Bootstrap Expectancy Calculator
A bootstrap expectancy calculator repeatedly resamples the signed outcomes you enter with replacement, calculates 5,000 reproducible sample means and reports a percentile interval around the entered arithmetic mean. The interval estimates sampling uncertainty under explicit assumptions; it is not a next-trade range or proof of a persistent edge.
Enter one consistent outcome sample
Use 10 to 1,000 signed values in one currency, percentage, pip or R-multiple convention. Zeros remain observations.
Enter 10 to 1,000 values in one unit. Wins are positive, losses negative and breakevens zero.
The selected central percentile interval from 5,000 seeded resampled means.
Seeded mean uncertainty estimate
Entered Strategy Robustness 1.0.0.
On smaller screens, scroll horizontally to inspect the complete calculation table.
| Bootstrap summary point | Value |
|---|
How the bootstrap expectancy interval is calculated
Bootstrap meanb = Mean of N draws with replacement
Percentile interval = Sorted bootstrap means at α ÷ 2 and 1 − α ÷ 2
Version 1.0.0 keeps all positive, negative and zero observations. It calculates the entered arithmetic mean, derives a deterministic seed, then builds 5,000 resamples. Every resample contains N draws from the N entered outcomes with replacement.
The engine sorts the 5,000 resampled means and uses Type-7 linear interpolation. A 95% interval reads the 2.5th and 97.5th percentiles; 90% and 99% use their corresponding two-sided tail probabilities.
Bootstrap standard error is the N-minus-one sample standard deviation of the 5,000 resampled means. It describes dispersion across the finite seeded resamples and is not the standard deviation of individual trade outcomes.
Worked example from the audited fixture
The audited fixture enters ten identical outcomes of 2 in one unspecified but consistent unit and selects 95% confidence.
- Every resample contains ten copies of 2. Every resampled mean is therefore 2, so the entered mean, bootstrap median, lower bound and upper bound are all 2.
- Because none of the 5,000 resampled means differs, interval width and bootstrap standard error are both zero. This deterministic case validates the resampling and percentile boundaries; it does not imply certainty in a real strategy.
Reproduce it: select “Load audited example” above. The engine retains full precision and rounds only visible output.
How to interpret the result
- The entered sample mean is the descriptive expectancy of the supplied observations only.
- The bootstrap interval is built from repeated resampling of that same sample. It does not include errors caused by missing, selected or misclassified trades.
- A wider interval indicates greater resampling uncertainty for the entered sample and selected confidence level, not greater guaranteed future loss.
- Whether zero falls inside the interval is descriptive. Version 1.0.0 does not convert that position into a significance test, edge label or trading decision.
Assumptions and limits
- Individual resampling assumes observations can be treated as exchangeable; serial dependence and volatility clustering can invalidate that simplification.
- Small or unrepresentative samples can yield unstable or misleading intervals.
- The percentile method can have imperfect coverage and version 1.0.0 does not calculate BCa, studentized or block-bootstrap intervals.
- All outcomes must use one unit and one gross-or-net cost convention; the display does not convert them.
- No future expectancy, win probability, statistical significance, sample-sufficiency grade, signal or recommendation is generated.
Monte Carlo vs bootstrap vs walk-forward efficiency
These tools answer separate questions. Monte Carlo summarizes hypothetical resampled paths, bootstrap estimates uncertainty around one entered statistic, and walk-forward efficiency compares entered IS and OOS rates. None substitutes for audited records, a documented test design or execution evidence.
| Measure | Evidence entered | Question answered | Main boundary |
|---|---|---|---|
| Monte Carlo equity | Entered percentage returns | Seeded terminal-equity and drawdown path distribution | Not a forecast or exhaustive loss boundary. |
| Bootstrap expectancy | Entered signed outcomes | Percentile interval for resampled arithmetic means | Not a next-trade prediction interval. |
| Walk-forward efficiency | Entered IS and OOS window results | Aggregate OOS result rate divided by aggregate IS result rate | Not an optimisation or robustness verdict. |
| Risk of ruin | Assumed win rate, payoff and fixed risk | Finite-horizon threshold-hit estimate | A separate parametric two-outcome model. |
Frequently asked questions
- It estimates resampling uncertainty around the arithmetic mean of the entered signed outcomes under an exchangeable empirical draw-pool assumption.
- Each of 5,000 seeded resamples contains the same number of observations as the original sample, drawn from that sample with replacement.
- Version 1.0.0 sorts the resampled means and uses Type-7 linear interpolation at the two central interval endpoints.
- No. It is an interval across resampled sample means and is not a prediction interval for one future outcome.
- You can use money, percentage, pips or R multiples only when every outcome uses the same unit and gross-or-net convention.
- Zeros remain observations and can be drawn into any resample; they are not removed or treated as missing values.
- No. The page does not test selection bias, dependence, regime stability, multiple testing or future relevance and creates no edge verdict.
- The resamples cannot introduce outcomes absent from the entered evidence, so a selected or unrepresentative small sample can understate uncertainty.
Sources and methodology
- NIST/SEMATECH — Bootstrap Plot — Official explanation of resampling with replacement and percentile uncertainty intervals.
- CFTC — Commodity trading systems — Official caution on simulated and hypothetical performance evidence.
The immutable implementation contract fixes the seed, resampling count, quantile convention, duration weighting, invalid states and permanent exclusions so later copy or layout edits cannot silently alter the arithmetic.
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Before treating any return, outcome or window result as net and comparable, confirm which spread, commission, financing, conversion and execution conventions apply to the broker entity and account used. These browser calculations do not retrieve statements or certify that entered records are complete.
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