Confidence interval (win rate and expectancy)
A confidence interval is a range computed from a sample that, under the assumptions of the method, would contain the true value of a statistic in a stated share of repeated samples, typically 95%. For trading statistics it turns a single win rate or average trade into the range of values the data cannot rule out.
Senzoukria · Glossary · Updated September 2026
At a glance
- Win rate (normal approximation)
- p ± 1.96 × √[p(1 − p) ÷ n]
- Average trade
- mean ± 1.96 × s ÷ √n
- 55% on 100 trades
- About 45.2% to 64.8%
- Width shrinks with
- √n: four times the trades halve the width
Win rate
A measured win rate p on n independent trades has a standard error of √[p(1 − p) ÷ n]. For 55 winners out of 100 trades, that is √(0.55 × 0.45 ÷ 100) ≈ 0.0497, and the 95% interval is 0.55 ± 1.96 × 0.0497, from about 45.2% to 64.8%. If the strategy's breakeven win rate is 50%, the data are compatible with a losing strategy. With 400 trades and the same 55%, the interval narrows to about 50.1% to 59.9%.
For small samples or win rates near 0% or 100%, the Wilson score interval behaves better than the normal approximation, which can produce impossible bounds below zero or above one.
Average trade
For an average trade, the standard error is the standard deviation of trade results divided by √n. A record of 100 trades with a mean of +30 dollars and a standard deviation of 200 has a standard error of 20 and a 95% interval of 30 ± 39.2, from about −9 to +69. Zero is inside the interval: the sample does not establish a positive expectancy, even though the average is positive. Trade results are often skewed and fat-tailed, so a bootstrap interval is a useful cross-check.
What the interval does and does not mean
- It describes sampling uncertainty under the assumption that trades are independent draws from a stable process. Regime changes and clustering make real uncertainty larger.
- It does not correct for selection. The interval around the best of 50 configurations is too narrow, because the choice already favored a lucky sample.
- A 95% interval is not a 95% probability that the true value lies in this particular range; it is a statement about the procedure's long-run coverage.
In Senzoukria
The desktop does not print confidence intervals next to its statistics. It addresses sample uncertainty with other signals: a warning under 20 trades that the ratios are exact but not significant, a verdict line driven by the SQN, which grows with the square root of the trade count, a permutation p-value and a deflated Sharpe in the Gauntlet, and a message in the prop firm panels when too few sessions exist for reshuffling to produce different paths. The formulas above can be applied directly to the win rate, average and trade count shown in the session report.
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Frequently asked questions
- How many trades do I need for a reliable win rate?
- It depends on how close the win rate is to the breakeven. To distinguish 55% from 50% with a 95% interval that excludes 50%, you need roughly 400 independent trades. Distinguishing 70% from 50% takes far fewer. Clustering of outcomes increases the number needed.
- Why is my positive average trade not significant?
- Because the dispersion of trade results is large compared with the average. A mean of 30 dollars with a standard deviation of 200 needs about 170 trades before the 95% interval excludes zero, assuming independent trades.