Centre below market | 16.944611 | 0.214240 | 
| Plain histories with fair hourly signs / Centre below market | −26.634951 | −2.442038 | 
| Plain histories with fair hourly signs / Centre below market | 20.849032 | 3.671770 | 
| Plain histories with fair hourly signs / Centre below market | 17.072940 | 3.138547 | 
| Plain histories with fair hourly signs / Centre below market | −6.125789 | −1.028521 | 
| Plain histories with fair hourly signs / Centre below market | 19.813914 | 2.776702 | 
| Plain histories with fair hourly signs / Centre below market | 0.718564 | −1.243736 | 
| Plain histories with fair hourly signs / Centre below market | 10.662869 | 1.499185 | 
| Plain histories with fair hourly signs / Centre below market | −12.581963 | −0.949110 | 
| Plain histories with fair hourly signs / Centre below market | −12.181315 | −0.965249 | 
| Plain histories with fair hourly signs / Centre below market | −16.157841 | −1.233170 | 
| Plain histories with fair hourly signs / Centre below market | 3.877785 | 0.017748 | 
| Plain histories with fair hourly signs / Centre below market | −3.627947 | −0.919319 | 
| Plain histories with fair hourly signs / Centre below market | −38.137921 | −1.003820 | 
| Plain histories with fair hourly signs / Centre below market | 26.242394 | 4.113614 | 
| Plain histories with fair hourly signs / Centre below market | −7.750262 | 0.428678 | 
| Plain histories with fair hourly signs / Centre below market | 15.372761 | 0.077482 | 
| Plain histories with fair hourly signs / Centre below market | 5.474252 | −2.029407 | 
| Plain histories with fair hourly signs / Centre below market | −1.367975 | −0.540517 | 
| Plain histories with fair hourly signs / Centre below market | 15.587457 | 2.273663 | 
| Plain histories with fair hourly signs / Centre below market | 3.840177 | −0.672494 | 
| Plain histories with fair hourly signs / Centre below market | 12.866959 | 0.847662 | 
| Plain histories with fair hourly signs / Centre below market | 7.390642 | −0.862872 | 
| Plain histories with fair hourly signs / Centre below market | 10.766542 | 1.086148 | 
| Plain histories with fair hourly signs / Centre below market | 21.721642 | 3.306675 | 
| Plain histories with fair hourly signs / Centre below market | −6.182090 | −0.937128 | 
| Plain histories with fair hourly signs / Centre below market | −26.495038 | −0.617071 | 
| Plain histories with fair hourly signs / Centre below market | −18.288491 | −1.481269 | 
| Plain histories with fair hourly signs / Centre below market | −14.228523 | −1.143054 | 
| Plain histories with fair hourly signs / Centre below market | −11.949484 | −0.735614 | 
| Plain histories with fair hourly signs / Centre below market | 7.142524 | 0.498654 | 
| Plain histories with fair hourly signs / Centre below market $\cdot$ fitted line | −38.137921 | −3.30763112 | 
| Plain histories with fair hourly signs / Centre below market $\cdot$ fitted line | 27.001265 | 2.40150945 | 
| Plain histories with fair hourly signs / Centre above market | −1.784628 | −1.412061 | 
| Plain histories with fair hourly signs / Centre above market | −25.096659 | 4.852255 | 
| Plain histories with fair hourly signs / Centre above market | −7.993314 | 0.399197 | 
| Plain histories with fair hourly signs / Centre above market | −5.469299 | 0.615564 | 
| Plain histories with fair hourly signs / Centre above market | −5.915495 | 0.493193 | 
| Plain histories with fair hourly signs / Centre above market | 6.329479 | −1.140933 | 
| Plain histories with fair hourly signs / Centre above market | 0.560523 | −0.959153 | 
| Plain histories with fair hourly signs / Centre above market | −7.939371 | 0.800363 | 
| Plain histories with fair hourly signs / Centre above market | −15.551538 | 0.850827 | 
| Plain histories with fair hourly signs / Centre above market | 10.977917 | −1.329237 | 
| Plain histories with fair hourly signs / Centre above market | −11.607140 | 0.546191 | 
| Plain histories with fair hourly signs / Centre above market | 0.796973 | −0.584204 | 
| Plain histories with fair hourly signs / Centre above market | −44.169851 | 8.489545 | 
| Plain histories with fair hourly signs / Centre above market | 5.705531 | −2.111964 | 
| Plain histories with fair hourly signs / Centre above market | −6.520506 | 0.442242 | 
| Plain histories with fair hourly signs / Centre above market | −2.705962 | −1.417629 | 
| Plain histories with fair hourly signs / Centre above market | 31.248575 | −0.940673 | 
| Plain histories with fair hourly signs / Centre above market | 14.662556 | −0.882738 | 
| Plain histories with fair hourly signs / Centre above market | 14.826861 | −2.424299 | 
| Plain histories with fair hourly signs / Centre above market | 46.795464 | 1.617220 | 
| Plain histories with fair hourly signs / Centre above market | −0.853069 | −0.925924 | 
| Plain histories with fair hourly signs / Centre above market | 2.038768 | −1.783676 | 
| Plain histories with fair hourly signs / Centre above market | −3.356909 | −0.136502 | 
| Plain histories with fair hourly signs / Centre above market | −6.107192 | −0.599902 | 
| Plain histories with fair hourly signs / Centre above market | 24.181641 | −1.612255 | 
| Plain histories with fair hourly signs / Centre above market | −12.831603 | 1.184613 | 
| Plain histories with fair hourly signs / Centre above market | 0.000384 | −0.420569 | 
| Plain histories with fair hourly signs / Centre above market | 15.392498 | −0.544333 | 
| Plain histories with fair hourly signs / Centre above market | 7.088972 | −1.417865 | 
| Plain histories with fair hourly signs / Centre above market | −2.348706 | −0.330628 | 
| Plain histories with fair hourly signs / Centre above market | −39.028406 | 6.962241 | 
| Plain histories with fair hourly signs / Centre above market | 9.231091 | −0.554733 | 
| Plain histories with fair hourly signs / Centre above market | −6.576908 | 0.035062 | 
| Plain histories with fair hourly signs / Centre above market | −27.255492 | 6.033505 | 
| Plain histories with fair hourly signs / Centre above market | −5.334212 | 0.183653 | 
| Plain histories with fair hourly signs / Centre above market | −5.924566 | 0.194990 | 
| Plain histories with fair hourly signs / Centre above market | −3.263606 | −0.729442 | 
| Plain histories with fair hourly signs / Centre above market | 31.207993 | −1.034684 | 
| Plain histories with fair hourly signs / Centre above market | −6.586382 | 0.442643 | 
| Plain histories with fair hourly signs / Centre above market | 50.794950 | −1.306108 | 
| Plain histories with fair hourly signs / Centre above market | 1.786729 | −0.816172 | 
| Plain histories with fair hourly signs / Centre above market | 18.929033 | −1.127794 | 
| Plain histories with fair hourly signs / Centre above market | 13.495228 | −0.648416 | 
| Plain histories with fair hourly signs / Centre above market | 13.685978 | −1.652610 | 
| Plain histories with fair hourly signs / Centre above market | −5.201909 | −1.431372 | 
| Plain histories with fair hourly signs / Centre above market | 8.956537 | −0.428491 | 
| Plain histories with fair hourly signs / Centre above market | −10.762970 | 1.052523 | 
| Plain histories with fair hourly signs / Centre above market | 3.838298 | −0.543496 | 
| Plain histories with fair hourly signs / Centre above market | −34.116008 | −0.559149 | 
| Plain histories with fair hourly signs / Centre above market $\cdot$ fitted line | −44.169851 | 3.44087451 | 
| Plain histories with fair hourly signs / Centre above market $\cdot$ fitted line | 50.794950 | −3.71494722 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −3.291914 | −0.760912 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 11.117133 | −1.641086 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 23.761980 | 3.867047 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −10.970425 | −0.945161 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 11.387053 | −1.398808 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −25.640392 | −1.452966 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −3.815175 | −1.535519 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 21.118601 | 2.237991 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 48.292407 | 1.072097 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 8.584325 | −1.130555 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −24.689364 | −0.824130 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −8.379984 | −1.030562 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 27.036760 | −2.478960 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 34.664334 | 0.979221 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −9.696077 | −1.377900 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −22.079530 | −1.635164 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 52.688494 | 9.973761 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 29.576081 | −0.094089 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 7.805750 | 1.365123 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 11.071320 | −1.304116 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 17.364397 | 2.797086 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 1.928078 | −1.200369 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −25.495042 | −2.700811 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −27.150312 | −1.912070 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −28.556766 | −1.813482 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −5.818449 | −1.169644 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −14.394955 | −1.657868 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −11.021327 | −0.874626 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 9.462204 | −0.727685 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −27.435504 | −1.215318 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −21.059989 | −1.532942 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −15.252376 | −1.413611 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 21.771038 | 3.883677 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −50.418822 | −0.651233 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −22.264898 | −2.208642 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 6.676235 | −1.733141 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −15.884164 | −1.012120 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 0.169096 | −0.887500 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 16.210653 | −0.446104 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | 0.128160 | −1.143831 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −32.575578 | −0.775245 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −22.751584 | −1.504201 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −16.309271 | −1.260109 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −15.217786 | −1.332932 | 
| Volatility-scaled histories with fair hourly signs / Centre below market | −11.287867 | −1.388383 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −31.423949 | 6.149218 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 13.520007 | −1.599674 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −10.719388 | 1.217374 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −0.988302 | −2.117870 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 5.056245 | −0.998836 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −22.715022 | 3.790396 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 0.899224 | −1.685433 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −13.191699 | 3.498963 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 43.895338 | 2.298190 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −14.173145 | 3.025843 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −17.171425 | 3.151480 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −12.675344 | 1.283613 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 14.773087 | −0.152180 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −6.940155 | −0.812746 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 11.472358 | −1.792415 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 24.659525 | −0.937822 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 2.626596 | 0.180319 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 7.795697 | −1.107270 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 0.817437 | −1.526984 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −7.761589 | 0.066662 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 18.493088 | −1.424309 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −11.821953 | 0.794236 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 18.908271 | −1.458630 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 8.195619 | −1.037592 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 10.876119 | −1.296530 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 6.074333 | −1.036775 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −3.074747 | −1.552649 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −51.276016 | 1.167397 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −18.874046 | −1.588308 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 40.089908 | −0.455088 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 1.957040 | −1.008681 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −46.221318 | 0.637902 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −23.434305 | −0.595274 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −23.674537 | 3.962220 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 4.578749 | −1.894434 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 5.400449 | −1.682689 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −6.087581 | −1.781935 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 15.258181 | −0.940658 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 7.042614 | −1.531679 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −9.583205 | 0.071049 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −13.721794 | −1.386805 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −7.910049 | −1.373126 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 6.701850 | −0.842707 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −33.479033 | 0.483409 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −8.152441 | −0.369507 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 47.548972 | 1.722648 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 3.364258 | −1.680815 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −20.107294 | −0.362270 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 36.350082 | −1.330396 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 7.837506 | −2.217103 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | −16.551818 | 2.019217 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 10.548668 | −1.128251 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 15.586943 | −1.053711 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 17.343202 | −1.908866 | 
| Volatility-scaled histories with fair hourly signs / Centre above market | 1.100087 | 0.827362 | 
| Rising plain histories / Centre below market | 4.782941 | −0.197855 | 
| Rising plain histories / Centre below market | 7.490078 | 0.200699 | 
| Rising plain histories / Centre below market | 7.231384 | 0.153750 | 
| Rising plain histories / Centre below market | 9.865321 | −1.324923 | 
| Rising plain histories / Centre below market | 10.821399 | −0.804630 | 
| Rising plain histories / Centre below market | −0.796970 | −1.550386 | 
| Rising plain histories / Centre below market | 8.186949 | 0.681671 | 
| Rising plain histories / Centre below market | 8.636648 | 0.956076 | 
| Rising plain histories / Centre below market | −1.914843 | −1.041210 | 
| Rising plain histories / Centre below market | 12.460398 | 2.371973 | 
| Rising plain histories / Centre below market | 6.577606 | −1.000974 | 
| Rising plain histories / Centre below market | 9.558581 | 0.974383 | 
| Rising plain histories / Centre below market | 12.965857 | 0.239904 | 
| Rising plain histories / Centre below market | 9.953851 | −1.001155 | 
| Rising plain histories / Centre below market | −1.035085 | −1.422166 | 
| Rising plain histories / Centre below market | 8.906338 | 1.339885 | 
| Rising plain histories / Centre below market | −1.035085 | −1.400387 | 
| Rising plain histories / Centre below market | −0.796970 | −1.046915 | 
| Rising plain histories / Centre below market | 9.432423 | 0.913851 | 
| Rising plain histories / Centre below market | −9.861665 | −1.166941 | 
| Rising plain histories / Centre below market | −1.035085 | −1.417351 | 
| Rising plain histories / Centre below market | 6.577606 | −0.867887 | 
| Rising plain histories / Centre below market | 6.577606 | −0.867887 | 
| Rising plain histories / Centre below market | 10.776275 | −0.803097 | 
| Rising plain histories / Centre below market | 12.957117 | 0.209337 | 
| Rising plain histories / Centre below market | 32.038996 | 3.713940 | 
| Rising plain histories / Centre below market | 7.149381 | −0.797491 | 
| Rising plain histories / Centre below market | 12.965857 | 0.188433 | 
| Rising plain histories / Centre below market | −1.035085 | −1.423065 | 
| Rising plain histories / Centre below market | −2.041879 | −0.995388 | 
| Rising plain histories / Centre below market | 6.577606 | −0.975865 | 
| Rising plain histories / Centre below market | 9.481577 | −1.441594 | 
| Rising plain histories / Centre below market | 8.859326 | 0.603336 | 
| Rising plain histories / Centre below market | 12.817046 | 0.257962 | 
| Rising plain histories / Centre below market | −14.395141 | −1.921603 | 
| Rising plain histories / Centre below market | 11.358125 | 0.173704 | 
| Rising plain histories / Centre below market | 12.965857 | 0.146001 | 
| Rising plain histories / Centre below market | −1.035085 | −1.399259 | 
| Rising plain histories / Centre below market | 9.865321 | −1.322289 | 
| Rising plain histories / Centre below market | −0.796970 | −1.555149 | 
| Rising plain histories / Centre below market | −49.217191 | −1.152239 | 
| Rising plain histories / Centre below market | 8.936429 | 1.321802 | 
| Rising plain histories / Centre below market | −1.035085 | −1.430910 | 
| Rising plain histories / Centre below market | 11.987120 | 0.176365 | 
| Rising plain histories / Centre below market | 9.684983 | −1.263779 | 
| Rising plain histories / Centre below market | −2.901449 | −0.772284 | 
| Rising plain histories / Centre below market | −0.796970 | −1.555149 | 
| Rising plain histories / Centre below market | 0.006863 | −1.534621 | 
| Rising plain histories / Centre below market | 8.966234 | 0.216421 | 
| Rising plain histories / Centre below market | 14.332928 | −1.133729 | 
| Rising plain histories / Centre below market | 8.936429 | 0.111900 | 
| Rising plain histories / Centre below market | 11.358125 | 0.189037 | 
| Rising plain histories / Centre above market | 0.519517 | −0.669451 | 
| Rising plain histories / Centre above market | −31.338683 | 5.965692 | 
| Rising plain histories / Centre above market | −0.803100 | −0.652268 | 
| Rising plain histories / Centre above market | −7.937806 | −1.023010 | 
| Rising plain histories / Centre above market | −31.879031 | 0.585702 | 
| Rising plain histories / Centre above market | 0.834842 | −0.886285 | 
| Mirrored plain histories / Centre below market | 3.750554 | −1.108003 | 
| Mirrored plain histories / Centre below market | 14.563591 | 1.731568 | 
| Mirrored plain histories / Centre below market | 3.782197 | −1.773444 | 
| Mirrored plain histories / Centre below market | 15.481666 | 1.705012 | 
| Mirrored plain histories / Centre below market | 14.563591 | 1.720095 | 
| Mirrored plain histories / Centre below market | 3.455238 | −0.019224 | 
| Mirrored plain histories / Centre below market | 9.681818 | 1.118949 | 
| Mirrored plain histories / Centre below market | −12.898268 | −0.751162 | 
| Mirrored plain histories / Centre below market | 8.309901 | −2.116398 | 
| Mirrored plain histories / Centre below market | 3.750554 | −1.099748 | 
| Mirrored plain histories / Centre below market | 32.202372 | 5.187639 | 
| Mirrored plain histories / Centre below market | 3.782197 | −1.768356 | 
| Mirrored plain histories / Centre below market | 14.563591 | 1.724157 | 
| Mirrored plain histories / Centre below market | 3.782197 | −1.773444 | 
| Mirrored plain histories / Centre below market | 3.782197 | −1.760778 | 
| Mirrored plain histories / Centre below market | 3.782197 | −1.773019 | 
| Mirrored plain histories / Centre below market | 3.782197 | −1.773743 | 
| Mirrored plain histories / Centre below market | 14.702373 | 0.611213 | 
| Mirrored plain histories / Centre below market | 18.955746 | 0.611056 | 
| Mirrored plain histories / Centre below market | 3.782197 | −1.761822 | 
| Mirrored plain histories / Centre below market | 3.782197 | −1.769527 | 
| Mirrored plain histories / Centre below market | 7.921213 | −0.704883 | 
| Mirrored plain histories / Centre below market | 31.338683 | 0.609958 | 
| Mirrored plain histories / Centre below market | 18.955746 | 0.611056 | 
| Mirrored plain histories / Centre below market | 14.563591 | 1.735127 | 
| Mirrored plain histories / Centre below market | −3.843157 | −1.777174 | 
| Mirrored plain histories / Centre above market | −11.042852 | 0.570841 | 
| Mirrored plain histories / Centre above market | −7.198756 | 0.193112 | 
| Mirrored plain histories / Centre above market | −9.131364 | 0.185120 | 
| Mirrored plain histories / Centre above market | −8.877113 | 1.401496 | 
| Mirrored plain histories / Centre above market | −9.681444 | −0.815887 | 
| Mirrored plain histories / Centre above market | −7.851435 | 0.483036 | 
| Mirrored plain histories / Centre above market | −8.025207 | 0.461933 | 
| Mirrored plain histories / Centre above market | −9.773449 | −1.237879 | 
| Mirrored plain histories / Centre above market | −7.851435 | 0.458360 | 
| Mirrored plain histories / Centre above market | −8.038514 | 1.290752 | 
| Mirrored plain histories / Centre above market | −8.025207 | 0.715766 | 
| Mirrored plain histories / Centre above market | −7.851435 | 0.459708 | 
| Mirrored plain histories / Centre above market | −7.935613 | 0.449939 | 
| Mirrored plain histories / Centre above market | −8.025207 | 0.464625 | 
| Mirrored plain histories / Centre above market | −9.773449 | −1.436027 | 
| Mirrored plain histories / Centre above market | −6.136003 | −0.033884 | 
| Mirrored plain histories / Centre above market | −12.910559 | 0.265164 | 
| Mirrored plain histories / Centre above market | −10.025907 | −1.465688 | 
| Mirrored plain histories / Centre above market | −8.025207 | 0.461583 | 
| Mirrored plain histories / Centre above market | −10.025907 | −1.465636 | 
| Mirrored plain histories / Centre above market | −7.851435 | 0.452993 | 
| Mirrored plain histories / Centre above market | −27.487728 | 5.822275 | 
| Mirrored plain histories / Centre above market | −8.025207 | 0.464723 | 
| Mirrored plain histories / Centre above market | −9.284101 | −1.384515 | 
| Mirrored plain histories / Centre above market | −2.433065 | −0.226385 | 
| Mirrored plain histories / Centre above market | −10.026598 | −0.976805 | 
| Mirrored plain histories / Centre above market | −8.877113 | 1.369531 | 
| Mirrored plain histories / Centre above market | −7.851435 | 0.452222 | 
| Mirrored plain histories / Centre above market | −8.938384 | 1.431588 | 
| Mirrored plain histories / Centre above market | −7.678500 | 1.107289 | 
| Mirrored plain histories / Centre above market | −7.678500 | 1.107289 | 
| Mirrored plain histories / Centre above market | −18.831761 | 2.847509 | 
| Mirrored plain histories / Centre above market | −9.881411 | −0.781682 | 
| Mirrored plain histories / Centre above market | −8.025207 | 0.464625 | 
| Mirrored plain histories / Centre above market | −27.473287 | 0.374488 | 
| Mirrored plain histories / Centre above market | −3.020103 | −0.255891 | 
| Mirrored plain histories / Centre above market | −12.910559 | 0.290812 | 
| Mirrored plain histories / Centre above market | −11.987120 | 0.206501 | 
| Mirrored plain histories / Centre above market | −7.678500 | 1.136627 | 
| Mirrored plain histories / Centre above market | −8.025207 | 0.461853 | 
| Mirrored plain histories / Centre above market | −12.910559 | 0.281325 | 
| Mirrored plain histories / Centre above market | −7.851435 | 0.452270 | 
| Mirrored plain histories / Centre above market | −13.095680 | 1.528909 | 
| Mirrored plain histories / Centre above market | −10.025907 | −1.427941 | 
| Mirrored plain histories / Centre above market | −8.025207 | 0.579185 | 
| Mirrored plain histories / Centre above market | −8.025207 | 0.472617 | 
| Mirrored plain histories / Centre above market | −6.487177 | 0.651868 | 
| Mirrored plain histories / Centre above market | −11.550183 | 0.308472 | 
| Mirrored plain histories / Centre above market | −8.025207 | 0.468854 | 
| Mirrored plain histories / Centre above market | −8.025207 | 0.552279 | 
| Mirrored plain histories / Centre above market | −9.750610 | −1.400611 | 
| Mirrored plain histories / Centre above market | −12.817046 | 0.281453 | 
| Mirrored plain histories / Centre above market | −11.987120 | 0.218711 | 
| Mirrored plain histories / Centre above market | −8.025207 | 0.552279 | 
| Mirrored plain histories / Centre above market | −12.910559 | 0.269698 | 
| Mirrored plain histories / Centre above market | −7.851435 | 0.458640 | 
| Mirrored plain histories / Centre above market | −9.284101 | −1.397424 | 
| Mirrored plain histories / Centre above market | −9.750610 | −1.429182 | 
| Mirrored plain histories / Centre above market | −7.851435 | 0.591677 | 
| Mirrored plain histories / Centre above market | −7.851435 | 0.458554 | 
| Mirrored plain histories / Centre above market | −11.987120 | 0.219707 | 
| Mirrored plain histories / Centre above market | 7.727773 | −1.429811 | 
| Mirrored plain histories / Centre above market | −7.851435 | 0.593223 | 
| Mirrored plain histories / Centre above market | −7.851435 | 0.457723 | 
| Mirrored plain histories / Centre above market | −8.877113 | 1.377165 | 
| Mirrored plain histories / Centre above market | −8.580206 | 0.882407 | 
| Mirrored plain histories / Centre above market | −9.284101 | −1.384515 | 
| Mirrored plain histories / Centre above market | −6.524479 | 0.305701 | 
| Mirrored plain histories / Centre above market | −7.851435 | 0.452270 | 
| Mirrored plain histories / Centre above market | −9.773449 | −1.426969 | 
| Mirrored plain histories / Centre above market | −8.938384 | 0.126146 | 
| Mirrored plain histories / Centre above market | −11.987120 | 0.221615 | 
| Mirrored plain histories / Centre above market | −8.877113 | 1.240677 | 
| Rising volatility-scaled histories / Centre below market | 23.962638 | 2.909668 | 
| Rising volatility-scaled histories / Centre below market | 17.495950 | 0.507433 | 
| Rising volatility-scaled histories / Centre below market | −8.189299 | −0.980199 | 
| Rising volatility-scaled histories / Centre below market | 17.089024 | 1.975755 | 
| Rising volatility-scaled histories / Centre below market | 18.689346 | −0.811030 | 
| Rising volatility-scaled histories / Centre below market | 16.755350 | 2.595634 | 
| Rising volatility-scaled histories / Centre below market | 54.638278 | 2.642215 | 
| Rising volatility-scaled histories / Centre below market | 16.313644 | 2.041370 | 
| Rising volatility-scaled histories / Centre below market | 14.040922 | 2.215704 | 
| Rising volatility-scaled histories / Centre below market | 23.879658 | 0.458993 | 
| Rising volatility-scaled histories / Centre below market | −18.683630 | −1.003790 | 
| Rising volatility-scaled histories / Centre below market | 31.087733 | −1.437528 | 
| Rising volatility-scaled histories / Centre below market | 7.128745 | 0.882645 | 
| Rising volatility-scaled histories / Centre below market | 16.706015 | 0.316979 | 
| Rising volatility-scaled histories / Centre below market | −3.040360 | −0.495310 | 
| Rising volatility-scaled histories / Centre below market | −0.206689 | −2.235431 | 
| Rising volatility-scaled histories / Centre below market | 18.239318 | 3.333805 | 
| Rising volatility-scaled histories / Centre below market | 10.764488 | 0.367082 | 
| Rising volatility-scaled histories / Centre below market | −32.853047 | −0.548630 | 
| Rising volatility-scaled histories / Centre below market | −49.478924 | 2.298839 | 
| Rising volatility-scaled histories / Centre below market | 24.115890 | 4.983536 | 
| Rising volatility-scaled histories / Centre below market | 22.997675 | 0.491083 | 
| Rising volatility-scaled histories / Centre below market | 3.418408 | −1.008685 | 
| Rising volatility-scaled histories / Centre below market | 15.495828 | 0.469977 | 
| Rising volatility-scaled histories / Centre below market | 25.255516 | 4.680521 | 
| Rising volatility-scaled histories / Centre below market | 25.255516 | 4.680521 | 
| Rising volatility-scaled histories / Centre below market | 27.184292 | 5.497518 | 
| Rising volatility-scaled histories / Centre below market | 7.257625 | −0.136683 | 
| Rising volatility-scaled histories / Centre below market | 55.534653 | 0.852269 | 
| Rising volatility-scaled histories / Centre below market | 24.978786 | 3.852021 | 
| Rising volatility-scaled histories / Centre below market | 23.521850 | 0.229787 | 
| Rising volatility-scaled histories / Centre below market | 6.095097 | 0.270931 | 
| Rising volatility-scaled histories / Centre below market | 17.726355 | 2.420978 | 
| Rising volatility-scaled histories / Centre below market | −3.400590 | −2.480263 | 
| Rising volatility-scaled histories / Centre below market | 27.664970 | 0.343236 | 
| Rising volatility-scaled histories / Centre below market | −16.622189 | −0.707441 | 
| Rising volatility-scaled histories / Centre below market | 20.214435 | 4.088063 | 
| Rising volatility-scaled histories / Centre below market | 14.032169 | 2.014171 | 
| Rising volatility-scaled histories / Centre below market | 6.353933 | 0.154140 | 
| Rising volatility-scaled histories / Centre below market | 18.706784 | −0.149207 | 
| Rising volatility-scaled histories / Centre below market | 18.847476 | 2.711739 | 
| Rising volatility-scaled histories / Centre below market | 9.078417 | 1.664937 | 
| Rising volatility-scaled histories / Centre below market | 27.400490 | 0.073730 | 
| Rising volatility-scaled histories / Centre below market | 6.239331 | 0.523446 | 
| Rising volatility-scaled histories / Centre below market | 18.847476 | 2.711739 | 
| Rising volatility-scaled histories / Centre below market | 23.319105 | 0.211182 | 
| Rising volatility-scaled histories / Centre below market | 3.620523 | −0.679469 | 
| Rising volatility-scaled histories / Centre below market | 7.438699 | −0.217613 | 
| Rising volatility-scaled histories / Centre below market | 21.508419 | 1.343109 | 
| Rising volatility-scaled histories / Centre below market | 1.498081 | −0.206874 | 
| Rising volatility-scaled histories / Centre below market | −47.583280 | 2.149233 | 
| Rising volatility-scaled histories / Centre below market | −2.185184 | 0.296062 | 
| Rising volatility-scaled histories / Centre below market | −17.059306 | −1.389952 | 
| Rising volatility-scaled histories / Centre below market | 23.293249 | 4.402579 | 
| Rising volatility-scaled histories / Centre below market | −2.224921 | −0.939623 | 
| Rising volatility-scaled histories / Centre below market | −26.064456 | −1.099109 | 
| Rising volatility-scaled histories / Centre below market | 20.291495 | 2.385548 | 
| Rising volatility-scaled histories / Centre below market | 14.149173 | −0.492062 | 
| Rising volatility-scaled histories / Centre below market | −16.622189 | −0.707441 | 
| Rising volatility-scaled histories / Centre below market | 24.195010 | 3.538753 | 
| Rising volatility-scaled histories / Centre below market | 11.530652 | 0.332519 | 
| Rising volatility-scaled histories / Centre below market | 2.507007 | 0.379486 | 
| Rising volatility-scaled histories / Centre above market | −40.718195 | 8.740577 | 
| Rising volatility-scaled histories / Centre above market | −53.268427 | 11.910662 | 
| Rising volatility-scaled histories / Centre above market | −16.424377 | 2.346078 | 
| Rising volatility-scaled histories / Centre above market | −53.117128 | 12.344793 | 
| Rising volatility-scaled histories / Centre above market | 14.103100 | −0.817835 | 
| Rising volatility-scaled histories / Centre above market | −42.753159 | 9.633335 | 
| Rising volatility-scaled histories / Centre above market | −5.521935 | 0.766592 | 
| Rising volatility-scaled histories / Centre above market | 12.796922 | −1.168794 | 
| Rising volatility-scaled histories / Centre above market | 7.954317 | −2.241459 | 
| Rising volatility-scaled histories / Centre above market | 50.817055 | −0.533456 | 
| Rising volatility-scaled histories / Centre above market | 15.750859 | −2.305805 | 
| Rising volatility-scaled histories / Centre above market | 18.395910 | −1.919415 | 
| Rising volatility-scaled histories / Centre above market | 64.459803 | 11.138960 | 
| Rising volatility-scaled histories / Centre above market | −16.876391 | 0.952396 | 
| Rising volatility-scaled histories / Centre above market | 11.025787 | −1.711558 | 
| Rising volatility-scaled histories / Centre above market | 3.338775 | −1.308719 | 
| Rising volatility-scaled histories / Centre above market | 2.321519 | −0.635877 | 
| Rising volatility-scaled histories / Centre above market | 26.307178 | −2.260457 | 
| Rising volatility-scaled histories / Centre above market | −5.521935 | 0.766592 | 
| Rising volatility-scaled histories / Centre above market | −53.117128 | 12.344793 | 
| Rising volatility-scaled histories / Centre above market | 2.560455 | −1.603389 | 
| Rising volatility-scaled histories / Centre above market | −51.304626 | 10.909897 | 
| Rising volatility-scaled histories / Centre above market | 72.235138 | 2.756190 | 
| Rising volatility-scaled histories / Centre above market | 6.697829 | −0.850034 | 
| Rising volatility-scaled histories / Centre above market | 15.549989 | −2.429911 | 
| Rising volatility-scaled histories / Centre above market | −35.783409 | 7.966012 | 
| Rising volatility-scaled histories / Centre above market | −33.973955 | 5.684983 | 
| Rising volatility-scaled histories / Centre above market | −13.372732 | 0.643966 | 
| Rising volatility-scaled histories / Centre above market | −46.473796 | 0.581139 | 
| Rising volatility-scaled histories / Centre above market | 44.808994 | 1.218051 | 
| Rising volatility-scaled histories / Centre above market | −46.879342 | 10.652082 | 
| Rising volatility-scaled histories / Centre above market | −9.235975 | 1.800007 | 
| Rising volatility-scaled histories / Centre above market | −59.510414 | 0.625490 | 
| Rising volatility-scaled histories / Centre above market | −46.473796 | 0.581139 | 
| Rising volatility-scaled histories / Centre above market | 9.089048 | 0.908167 | 
| Rising volatility-scaled histories / Centre above market | 64.459803 | 11.138960 | 
| Rising volatility-scaled histories / Centre above market | −3.356894 | −1.417217 | 
| Rising volatility-scaled histories / Centre above market | 16.120206 | −1.508009 | 
| Mirrored volatility-scaled histories / Centre below market | −27.638429 | −0.810160 | 
| Mirrored volatility-scaled histories / Centre below market | −11.374617 | −1.174061 | 
| Mirrored volatility-scaled histories / Centre below market | −32.225639 | −1.248234 | 
| Mirrored volatility-scaled histories / Centre below market | 48.688398 | 10.427971 | 
| Mirrored volatility-scaled histories / Centre below market | 16.817089 | 2.082121 | 
| Mirrored volatility-scaled histories / Centre below market | 50.143183 | 10.955530 | 
| Mirrored volatility-scaled histories / Centre below market | −9.202243 | −1.356428 | 
| Mirrored volatility-scaled histories / Centre below market | 42.751876 | 9.555639 | 
| Mirrored volatility-scaled histories / Centre below market | −3.181077 | −2.003227 | 
| Mirrored volatility-scaled histories / Centre below market | −12.796922 | −1.216297 | 
| Mirrored volatility-scaled histories / Centre below market | 18.872214 | 2.291824 | 
| Mirrored volatility-scaled histories / Centre below market | −15.995112 | −2.617709 | 
| Mirrored volatility-scaled histories / Centre below market | −15.725512 | −2.429578 | 
| Mirrored volatility-scaled histories / Centre below market | −14.929143 | −2.202237 | 
| Mirrored volatility-scaled histories / Centre below market | −4.467588 | −0.694615 | 
| Mirrored volatility-scaled histories / Centre below market | 34.980370 | −0.636643 | 
| Mirrored volatility-scaled histories / Centre below market | −64.444939 | 10.800735 | 
| Mirrored volatility-scaled histories / Centre below market | 3.876771 | −0.473222 | 
| Mirrored volatility-scaled histories / Centre below market | −3.855381 | −1.538634 | 
| Mirrored volatility-scaled histories / Centre below market | −2.281763 | −0.659673 | 
| Mirrored volatility-scaled histories / Centre below market | 19.633341 | 2.531670 | 
| Mirrored volatility-scaled histories / Centre below market | −3.181077 | −2.003227 | 
| Mirrored volatility-scaled histories / Centre below market | 50.143183 | 10.955530 | 
| Mirrored volatility-scaled histories / Centre below market | 8.074594 | 1.479577 | 
| Mirrored volatility-scaled histories / Centre below market | −2.560455 | −1.381225 | 
| Mirrored volatility-scaled histories / Centre below market | 50.145994 | 10.901724 | 
| Mirrored volatility-scaled histories / Centre below market | −6.954544 | −0.820780 | 
| Mirrored volatility-scaled histories / Centre below market | 35.634079 | 7.776171 | 
| Mirrored volatility-scaled histories / Centre below market | 26.707594 | 5.088775 | 
| Mirrored volatility-scaled histories / Centre below market | 13.201208 | 0.597311 | 
| Mirrored volatility-scaled histories / Centre below market | 31.153676 | 0.348724 | 
| Mirrored volatility-scaled histories / Centre below market | 49.391155 | 0.513132 | 
| Mirrored volatility-scaled histories / Centre below market | −44.808994 | 1.413011 | 
| Mirrored volatility-scaled histories / Centre below market | 11.849685 | −1.252895 | 
| Mirrored volatility-scaled histories / Centre below market | 9.311827 | 1.947909 | 
| Mirrored volatility-scaled histories / Centre below market | 59.672067 | 0.557530 | 
| Mirrored volatility-scaled histories / Centre below market | 49.391155 | 0.513132 | 
| Mirrored volatility-scaled histories / Centre below market | −9.054198 | −1.490073 | 
| Mirrored volatility-scaled histories / Centre below market | −64.444939 | 10.800735 | 
| Mirrored volatility-scaled histories / Centre below market | 3.607371 | −0.030667 | 
| Mirrored volatility-scaled histories / Centre above market | −23.920123 | 3.012236 | 
| Mirrored volatility-scaled histories / Centre above market | −16.836722 | 0.439955 | 
| Mirrored volatility-scaled histories / Centre above market | 8.189299 | −0.918889 | 
| Mirrored volatility-scaled histories / Centre above market | −21.661713 | −1.220515 | 
| Mirrored volatility-scaled histories / Centre above market | −55.923391 | 2.343712 | 
| Mirrored volatility-scaled histories / Centre above market | −16.544374 | 1.850081 | 
| Mirrored volatility-scaled histories / Centre above market | −13.773356 | 1.998344 | 
| Mirrored volatility-scaled histories / Centre above market | −23.879658 | 0.478034 | 
| Mirrored volatility-scaled histories / Centre above market | 18.559339 | −1.077847 | 
| Mirrored volatility-scaled histories / Centre above market | −48.649525 | 10.074577 | 
| Mirrored volatility-scaled histories / Centre above market | −7.003397 | 0.705207 | 
| Mirrored volatility-scaled histories / Centre above market | −15.478000 | 0.465788 | 
| Mirrored volatility-scaled histories / Centre above market | 23.135870 | −2.068530 | 
| Mirrored volatility-scaled histories / Centre above market | 2.567755 | −0.471278 | 
| Mirrored volatility-scaled histories / Centre above market | −2.231198 | −1.087071 | 
| Mirrored volatility-scaled histories / Centre above market | 1.861741 | −1.148834 | 
| Mirrored volatility-scaled histories / Centre above market | 49.478924 | 2.765729 | 
| Mirrored volatility-scaled histories / Centre above market | −11.321754 | 0.964709 | 
| Mirrored volatility-scaled histories / Centre above market | −45.724301 | 8.874165 | 
| Mirrored volatility-scaled histories / Centre above market | −10.725990 | 0.268941 | 
| Mirrored volatility-scaled histories / Centre above market | −14.928168 | 0.407723 | 
| Mirrored volatility-scaled histories / Centre above market | −24.477936 | 4.024665 | 
| Mirrored volatility-scaled histories / Centre above market | −24.477936 | 4.024665 | 
| Mirrored volatility-scaled histories / Centre above market | 16.343246 | −1.148187 | 
| Mirrored volatility-scaled histories / Centre above market | −7.346203 | 0.002378 | 
| Mirrored volatility-scaled histories / Centre above market | −55.545554 | 0.762041 | 
| Mirrored volatility-scaled histories / Centre above market | −5.466475 | 0.760614 | 
| Mirrored volatility-scaled histories / Centre above market | −23.702091 | 0.344580 | 
| Mirrored volatility-scaled histories / Centre above market | −5.136162 | 0.283427 | 
| Mirrored volatility-scaled histories / Centre above market | −17.275689 | 2.168355 | 
| Mirrored volatility-scaled histories / Centre above market | −27.534695 | 0.432243 | 
| Mirrored volatility-scaled histories / Centre above market | 16.630138 | −0.777410 | 
| Mirrored volatility-scaled histories / Centre above market | −19.673378 | 3.745075 | 
| Mirrored volatility-scaled histories / Centre above market | −36.322651 | −0.180564 | 
| Mirrored volatility-scaled histories / Centre above market | −6.450475 | −0.930036 | 
| Mirrored volatility-scaled histories / Centre above market | −6.414265 | 0.180631 | 
| Mirrored volatility-scaled histories / Centre above market | −18.687035 | −0.100202 | 
| Mirrored volatility-scaled histories / Centre above market | −10.057463 | 0.028229 | 
| Mirrored volatility-scaled histories / Centre above market | −18.850607 | 2.235498 | 
| Mirrored volatility-scaled histories / Centre above market | −12.767423 | 1.705069 | 
| Mirrored volatility-scaled histories / Centre above market | −27.439901 | 0.081337 | 
| Mirrored volatility-scaled histories / Centre above market | −6.297101 | 0.572569 | 
| Mirrored volatility-scaled histories / Centre above market | −18.850607 | 2.235498 | 
| Mirrored volatility-scaled histories / Centre above market | −23.142820 | 0.215069 | 
| Mirrored volatility-scaled histories / Centre above market | −7.554765 | 0.140561 | 
| Mirrored volatility-scaled histories / Centre above market | −21.562842 | 1.481653 | 
| Mirrored volatility-scaled histories / Centre above market | −1.341661 | 0.512833 | 
| Mirrored volatility-scaled histories / Centre above market | 47.407156 | 1.980259 | 
| Mirrored volatility-scaled histories / Centre above market | 2.185184 | 0.317506 | 
| Mirrored volatility-scaled histories / Centre above market | 17.420357 | −1.412260 | 
| Mirrored volatility-scaled histories / Centre above market | −23.252983 | 4.454416 | 
| Mirrored volatility-scaled histories / Centre above market | 1.534571 | −1.058668 | 
| Mirrored volatility-scaled histories / Centre above market | 26.202382 | −1.130608 | 
| Mirrored volatility-scaled histories / Centre above market | −8.681492 | 0.065369 | 
| Mirrored volatility-scaled histories / Centre above market | −13.968357 | −0.484105 | 
| Mirrored volatility-scaled histories / Centre above market | 16.630138 | −0.777410 | 
| Mirrored volatility-scaled histories / Centre above market | −25.172277 | −0.662992 | 
| Mirrored volatility-scaled histories / Centre above market | −11.252922 | 0.330564 | 
| Mirrored volatility-scaled histories / Centre above market | −2.448369 | 0.372053 | 
| Mirrored volatility-scaled histories / Centre above market | 29.033116 | −1.146708 | 
| Reference line | — | 0 |


# H6 When the resettable floor runs out of budget {#bets/rearm}

**In these tests, the [resettable floor](./#glossary/resettable-floor) ran short of budget mainly in pools that just started.**

**Measure:** Share of tests with a serious [detachment](./#glossary/detachment) during the 30-day trend.

**Compared:** Keeping the resettable floor with switching to the deployed floor, from the same stuck state.

**Same for both:** The quiet period, the trend’s prices and every other setting.

**Higher means:** More tests lost a quarter of the depth at the market price for a day.

The resettable floor lets the pool spend recorded profit on [re-pegs](./#glossary/re-peg). It refuses a re-peg that would push [virtual price](./#glossary/virtual-price) down to 1. Virtual price is the pool’s accounting value per share. While its budget is spent, it blocks re-pegs like the deployed floor.

> **Common misunderstanding:** “The resettable floor can never run out of budget.”
>
> **What is true.**
>
> It can. It refuses a re-peg that would push virtual price down to 1. In these tests that happened mainly in pools that had just started. Some of those pools stayed detached through long quiet periods.

### With budget left, it handled large trends

In 320 spliced tests, the pool faced the largest 30-day rise and largest 30-day fall in the recorded price history. Each came after 0 to 180 quiet days, sometimes straight after an earlier trend. No serious detachment followed. One trend’s gross repairs used 1.47 [percentage points](./#glossary/percentage-point) of virtual price on average. The worst 30 days used 2.80 percentage points.

### Where it ran short

Refusals happened in 70 of 100 plain histories, but mostly in the first day. Virtual price starts at 1 in the simulator, so a new pool has no budget yet. After the first month, refusals happened in only 4 of 100 plain histories. They happened in 10 of 100 [volatility](./#glossary/volatility)-scaled histories. Of those pools, 13 first refused within 14.63 days of starting. One volatility-scaled pool first ran short on day 46.47.

### Quiet trading did not always restore attachment

From those stuck pools, we added quiet trading, then a large trend. On plain histories, 30 quiet days were enough: no serious detachment followed. On volatility-scaled histories, 36.25% to 37.50% of tests had a serious [episode](./#glossary/episode) during the trend, after 180 quiet days. Nearly all came from 4 of the 10 pools. Those pools were still detached when the trend began. These are mostly episodes carried over from before the trend. The deployed floor did as badly or worse in the same tests.

Each panel starts from pools that refused a repair after their first month: 4 plain and 10 volatility-scaled pools. Each pool contributes 16 tests, with hourly shifts in the trend’s start. Pools receive equal weight.

Solid lines use the largest rise. Dashed lines use its mirrored fall. Both floors start from the same stuck state. A serious episode can already be open when the trend begins.

Only 4 and 10 pools reached this state, so these shares are rough.

**More detail: waiting and spending**

The tests use the proposal, original [EMA](./#glossary/ema) half-lives and 1.20% annual [donations](./#glossary/donation). Each stuck pool was copied before applying the two different floors.

From the first refusal in each history, the next re-peg came after a median of 60 minutes on plain histories. The volatility-scaled median was 25 minutes. These medians use 70 and 76 histories. All reached a next re-peg.

For the pools refusing after their first month, the next re-peg came after a median of 39 hours on plain histories. The volatility-scaled median was 14 hours. These medians use 4 and 10 pools. All reached a next re-peg.

A first re-peg does not mean the pool stays attached through the next trend. The spending sizes above are observations, not a tested spending limit.

[← previous](./#bets/switch)[next $\to$](./#bets/who)

**Chart data $\cdot$ Serious detachment after quiet trading**

% of tests (pools $\times$ hourly start shifts)
| Panel / curve | Coordinate $\cdot$ Quiet trading before the trend, days | % of tests (pools $\times$ hourly start shifts) | Tests per trend (pools $\times$ hourly start shifts) | 
| --- | --- | --- | --- |
| Plain histories / Resettable floor $\cdot$ rise | 0 | 100.00 | 64 | 
| Plain histories / Resettable floor $\cdot$ rise | 7 | 96.88 | 64 | 
| Plain histories / Resettable floor $\cdot$ rise | 30 | 0.00 | 64 | 
| Plain histories / Resettable floor $\cdot$ rise | 90 | 0.00 | 64 | 
| Plain histories / Resettable floor $\cdot$ rise | 180 | 0.00 | 64 | 
| Plain histories / Resettable floor $\cdot$ fall | 0 | 75.00 | 64 | 
| Plain histories / Resettable floor $\cdot$ fall | 7 | 75.00 | 64 | 
| Plain histories / Resettable floor $\cdot$ fall | 30 | 0.00 | 64 | 
| Plain histories / Resettable floor $\cdot$ fall | 90 | 0.00 | 64 | 
| Plain histories / Resettable floor $\cdot$ fall | 180 | 0.00 | 64 | 
| Plain histories / Deployed floor $\cdot$ rise | 0 | 100.00 | 64 | 
| Plain histories / Deployed floor $\cdot$ rise | 7 | 100.00 | 64 | 
| Plain histories / Deployed floor $\cdot$ rise | 30 | 6.25 | 64 | 
| Plain histories / Deployed floor $\cdot$ rise | 90 | 0.00 | 64 | 
| Plain histories / Deployed floor $\cdot$ rise | 180 | 0.00 | 64 | 
| Plain histories / Deployed floor $\cdot$ fall | 0 | 100.00 | 64 | 
| Plain histories / Deployed floor $\cdot$ fall | 7 | 100.00 | 64 | 
| Plain histories / Deployed floor $\cdot$ fall | 30 | 100.00 | 64 | 
| Plain histories / Deployed floor $\cdot$ fall | 90 | 100.00 | 64 | 
| Plain histories / Deployed floor $\cdot$ fall | 180 | 100.00 | 64 | 
| Volatility-scaled histories / Resettable floor $\cdot$ rise | 0 | 81.25 | 160 | 
| Volatility-scaled histories / Resettable floor $\cdot$ rise | 7 | 70.00 | 160 | 
| Volatility-scaled histories / Resettable floor $\cdot$ rise | 30 | 55.00 | 160 | 
| Volatility-scaled histories / Resettable floor $\cdot$ rise | 90 | 46.25 | 160 | 
| Volatility-scaled histories / Resettable floor $\cdot$ rise | 180 | 36.25 | 160 | 
| Volatility-scaled histories / Resettable floor $\cdot$ fall | 0 | 70.00 | 160 | 
| Volatility-scaled histories / Resettable floor $\cdot$ fall | 7 | 70.00 | 160 | 
| Volatility-scaled histories / Resettable floor $\cdot$ fall | 30 | 55.00 | 160 | 
| Volatility-scaled histories / Resettable floor $\cdot$ fall | 90 | 46.88 | 160 | 
| Volatility-scaled histories / Resettable floor $\cdot$ fall | 180 | 37.50 | 160 | 
| Volatility-scaled histories / Deployed floor $\cdot$ rise | 0 | 84.38 | 160 | 
| Volatility-scaled histories / Deployed floor $\cdot$ rise | 7 | 80.00 | 160 | 
| Volatility-scaled histories / Deployed floor $\cdot$ rise | 30 | 62.50 | 160 | 
| Volatility-scaled histories / Deployed floor $\cdot$ rise | 90 | 52.50 | 160 | 
| Volatility-scaled histories / Deployed floor $\cdot$ rise | 180 | 46.88 | 160 | 
| Volatility-scaled histories / Deployed floor $\cdot$ fall | 0 | 98.75 | 160 | 
| Volatility-scaled histories / Deployed floor $\cdot$ fall | 7 | 99.38 | 160 | 
| Volatility-scaled histories / Deployed floor $\cdot$ fall | 30 | 100.00 | 160 | 
| Volatility-scaled histories / Deployed floor $\cdot$ fall | 90 | 99.38 | 160 | 
| Volatility-scaled histories / Deployed floor $\cdot$ fall | 180 | 99.38 | 160 |


# H7 Who carries each bet {#bets/who}

**[LPs](./#glossary/lp) and the YB holder carry the bet. Traders pay during [stalls](./#glossary/stall).**

**Measure:** Who holds the market position, pays interest or receives worse quotes.

**Compared:** The pool’s shareholders, its borrowing holder, traders and the [DAO](./#glossary/dao).

**Same for both:** The pool settings and market move being considered.

**Higher means:** The measured cost or position is larger for the named party.

| Who | What they carry | Measured size | 
| --- | --- | --- |
| LPs | The pool’s position, through the value of each share | The position gains or loses as prices move | 
| YB holder | The same position at about 2 times the size, because the holder borrows | Borrowing increases the size of the bet | 
| YB holder, as payer of [donation](./#glossary/donation) interest | Interest paid for [re-peg](./#glossary/re-peg) budget; most comes back over time | Accounting comparisons are shown below | 
| Traders | Worse quotes while the pool stalls | Large extra quoted cost: 192.15 bp to buy; 210.14 bp to sell | 
| The DAO | No share of pool fees, because the admin fee is zero | Admin fee: 0% | 

The quote test uses an order worth 0.50% of the pool’s value at that time. The current rule keeps the pool’s own fee and controller. Its [financing](./#glossary/financing) is the shared comparison bundle, not the deployed one. That bundle means 42.913386% reserved profit and a 1.50% [LevAMM](./#glossary/levamm) fee.

The low donation rate is 1.20% per year. These are extra quoted costs, not realised customer costs. See the [test-order comparison](./#detachment/trader-cost).

### Returned value against interest

The next table compares two financing bundles under current price rules. It divides the returned value forgone by the interest saved. The figures average these ratios across starting dates.

The 60- and 90-day figures use one [effective market window](./#glossary/effective-market-window).

| Time after the change | Returned value forgone $\div$ interest saved | 
| --- | --- |
| 7 days | 20.03% | 
| 30 days | 68.13% | 
| 60 days | 82.95% | 
| 90 days | 90.16% | 

In a separate full-history test, returned value was about 97.02% of gross interest. This used the faster-tracking setting with the [resettable floor](./#glossary/resettable-floor).

> **Common misunderstanding:** “Donation interest is money the YB holder loses.”
>
> **What is true.**
>
> Gross interest is not the holder’s net loss. In a full-history test, returned value was about 97.02% of the interest paid. That is an accounting ratio, not a repayment schedule.

In the current-rule tests, a supplied re-peg would be refused through 99.87% of serious-[episode](./#glossary/episode) time at 1.20% donations. At 6.00% donations, it would be refused through 99.71% of serious-episode time. These tests use plain histories and the shared financing bundle. See the [budget test](./#detachment/repairs).

[← previous](./#bets/rearm)[next $\to$](./#bets/selection)


# H8 What a convincing selection shows {#bets/selection}

**A convincing parameter choice names its promise and tests both price directions.**

**Measure:** Evidence that a parameter choice meets its stated promise.

**Compared:** A small set of settings, including the current ones.

**Same for both:** Named outcomes, spending limits, [service standards](./#glossary/service-standard) and market tests.

A convincing selection does seven things:

- **It names its promise.** Whose outcome counts, in which currency and over what time. It also names a spending limit and a service standard for traders.
- **It compares a small set of settings,** including the current ones. It changes one setting at a time where it can.
- **It tests every kind of market:** rising, falling, reversing and calm. It uses both families of rebuilt histories and the older history.
- **It holds the service standard on both families.** Our tests used serious [detachment](./#glossary/detachment) in at most 5.00% of years at 95% confidence. They also used at most 0.50% of the time.
- **It shows results across market conditions, including losses.** An average over rising histories can reward a directional position. The evaluation states the rule it uses to compare those outcomes.
- **It allows the answer “no setting qualifies”.** On our tests, that is today’s answer. See the [donation tests](./#detachment/donations).
- **It shows a profile, not one number.** The profile states the bet, its payoff, who pays the premium and the service results. It states what later evidence would count against the claimed benefit.

The post chose settings by average holder growth on one history. See the [concern about choosing settings](./#concerns).

[← previous](./#bets/who)[next $\to$](./#bets/profiles)


# H9 Profiles of the tested settings {#bets/profiles}

**Each tested setting has a profile: its bet, its premium and its service.**

**Measure:** Gross holder interest and first serious-[detachment](./#glossary/detachment) probability.

**Compared:** The deployed settings, the proposal and two resettable-floor settings.

**Same for both:** Full rebuilt histories, with the named bundle and [bootstrap](./#glossary/bootstrap) family.

**Higher means:** More interest paid, or more initially attached paths developing serious detachment.

The table separates the bet, funding and service. Missing measurements stay marked as untested. Quoted trader costs from different settings are not substituted.

| Setting | The bet | Gross interest, % starting holder equity/year | First serious episode within a year: plain | First serious episode within a year: volatility-scaled | On drift-free histories | Trader cost during serious detachment | 
| --- | --- | --- | --- | --- | --- | --- |
| Deployed current settings | Wait for the price to come back | Not priced for this exact [financing](./#glossary/financing) bundle | 81.00% (100 histories) | 100.00% (100 histories) | Not tested for this exact financing bundle. | Not tested for this exact bundle | 
| The post as proposed | Less budget, with the deployed floor | Not priced for this exact bundle | 53.00% (100 histories) | 100.00% (100 histories) | Plain: 97.66%; “[almost never](./#glossary/almost-never)”: no. [Volatility](./#glossary/volatility)-scaled: 99.61%; “almost never”: no. | Not tested for this exact bundle | 
| Post, [resettable floor](./#glossary/resettable-floor), halved [EMA](./#glossary/ema) half-lives; 1.20% [donations](./#glossary/donation) | Follow a move sooner | 2.28% | 2.73% (256 histories) | 6.64% (256 histories) | Plain: 0.39%; “almost never”: yes. Volatility-scaled: 5.86%; “almost never”: no. | Not tested for this exact bundle | 
| Post, resettable floor, original EMA half-lives; 1.60% donations | Follow a move with a reset floor | 3.04% | 2.73% (256 histories) | 8.98% (256 histories) | Plain: 1.17%; “almost never”: yes. Volatility-scaled: 6.25%; “almost never”: no. | Not tested for this exact bundle | 

The new column gives the chance of a first serious [episode](./#glossary/episode) by day 365. It also shows whether both “almost never” tests pass. Each measured drift-free [cell](./#glossary/cell) uses 256 histories with the shared comparison financing bundle.

The common-financing current-rule control uses 5% donations, 42.913386% reserved profit and a 1.50% [LevAMM](./#glossary/levamm) fee. It uses 256 histories. Its first serious-episode probabilities within a year are plain 64.84% and volatility-scaled 98.05%. Neither passes “almost never”.

The rising columns name their samples in each cell. The deployed row uses deployed financing. The proposal and both resettable-floor rows use the shared comparison financing. The proposal’s rising sample is the first 100 parents of its 256-history comparison.

The interest means use 100 paired histories over full 556-day paths. They are [annualised](./#glossary/annualised-return). Most interest returns: about 97.02% for halved EMA half-lives and 97.01% for original half-lives.

The separate common-financing control pays gross interest of 9.72% of starting holder equity per year. Its donation rate is 5% per year. Its [reserved profit fraction](./#glossary/reserved-profit-fraction) is 42.91%, rather than the deployed [WETH](./#glossary/weth) reference’s protected fraction. The [settings page](./#settings) explains that distinction.

The separate low-donation current-rule quote test adds 192.15 bp to buy and 210.14 bp to sell. For the proposal at 2.50% donations, extra quoted costs are 12.80 bp to buy and 16.89 bp to sell. Both use orders worth 0.50% of pool value. The proposal test uses the resettable floor and halved EMA half-lives.

The [quoted trader costs](./#detachment/trader-cost) use other bundles. The [detachment tests](./#detachment/donations) define serious episodes and both service limits.

[← previous](./#bets/selection)[next $\to$](./#concerns)


# Concerns about the evidence {#concerns}

**These concerns separate what the tests measure from what they leave untested.**

## Settings chosen on one history

**Assumed.** The parameter search ranks settings on one market history.

**Found.** On data the search did not use, the chosen settings show no reliable advantage in YB-position growth. YB-position growth is growth in the holder’s wealth after debt. The alternatives share the [donation](./#glossary/donation) rate and the fraction of recorded profit protected from spending. ([evidence](./#proposal/selection)).

**A convincing test would show.** Chosen settings gain against alternatives sharing the donation rate and the protected fraction of recorded profit. The test uses market periods left out of the selection.

**Found.** On the team’s tested grid, holder growth closely followed changes in the [ETH](./#glossary/eth) value of leftover [crvUSD](./#glossary/crvusd), after debt. See the [evidence](./#bets/direction).

## Financing inside the headline score

**Assumed.** [LP/xyk](./#glossary/lp-xyk) compares a share’s growth with a fee-free reference pool. The score subtracts the charge for capital supplied through donated shares.

**Found.** In [WETH](./#glossary/weth) tests that start from recorded pool states, the proposal’s smaller donation charge raises early LP/xyk. WETH is a token representing ETH, Ethereum’s asset. Growth in the [market value](./#glossary/market-value) of each share is lower than under current settings. ([evidence](./#proposal/channels)).

**A convincing test would show.** The test reports growth in the market value of each share beside LP/xyk. The test also [reports](./#glossary/report) the holder’s wealth. Donations and returned value are each counted separately.

## Trading supplied to the simulator

**Assumed.** [Arbitrage](./#glossary/arbitrage)-only runs simulate arbitrage and the YB holder. Arbitrage trades profit from price differences between markets. Those runs omit other user activity. A [ping](./#glossary/ping) supplies a recorded user-operation time without copying that user’s asset transfer.

**Found.** [Replaying](./#glossary/replay) recorded user operations improves on the price-path formula over the same monthly WETH windows. For these [centred](./#glossary/centred-pool) WETH windows, the reference formula uses squared logarithmic price moves. The general formula also accounts for the pool’s opening holdings. Pings add almost nothing on those windows. ([evidence](./#simulation/skill)).

**A convincing test would show.** The proposal’s simulation setup has lower squared prediction error than the formula for identical starting states and periods. Those states and periods were not used to choose the settings.

## Small errors in the inputs

**Assumed.** One supplied set of inputs sets each run’s path. The inputs are token valuations, price reports and operation times. A price report is a message that carries an outside price.

**Found.** On the same [WBTC](./#glossary/wbtc) history, reruns with plausible input errors change the proposal’s [stall](./#glossary/stall) classification. A stall is a large, lasting gap between the pool’s centre price, [price_scale](./#glossary/price_scale), and the market price. WBTC is a Bitcoin token on Ethereum. The classification under current settings stays fixed across those reruns. ([evidence](./#simulation/noise)).

**A convincing test would show.** Return and stall results keep the same interpretation under plausible input errors. Those results keep the same interpretation on unused market periods.

## Customer choices

**Assumed.** The replay copies customer activity that was recorded. The replay does not estimate choices under changed quotes. The customer-response page describes this limit. The same limit is shared across this field of research.

**Found.** The test uses WETH trades at the sizes that were recorded. The proposal gives a worse median execution price than deployed current settings. ([evidence](./#proposal/demand)).

**A convincing test would show.** A model of customer choices reproduces where orders go, their size, their timing and changes in liquidity. The check uses observations left out of the fit.

## The profit floor and financing

**Assumed.** The gate preserves a cumulative floor in the pool’s internal accounts. Cumulative means the protected profit is carried forward. Donations help pay for [re-pegs](./#glossary/re-peg). A re-peg moves the pool’s centre price.

**Found.** Removing that floor shortens the September stalls. On the same Bitcoin path, growth in the market value of each WBTC pool share rises. For [cbBTC](./#glossary/cbbtc), that growth falls. cbBTC is another token representing Bitcoin. ([evidence](./#repeg/removal)).

**A convincing test would show.** The comparison varies [financing](./#glossary/financing) and spending rules together. It measures wealth at market prices and stall duration across trends, reversals and wrong reference prices.

## Price reports sent to the policy

**Assumed.** The tests supply each report’s time and price. A report is a message that carries an outside reference price. Some periods have no recorded report. For those periods the test uses a generated report.

**Found.** The tests change only the price rule. Financing stays fixed. The policy receives no price reports. The uncertainty intervals for the return difference include both gains and losses. ([evidence](./#proposal/channels)).

**A convincing test would show.** The measured gain remains under the report times that were observed. The gain also remains under plausible delivery errors. Generated inputs are checked against real reports.

## Detachment on other histories

**Assumed.** The history used to tune the settings is only one arrangement of market moves.

**Found.** Serious [detachment](./#glossary/detachment) means too little trading depth remains at the market price. Some settings pass its rarity limits on plain rebuilt histories. These settings use a [resettable floor](./#glossary/resettable-floor), which lowers the protected threshold after an allowed move below it. The settings fail when each move is scaled to the [volatility](./#glossary/volatility) of its new date. ([evidence](./#detachment/donations)).

**A convincing test would show.** Depth and growth results stay comparable on unused periods. The results also stay comparable when histories are rebuilt in several ways.

## Two common beliefs about harvesting

**Assumed.** Two common beliefs predict larger gains from harvesting.

**Found.** **Misunderstanding 1.** “The new parameters make the pool harvest more volatility.”

**What is true.** Holding equal value in each asset maximises harvesting. Near that balance, tighter tracking barely changes the gain.

**Misunderstanding 2.** “[Concentrated liquidity](./#glossary/concentrated-liquidity) multiplies the harvesting gain.”

**What is true.** Concentration makes the pool buy and sell larger amounts after price moves. The harvesting premium stays about the same size as in an ordinary pool. ([evidence](./#harvesting/parameters)).

**A convincing test would show.** One comparison uses the same price path and financing. It separates harvesting from gains or losses caused by the asset mix, losses on trades, and fees.

## What the evidence supports

**Measure:** growth in the market value of each pool share, in [percentage points](./#glossary/percentage-point) per year.

**Compared:** the full proposal with deployed current settings.

**Same for both:** observed WETH starting states, market prices and recorded operation times.

**Higher means:** the share’s market value grew faster.

The full proposal’s growth is lower at every reported horizon. The early LP/xyk advantage comes from lower financing. LP/xyk subtracts the charge for donations actually supplied. The tested comparisons show a higher risk of stalls.

[← previous](./#bets/profiles)[next $\to$](./#misunderstandings)


# Common misunderstandings {#misunderstandings}

**Each entry states a common belief, what our tests found and where the evidence is.**

## How pools earn

> **Common misunderstanding:** “[Donations](./#glossary/donation) are earnings of the pool.”
>
> **What is true.**
>
> Donations bring outside capital into the pool. Interest paid by the YB holder funds them. [LP/xyk](./#glossary/lp-xyk) subtracts the donation charge, so donated value never counts as the pool's own earnings.

Read the evidence: [A1 What a pool share is worth](./#earnings/measure/m-donations-earnings).

> **Common misunderstanding:** “A yearly rate tells us next year's return.”
>
> **What is true.**
>
> Yearly rates make periods of different lengths comparable. A rate measured over a few months does not predict the next year. The market's direction changes results from one window to the next.

Read the evidence: [A3 What contributed to the live pools’ returns](./#earnings/live/m-yearly-rate-forecast).

> **Common misunderstanding:** “A 10% fall undoes a 10% rise.”
>
> **What is true.**
>
> Percentage moves compound. After a 10% rise, a 10% fall leaves the price at 99% of its start. Each percentage change applies to the price reached after the move before it.

Read the evidence: [B1 How rebalancing earns a gain](./#harvesting/rebalancing/m-percentage-roundtrip).

> **Common misunderstanding:** “Harvesting [volatility](./#glossary/volatility) guarantees a gain.”
>
> **What is true.**
>
> In this rise-and-fall example, rebalancing loses less than holding the opening coins. It ends at 99.75% of starting wealth. Holding ends at 99.50%. Both lose money.

Read the evidence: [B1 How rebalancing earns a gain](./#harvesting/rebalancing/m-harvesting-guaranteed-gain).

> **Common misunderstanding:** “[Arbitrage](./#glossary/arbitrage) traders drain the pool's [LPs](./#glossary/lp).”
>
> **What is true.**
>
> Arbitrage does take value from the pool. [LVR](./#glossary/lvr) measures that loss before fees. On the live pools, fees repay 95.8% to 97.9% of it.

Read the evidence: [B3 How fees repay the trading loss](./#harvesting/fees/m-arbitrage).

> **Common misunderstanding:** “The new parameters make the pool harvest more volatility.”
>
> **What is true.**
>
> Harvesting is largest when the pool holds equal value in its two assets. The new parameters keep the pool only slightly closer to that balance. Small improvements near equal values barely change harvesting. Changing settings cannot create more market price variation.
>
> The proposal keeps [price_scale](./#glossary/price_scale), the pool’s central price, closer to the market. Across the tested starts and activity setups, the average distance shrinks by 0.48 to 0.68 [percentage points](./#glossary/percentage-point) of price.
>
> Harvesting barely changes over the 7- and 30-day periods. The change is at most 0.0021 percentage points per year in either direction.

Read the evidence: [B5 Two common misunderstandings about harvesting](./#harvesting/parameters/m-harvest-parameters).

> **Common misunderstanding:** “[Concentrated liquidity](./#glossary/concentrated-liquidity) harvests A times more volatility.”
>
> **What is true.**
>
> Here, “A times” is the multiplier claimed in the misunderstanding. Greater concentration makes the pool trade more after a small price move. The pool loses more to arbitrageurs, traders profiting from price differences. These traders also pay more fees, which repay most of that loss.
>
> The harvesting premium at equal asset values stays the same on that price history. The arbitrage cost left unpaid by fees can rise.

Read the evidence: [B5 Two common misunderstandings about harvesting](./#harvesting/parameters/m-concentration).

## The profit floor and detachment

> **Common misunderstanding:** “The profit floor protects the [market value](./#glossary/market-value) of LP shares.”
>
> **What is true.**
>
> The floor protects [virtual price](./#glossary/virtual-price), the pool's internal accounting value per share. The market value of a share can still fall. Once the buffer above the floor is spent, the floor can block [re-pegs](./#glossary/re-peg) and leave the pool [stalled](./#glossary/stall).

Read the evidence: [F1 The profit floor guards the books, then locks the pool](./#repeg/protection/m-profit-floor).

> **Common misunderstanding:** “Pools facing the same prices gain equally from removing the floor.”
>
> **What is true.**
>
> On the same September Bitcoin prices, removing the floor raised growth in [WBTC](./#glossary/wbtc)'s market value per LP share by 10.70 pp/yr. It lowered [cbBTC](./#glossary/cbbtc)'s by 4.37 pp/yr. The pools started in different states, and the starting state decided the sign.

Read the evidence: [F2 Removing the floor in September](./#repeg/removal/m-same-prices-gate-gains).

> **Common misunderstanding:** “A detached pool loses mainly because it stops harvesting volatility.”
>
> **What is true.**
>
> On live WBTC prices, the [missed harvesting](./#glossary/missed-harvesting) totals only 0.038 percentage points over 128 days. The market's direction decides each stall. In 14 of 18 live Bitcoin stalls, the pool ended ahead of holding its opening coins.

Read the evidence: [G3 The directional bet decides the live stall outcome](./#detachment/costs/m-missed-harvesting).

> **Common misunderstanding:** “Faster tracking would fix [detachment](./#glossary/detachment).”
>
> **What is true.**
>
> Under the deployed gate, the budget blocks repairs, not the speed. During serious detachment, the budget would refuse the next step through 99.87% of the time at 1.20% donations. Faster tracking cannot move the centre while the budget refuses.

Read the evidence: [G4 Repairing a detached pool needs capital](./#detachment/repairs/m-tracking-speed).

> **Common misunderstanding:** “A large enough donation can always fund a repair.”
>
> **What is true.**
>
> Donations are capped, and the cap can bind. At 1.20% yearly donations, no permitted donation passes the gate at 24.70% of serious-[episode](./#glossary/episode) peaks. At 6.00% the share is 4.55%.

Read the evidence: [G4 Repairing a detached pool needs capital](./#detachment/repairs/m-donation-cap-repair).

> **Common misunderstanding:** “Keeping the pool attached always makes LPs and holders richer.”
>
> **What is true.**
>
> In these tests, staying attached did not reliably raise wealth. The settings that keep detachment rare grew the holder's position more slowly than the control. The growth differences are −4.03 and −4.30 pp/yr. Forcing attachment, with its funding counted, gave mixed results across histories.

Read the evidence: [G6 Staying attached does not reliably raise wealth](./#detachment/funded/m-attached-wealth).

## The proposal and its tests

> **Common misunderstanding:** “One simulation run gives a definite answer.”
>
> **What is true.**
>
> Small, plausible errors in the inputs can change whether the proposal stalls on the same WBTC history. The classification under current settings stays fixed. One run can therefore mislead.

Read the evidence: [C3 Small input errors can change whether the pool stalls](./#simulation/noise/m-single-run).

> **Common misunderstanding:** “Three Bitcoin pools give three independent tests.”
>
> **What is true.**
>
> The three Bitcoin pools face the same Bitcoin price moves. Counting each pool separately overstates the evidence. The study window holds only about 3 distinct Bitcoin market events.

Read the evidence: [C3 Small input errors can change whether the pool stalls](./#simulation/noise/m-independent-bitcoin-pools).

> **Common misunderstanding:** “The simulator shows how customers would react to the new fees.”
>
> **What is true.**
>
> These simulations copy recorded customer trades, or leave customers out. They do not predict how customers respond to different quotes. Modelling that response remains an open problem across the field.

Read the evidence: [C4 How customers respond remains an open problem](./#simulation/limits/m-customer-responses).

> **Common misunderstanding:** “Higher volume on stall days shows that stalls attract customers.”
>
> **What is true.**
>
> Customer volume did rise on stall days. The market also moved more on those days. This comparison cannot separate the stall from the busier market.

Read the evidence: [C4 How customers respond remains an open problem](./#simulation/limits/m-stalls-attract-volume).

> **Common misunderstanding:** “The range of outcomes across rebuilt histories is the uncertainty of the average.”
>
> **What is true.**
>
> The range shows how much results differ from one rebuilt history to another. It is not a [confidence interval](./#glossary/confidence-interval) for the average result.

Read the evidence: [D1 Why one price history is not enough](./#resampling/why/m-outcome-range-average).

> **Common misunderstanding:** “Testing on rebuilt histories is a fresh, independent test.”
>
> **What is true.**
>
> Rebuilt histories reuse moves from the original history, the same history used to choose the settings. They show how results depend on the order of moves. They do not undo the choice.

Read the evidence: [D1 Why one price history is not enough](./#resampling/why/m-independent-bootstrap).

> **Common misunderstanding:** “Each part of the proposal adds to its gain.”
>
> **What is true.**
>
> On the tuning history, changing [financing](./#glossary/financing) alone lowers LP/xyk. Changing only the external-price rules also lowers it. Only the combination produces the original gain.

Read the evidence: [E1 The proposal’s original test and its separate changes](./#proposal/test/m-proposal-parts).

> **Common misunderstanding:** “The proposal gains because its price rules trade better.”
>
> **What is true.**
>
> The early gain in LP/xyk comes from the financing change. Financing alone raises LP/xyk at 7 and 30 days. The advantage turns negative at 60 and 90 days. The longest horizons use one [effective market window](./#glossary/effective-market-window).
>
> The full proposal lowers growth in the market value of each share at every horizon.

Read the evidence: [E2 The early gain comes from changing financing](./#proposal/channels/m-financing-gain).

> **Common misunderstanding:** “Settings that won on the tuning history will keep winning.”
>
> **What is true.**
>
> On data left out of the selection, the chosen settings show no reliable advantage over settings with the same financing. On older history, their mean advantage is negative.

Read the evidence: [E4 Selected settings on unused and older data](./#proposal/selection/m-winning-settings).

## Choosing parameters (chapter H)

> **Common misunderstanding:** “A re-peg sells the pool's coins at the market price.”
>
> **What is true.**
>
> Changing the centre price does not itself transfer coins. It changes the pool’s future quotes and its accounting value. Donated shares can also be burned during the same update.

Read the evidence: [H1 A re-peg setting is a bet on whether a move lasts](./#bets/mechanism/m-repeg-coin-sale).

> **Common misunderstanding:** “Some re-peg rule wins whatever prices do next.”
>
> **What is true.**
>
> Resetting can help when a move continues. Keeping the old centre can help when prices return. The full sequence of prices decides which finishes ahead.

Read the evidence: [H1 A re-peg setting is a bet on whether a move lasts](./#bets/mechanism/m-rule-always-wins).

> **Common misunderstanding:** “The [reserved profit fraction](./#glossary/reserved-profit-fraction) is income for the [DAO](./#glossary/dao).”
>
> **What is true.**
>
> The YB pools charge no admin fee, so the reserved fraction pays nobody outside the pool. A higher fraction protects more of each new profit and leaves less budget for re-pegs.

Read the evidence: [H2 What each setting bets on](./#bets/settings/m-reserved-profit).

> **Common misunderstanding:** “The setting that earned most on past prices is the best setting.”
>
> **What is true.**
>
> On the team’s tested grid, the holder’s growth moved almost exactly with one market term. It is the change in the [ETH](./#glossary/eth) value of the holder’s leftover [crvUSD](./#glossary/crvusd), after debt.

Read the evidence: [H3 Returns on the team’s tested grid](./#bets/direction/m-best-past-setting).

> **Common misunderstanding:** “Rebuilt price histories have no built-in direction.”
>
> **What is true.**
>
> Rebuilt histories reuse the original moves, and the original history rose. On average, plain rebuilt histories rise by +24.68 log pp/yr. Volatility-scaled ones rise by +42.46 log pp/yr.

Read the evidence: [H3 Returns on the team’s tested grid](./#bets/direction/m-rebuilt-history-drift).

> **Common misunderstanding:** “The pool detaches because prices rose.”
>
> **What is true.**
>
> The deployed floor stalls after large falls as well as large rises. For the proposal with that floor, a first serious episode was more common without the rise. It occurred in 97.66% of 256 [drift-free histories](./#glossary/drift-free-history), against 55.08% of their rising parents. Under the current rule, the share stayed near 100%.

Read the evidence: [H4 The gate on histories with no built-in direction](./#bets/drift-free/m-detachment-rising-prices).

> **Common misunderstanding:** “The [resettable floor](./#glossary/resettable-floor) can never run out of budget.”
>
> **What is true.**
>
> It can. It refuses a re-peg that would push virtual price down to 1. In these tests that happened mainly in pools that had just started. Some of those pools stayed detached through long quiet periods.

Read the evidence: [H6 When the resettable floor runs out of budget](./#bets/rearm/m-resettable-budget).

> **Common misunderstanding:** “Donation interest is money the YB holder loses.”
>
> **What is true.**
>
> Gross interest is not the holder’s net loss. In a full-history test, returned value was about 97.02% of the interest paid. That is an accounting ratio, not a repayment schedule.

Read the evidence: [H7 Who carries each bet](./#bets/who/m-donation-interest).

[← previous](./#concerns)[next $\to$](./#glossary)


# Glossary {#glossary}

**Each entry defines one term used on this site.**

- A highlighted term opens its entry.
- Hovering over the term shows the same words.
- A difference in returns is stated in [percentage points](./#glossary/percentage-point) per year (pp/yr).
- An [LP](./#glossary/lp) return measures the value of one pool share.
- An LP is an owner of pool shares.
- A YB-position return is the holder’s [ETH](./#glossary/eth) or [BTC](./#glossary/btc) wealth left after [crvUSD](./#glossary/crvusd) debt.
- ETH and BTC are the risky assets in these pools.
- crvUSD is the stablecoin owed as debt.

**Ablation** — An [ablation](./#glossary/ablation) compares a group of changes with versions that leave some of those changes out. The comparison shows which changes account for the result.

**Almost never** — “[Almost never](./#glossary/almost-never)” means a tested setting passes both limits. The one-sided [Wilson upper bound](./#glossary/wilson-bound), an upper confidence limit, is at most 5.00% for first serious onset by day 365. The bound uses 95% confidence. Average time below serious depth is at most 0.50% over 556 days.   First-onset counts use paths that start outside the tier. See [episode counting](./#detachment/measure).

**AMM (automated market maker)** — An automated market maker holds assets and quotes a price for each trade. The quotes follow programmed rules.

**Amplification** — [Amplification](./#glossary/amplification) controls how concentrated the pool’s trading is. At the same pool value, a larger setting gives more depth near [price_scale](./#glossary/price_scale), the pool’s centre price. That larger setting can also remove more of that depth when the market moves away.

**Annualised return** — An [annualised return](./#glossary/annualised-return) divides a window’s log change by the window’s length in years. To find log change, first divide end value by start value. Then take the natural logarithm of that ratio. The site’s [rate convention](./#settings) puts windows of different lengths on the same scale.

**Arbitrage** — [Arbitrage](./#glossary/arbitrage) is a trade that earns a profit from a price difference between markets.

**Arbitrage fees** — [Arbitrage fees](./#glossary/arbitrage-fees) are the trading fees that arbitrage traders pay into the pool.

**Baseline** — A [baseline](./#glossary/baseline) is a simple prediction used as a reference. A more detailed model is judged against that prediction.

**Basis point** — A [basis point](./#glossary/basis-point), written bp, is one hundredth of a percentage point.

**Blockchain block** — A [blockchain block](./#glossary/blockchain-block) is a group of transactions recorded together on the blockchain.

**Book value** — [Book value](./#glossary/book-value) is the pool’s internal accounting value per share. Its calculation uses the [invariant](./#glossary/invariant), a value identifying the pool’s reserve curve. The calculation adjusts that value using price_scale, the pool’s central price.

**Bootstrap** — A [bootstrap](./#glossary/bootstrap) rebuilds a sample by drawing from the observed data. Each draw puts the chosen piece back, so that piece can appear again.

**BTC** — BTC denotes Bitcoin, the risky asset in these pools. [Wrapper tokens](./#glossary/wrapper-token) are the on-chain stand-ins for that Bitcoin.

**Burn** — A [burn](./#glossary/burn) removes LP shares from the supply. An LP share is one unit of ownership in the pool. Each remaining share then owns a larger fraction of the pool.

**cbBTC** — [cbBTC](./#glossary/cbbtc) is the Bitcoin token issued by Coinbase on Ethereum.

**Cell** — A [cell](./#glossary/cell) is one combination of settings in the grid the team searched.

**Centred pool** — A [centred pool](./#glossary/centred-pool) holds equal [market value](./#glossary/market-value) in cash and in the risky asset. Market value uses prices from outside the pool.

**Concentrated liquidity** — [Concentrated liquidity](./#glossary/concentrated-liquidity) places more trading capacity near the pool’s reference price. The reference price is the price the pool centres on. A small price move then changes the pool’s holdings by more.

**Concentration factor** — The [concentration factor](./#glossary/concentration-factor) compares trading depth with an equal-value constant-product pool’s depth at the same price. Divide the first depth by the second. A constant-product pool keeps the product of its two asset quantities fixed. A larger factor means a small price move trades more of the reserves.

**Confidence interval** — A [confidence interval](./#glossary/confidence-interval) shows the sampling uncertainty in a stated mean or probability. A wider interval means that quantity is estimated less precisely.

**Constant-product benchmark (xyk)** — The constant-product benchmark is a reference pool that trades without fees. The product of its two asset quantities stays constant. The benchmark starts with equal market value in each asset.

**crvUSD** — crvUSD is the stablecoin these pools use as cash. A stablecoin is a token meant to hold a steady value. The same token is the debt in these pools.

**Curvature-exposure gap** — 

**Measure:** estimated extra loss before fees for the centred pool, in percentage points of pool value.

**Compared:** that centred pool with the actual [off-centre](./#glossary/off-centre) pool.

**Same for both:** the prices, the pool value and the curve shape.

**Higher means:** less trading depth in the actual pool at the market price.

 The model assumes arbitrageurs correct every price move immediately. It ignores trading fees. The estimate does not measure money either pool actually gained or lost. Off-centre means the two assets have unequal market value.

**DAO** — [DAO](./#glossary/dao) stands for decentralised autonomous organisation. That community governs the protocol.

**Depth retained** — 

**Measure:** trading depth at the market price, as a percentage of centred depth.

**Compared:** this pool with an equally funded pool centred on the market.

**Same for both:** the curve shape, with trading fees left out.

**Higher means:** more of the centred pool’s depth remains at the market.

**Detachment** — [Detachment](./#glossary/detachment) means price_scale stays far enough from the market that the pool loses depth there. price_scale is the price the pool centres on. The lost depth is trading depth at the market price.

**Detachment tier** — A [detachment tier](./#glossary/detachment-tier) names how much depth remains against an equal-value centred pool. The names are warning, serious and severe. Lower retained depth means the same small order moves the price more. The [tier table](./#detachment/measure) gives the thresholds.

**Directional bet** — The directional part of return comes from the risky asset’s share of market value. The reference is equal value in the two assets. Holding more than half in that asset helps when its price rises. It hurts when the price falls.   Holding less than half does the opposite.

**Donation** — A [donation](./#glossary/donation) supplies capital from outside the pool. The pool mints designated LP shares for that capital. Those shares can be burned without taking their assets out. The assets then remain for the other shareholders.

**Donation burn** — A [donation burn](./#glossary/donation-burn) removes donated LP shares from supply. Their assets stay in the pool. Each remaining share then owns more of those assets.

**Drift-free history** — From one hour boundary to the next, the average of the possible next prices equals today's price. Random signs and a correction create this. Moves within an hour can still reveal that hour’s direction.

**Effective market window** — [Effective market windows](./#glossary/effective-market-window) estimate how many independent price stretches a test contains. The estimate allows for overlap between the test’s starting dates.

**Episode** — A depth [episode](./#glossary/episode) is a run below a named depth threshold. The run lasts at least 24 uninterrupted hours. The episode is dated from the run’s start. Runs that each qualify are joined when the recovery between them lasts less than 24 hours.

**ETH** — ETH is the native asset of the Ethereum network, that network’s own coin.

**Executable donation** — An [executable donation](./#glossary/executable-donation) is a simulated deposit that makes a named [re-peg](./#glossary/re-peg) affordable after a stated wait. A re-peg moves the pool’s centre price. The deposit follows rules for creating shares, locking them and limiting how many donated shares can exist. The [repair test](./#detachment/repairs) states the target and waiting time.

**Execution cost** — [Execution cost](./#glossary/execution-cost) is how much worse a trade’s price is than the outside market price. The cost includes fees. The unit is basis points of the order’s value. A larger cost means the buyer pays more or the seller receives less.

**Exponential moving average (EMA)** — An exponential moving average smooths prices by giving older prices less weight. The half-life is the time for one observation’s weight to fall by half.

**External mark** — The [external mark](./#glossary/external-mark) is a reference price from outside the pool. The tests use it to value assets and trades.

**Fee band** — The [fee band](./#glossary/fee-band) is the range around the market price where arbitrage does not pay. Inside the band, the price advantage is too small to cover the fee. The band applies on both sides of the market price.

**Financing** — [Financing](./#glossary/financing) is outside capital supplied through donations. The YB holder pays the interest that funds these donations. [LP/xyk](./#glossary/lp-xyk), the share’s growth score against a reference pool, subtracts the charge for that capital. The holder’s own net return also counts value returned through the pool.

**First-onset probability** — [First-onset probability](./#glossary/first-onset-probability) is the share of paths whose first qualifying episode starts by a stated day. Only paths that start outside the tier are counted. A larger share means more of those paths develop an episode.

**Funded attached pool** — A [funded attached pool](./#glossary/funded-attached-pool) is a simulated pool held at the market centre. The pool receives the same prices, chances to update and price [reports](./#glossary/report) as its control. The return includes reserve funding, withdrawals and execution charges. Reserve funding is capital added to keep the pool at the centre.

**Headroom** — [Headroom](./#glossary/headroom) equals [virtual price](./#glossary/virtual-price) divided by the protected profit floor, minus one. Virtual price is the pool’s internal accounting index per share. A larger positive value means a larger accounting buffer for re-pegs. A re-peg moves the pool’s centre price.

**Held-out test** — A [held-out test](./#glossary/held-out-test) scores a choice on data that were left out when the choice was made.

**Impermanent loss** — [Impermanent loss](./#glossary/impermanent-loss) is the shortfall of a fee-free constant-product pool against holding its starting coins. Both sides are valued at the comparison price.

**Input-noise ensemble** — An [input-noise ensemble](./#glossary/input-noise-ensemble) repeats one history many times. Each repeat uses a different small measurement error that could plausibly have occurred. Each run is one of those repeats.

**Invariant** — The invariant is a value that identifies the reserve curve used by the pool’s pricing rule. Before fees, a swap moves the reserves along that curve.

**Inventory** — [Inventory](./#glossary/inventory) is the set of assets the pool holds.

**LevAMM** — [LevAMM](./#glossary/levamm) is the contract that manages the debt-financed [YB position](./#glossary/yb-position). That position holds pool shares and owes debt. LevAMM adjusts the borrowing and the pool shares.

**Liquidity depth** — [Liquidity depth](./#glossary/liquidity-depth) measures how much can trade for a small price change. At a stated price, more depth means the same order moves the price less.

**Liquidity pool** — A [liquidity pool](./#glossary/liquidity-pool) holds assets that traders can buy or sell. The pool’s rules set the prices of those trades.

**Log growth** — First divide the end value by the start value. Take the natural logarithm of that ratio. [Log growth](./#glossary/log-growth) divides this result by the time that passed. Larger log growth means faster growth in proportion to wealth.

**Log return** — First divide the end value by the start value. The natural logarithm of that ratio is the [log return](./#glossary/log-return). Log returns add across periods that follow one another.

**LP** — An LP is a liquidity provider. The provider owns shares in a liquidity pool.

**LP/xyk** — LP/xyk starts from yearly log growth in the market value of one LP share. Subtract the reference pool’s yearly log growth on the same price path.   The reference charges no trading fees. Its trades keep the product of its two asset quantities fixed. It starts with equal market value in both assets.   Then subtract the charge for donations actually supplied during that period, using the same yearly log-growth scale. A positive value means the share beats the reference after that charge. The score uses percentage points per year.

**lp_xcp_profit** — [lp_xcp_profit](./#glossary/lp_xcp_profit) stores the protected accounting value of one share. The re-peg checks compare that value with virtual price. Virtual price is the pool’s internal accounting index per share. A re-peg updates the pool’s centre price.

**LT** — [LT](./#glossary/lt) is the YieldBasis liquidity token. Deposits and withdrawals change the capital the YB position manages.

**LVR** — [LVR](./#glossary/lvr) is the shortfall from trading the pool’s reserves at a stale pool price. A stale price is the pool’s old quote, not the current outside price. The shortfall is measured before fees. Larger LVR means more value was transferred by those trades.

**Market value** — Market value is what the pool’s actual assets are worth. The prices come from outside the pool.

**Market-valued LP measure (M)** — [M](./#glossary/m) compares the market value of one pool share with a fee-free reference pool. The reference pool’s value follows the square root of the risky asset’s price. M divides the share’s market value by that price factor. Growth in M means the share beat the reference pool before the donation charge.

**Missed harvesting** — Harvesting is the rebalancing part of return.   

**Measure:** equal-value harvesting minus harvesting at the mix the pool held, in percentage points of pool value.

**Compared:** equal value in the two assets with the mix the pool actually held.

**Same for both:** the prices.

**Higher means:** the drift from equal value gave up more harvesting.

**Native flow** — [Native flow](./#glossary/native-flow) is trading and liquidity that arrives for a reason other than arbitrage. Arbitrage means earning a profit from a price gap.

**Off-centre** — An off-centre pool holds unequal market value in its two assets. Market value uses prices from outside the pool.

**Oracle** — An [oracle](./#glossary/oracle) supplies reference prices from outside the pool.

**Origin** — An [origin](./#glossary/origin) is the start date and the recorded pool state a simulation starts from.

**Payoff diagram** — A [payoff diagram](./#glossary/payoff-diagram) charts what a choice gains or loses against the price move that follows it.

**Percentage point** — A percentage point is the difference between two percentage rates.

**Ping** — A [ping](./#glossary/ping) lets the simulated pool update at a recorded user-operation time. The ping does not copy that user’s transfer of assets. Simulated arbitrage can still change the balances. Simulated activity in the YB position can still change the balances too.

**Price impact** — [Price impact](./#glossary/price-impact) is the change in the execution price that comes from the size of a trade.

**price_scale** — price_scale is the pool’s internal centre price. The pool concentrates its liquidity near that price.

**Quartile** — [Quartiles](./#glossary/quartile) divide a sorted set of observations into four groups of equal size. The lower and upper quartiles enclose the middle half of the observations.

**QV (quadratic variation)** — Quadratic variation adds the squares of changes in the log price. The changes are taken at the stated sampling frequency. Squaring means a rise and a fall do not cancel.

**Rank correlation** — [Rank correlation](./#glossary/rank-correlation) measures how far two rankings agree. Zero means no overall linear association between their ranks. Positive one means the rankings are in the same order.

**Re-centre** — A pool [re-centres](./#glossary/re-centre) when price_scale moves back near the outside market price. price_scale is the pool’s centre price.

**Re-peg** — A re-peg moves price_scale, the pool’s centre price. The move changes the pool’s internal valuation. The move does not itself transfer coins.

**Recognised gain (recognised return)** — [Recognised return](./#glossary/recognised-gain) is yearly log growth in virtual price, the pool’s internal index. The measure then subtracts the charge for donations actually supplied, using the same yearly log-growth scale. The unit is percentage points per year (pp/yr). A larger value means the internal index grew faster after that charge.

**Repair requirement** — The [repair requirement](./#glossary/repair-requirement) is the smallest top-up that lets the named price-centre move pass the named gate. Both reserve assets increase by the same percentage. The profit floor, LP supply and unlocked shares stay fixed.   The requirement is a percentage of the pool’s current value at market prices. A larger figure means a larger accounting shortfall.

**Replay** — A [replay](./#glossary/replay) runs known inputs through the simulator again. Historical replay copies user operations that were recorded. Simulation replay reruns a history the simulator generated earlier.

**Report** — A report is a message sent to the pool’s policy. The message carries a reference price from outside the pool.

**Report delivery** — [Report delivery](./#glossary/report-delivery) sends reference-price messages to the policy. The policy can then use those outside prices.

**Resampling block** — A [resampling block](./#glossary/resampling-block) is a consecutive stretch of time copied together when a history is rebuilt.

**Reserved profit fraction** — The [reserved profit fraction](./#glossary/reserved-profit-fraction) is the share of cumulative recorded profit that re-pegs must keep. A higher fraction leaves less of that profit free to move price_scale. price_scale is the pool’s centre price.

**Resettable floor** — After an allowed re-peg crosses the old protected profit threshold, the experimental rule lowers it to the new virtual price. Later attempts must still pass the initial profit check. Virtual price must stay above 1.

**Service standard** — A [service standard](./#glossary/service-standard) states a limit on how often, and how long, the pool may be seriously detached.

**Skill** — [Skill](./#glossary/skill) is the share of a reference prediction’s [squared error](./#glossary/squared-error) removed by the model. The reference is the stated baseline, a simpler prediction.

**Squared error** — Squared error is the square of the gap between a prediction and the observed outcome. In a skill score, that error is the average over the scored windows.

**Stall** — A [stall](./#glossary/stall) is a gap between price_scale and the market that exceeds the limits in the [shared stall rule](./#settings). price_scale is the pool’s centre price. The limits cover the size of the gap and how long it lasts.

**Standard error** — A [standard error](./#glossary/standard-error) measures uncertainty in an estimated mean. The measure uses the sampling method stated with the estimate. A larger standard error means a less precise mean.

**tBTC** — [tBTC](./#glossary/tbtc) is the Threshold network’s token for Bitcoin on Ethereum.

**Unlabelled contracts** — [Unlabelled contracts](./#glossary/unlabelled-contracts) are trading contracts. The study’s activity labels did not name their purpose.

**UTC** — [UTC](./#glossary/utc) is Coordinated Universal Time. Every date and window on this site uses that clock.

**Virtual price** — Virtual price is the pool’s internal accounting index per share. The invariant is a value identifying the pool’s reserve curve. The figure is normalised with price_scale, the pool’s centre price. The profit gate uses this internal index.

**VirtualPool** — [VirtualPool](./#glossary/virtualpool) is a contract that routes trades involving the YB pool.

**Volatility** — [Volatility](./#glossary/volatility) measures the size of price fluctuations. Annual volatility is the square root of price-return variance, stated per year.

**Volatility clock** — The [volatility clock](./#glossary/volatility-clock) adds squared log-price changes over the stated period. A larger total means the pool experienced more market movement.

**Volatility harvesting** — [Volatility harvesting](./#glossary/volatility-harvesting) is the rebalancing part of return from repeatedly restoring chosen asset-value weights at market prices. At equal value in cash and the risky asset, it is the log-growth advantage over a fee-free constant-product pool. The pool and that benchmark follow the same price path. The [worked example](./#harvesting/rebalancing) explains why this differs from holding the opening coins.

**Volatility-scaled bootstrap** — A [volatility-scaled bootstrap](./#glossary/volatility-scaled-bootstrap) keeps each sampled move’s direction. The bootstrap scales that move’s size by volatility on the new date compared with the source date. The scaling changes when turbulent stretches occur. The scaling also changes the cumulative price path.

**WBTC** — [WBTC](./#glossary/wbtc) is a token for Bitcoin on Ethereum, backed by coins a custodian holds.

**WETH** — [WETH](./#glossary/weth) is the token form of ETH used by these pools.

**Wilson upper bound** — A Wilson upper bound is an upper confidence limit for an event’s probability. The inputs are the event count and the number of eligible paths. Fewer observations generally leave more room above the observed share.

**Wrapper token** — A wrapper token is a token built to stand for another asset on this blockchain.

**xcp_profit** — The [xcp_profit](./#glossary/xcp_profit) counter adds internal gains earned between re-pegs. A re-peg updates price_scale, the pool’s centre price. The counter does not subtract losses recorded at that update. The gate uses that profit history to set the protected accounting level.

**YB position** — The YB position owns LP shares and owes crvUSD debt. crvUSD is the stablecoin used as that debt. Net wealth is the outside value of the shares minus the debt. The result is expressed in the pool’s risky asset.

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