How to use the win rate confidence interval calculator
- Enter the number of trades behind the win rate: closed trades from one strategy, not a mix of several.
- Choose what you know: the number of winning trades or the win rate as a percentage.
- Enter the wins or the win rate. The wins cannot exceed the trades.
- Pick a confidence level. 95% is the usual choice; 90% gives a narrower range and 99% a wider one.
- Optionally enter your payoff, the average win divided by the average loss. It adds a break-even marker so you can see whether the range crosses it.
The calculator shows the plausible range of the true win rate, its lower and upper bound, the margin of error and the number of trades needed to get within plus or minus 5 and 3 percentage points. A bar chart places the range on a 0 to 100% axis and a line chart shows how the range narrows as trades are added.
The win rate confidence interval formula
The calculator uses the Wilson score interval. For an observed win rate p (wins divided by trades), n trades and a confidence level with normal quantile z:
centre = (p + z² / 2n) / (1 + z² / n)
half = z / (1 + z² / n) × √( p × (1 − p) / n + z² / 4n² )
range = centre − half to centre + half
The quantile z is 1.645 for 90% confidence, 1.960 for 95% and 2.576 for 99%. The margin of error is half the width of the range. The range is not exactly symmetric around p when the win rate is far from 50%, so read the margin as the average of the two sides.
Why Wilson. The textbook formula, p ± z√(p(1 − p)/n), has a flaw that matters to traders: at a win rate of 0% or 100% its range collapses to a single point, and with few trades it can run outside 0 to 100%. The Wilson interval stays inside the scale, behaves with small samples and is widely recommended as the replacement. The exact Clopper-Pearson interval is another option. It is built to cover the true win rate at least as often as the stated confidence, so its range is wider than it needs to be, which is why it is not used here.
To find the trades needed for a target margin, the calculator searches for the smallest n whose half-width is within the target at your win rate. The rough shortcut is n = z² × p × (1 − p) / margin². At the worst case of a 50% win rate and 95% confidence it gives 385 trades for plus or minus 5 points and 1,068 for plus or minus 3.
Worked example
A trader has 55 winning trades in 100, a payoff of 1 (wins and losses the same size) and a 95% confidence level.
These are the numbers the calculator opens with. With 55 wins in 100 trades, the true win rate could plausibly be anywhere from 45.2% to 64.4%.
The break-even win rate at an even payoff is 50%, and it sits inside that range. A 55% win rate looks like an edge, but 100 trades cannot separate it from a strategy that wins 50% or even 46% of the time. Raise the confidence level to 99% and the range for the same trades becomes 42.3% to 67.1%; lower it to 90% and it is 46.8% to 62.9%.
How many trades you need before a win rate means something
The range narrows with the square root of the number of trades, so each gain in certainty costs more trades than the last. This table holds the win rate at 55% and the confidence at 95%.
Twenty trades say almost nothing: the range covers a losing strategy and a very good one. Four times as many trades roughly halve the width, which is why the line chart flattens out. The lower end of the range for a 55% win rate first rises above 50% at 385 trades.
This is the working meaning of sample size. The question is not whether you have enough trades in total, but whether you have enough in the group you are judging. Split 300 trades across six setups and each setup has about 50, with a range of 25 points or more.
Reading the range against break-even
A win rate is only good or bad against what your payoff needs. The break-even win rate is 1 ÷ (1 + payoff): 50% for a payoff of 1, 40% for a payoff of 1.5 and 33.3% for a payoff of 2. The risk reward ratio calculator shows the same relationship from entry, stop and target.
Compare the range with that line and there are three cases:
- The whole range is above break-even. Even the pessimistic end clears it. At a payoff of 1.5 the break-even is 40.0%, below the lower bound of 45.2% in the example.
- The range crosses break-even. The data cannot say whether you are ahead or behind. This is the default case at an even payoff, and it is the usual state of a strategy with fewer than a few hundred trades.
- The whole range is below break-even. At this payoff the win rate looks too low, and the plan needs a better payoff or a better entry.
The check covers the win rate only. Your payoff has its own uncertainty, and the expectancy calculator combines the two into one figure.
Common win rate confidence mistakes
- Reading the measured win rate as exact. A 55% win rate from 100 trades is a point inside a 19-point range.
- Judging a strategy after 20 trades. The range at that size is about 40 points wide.
- Slicing the data until something looks good. Break 300 trades into setup, symbol and session groups and a few groups will show a high win rate by chance. Each slice also has a wide range.
- Mixing strategies in one sample. A win rate pooled from two different approaches describes neither.
- Tuning on the same data. If you adjusted the rules until the past looked good, the range from that past is too optimistic.
- Checking after every trade and stopping when it looks good. The result you stop on is biased upward.
- Treating win rate as profit. A strategy can have a high win rate and a negative expectancy; the article on win rate, profit factor, expectancy and R-multiple shows how the four fit together.
What the calculator does not know
It assumes the trades are independent and come from one strategy whose win rate did not change. If you changed the rules, the market regime shifted or you traded some setups differently, the real uncertainty is wider than the range shown.
It does not know how the sample was chosen. A sample picked after the fact, or tuned to look good, gives a range that is too narrow. It also describes the win rate only, not profit, and the Wilson interval is an approximation that is slightly less cautious than an exact method for samples of only a handful of trades. It cannot tell you whether to trade a strategy. Nothing here is investment advice.
Frequently asked questions
What is a confidence interval for a win rate?
It is a range of win rates that are consistent with the trades you have taken. A measured win rate is only an estimate of your true win rate, and the interval shows how far off it could plausibly be. With 55 wins in 100 trades at 95% confidence, the range is 45.2% to 64.4%.
How many trades do I need to trust my win rate?
It depends on how precise you need to be. At 95% confidence, a win rate near 55% needs 377 trades to be within plus or minus 5 points and 1,053 for plus or minus 3. The worst case, a win rate of 50%, needs 381 and 1,064.
How do you calculate the confidence interval of a win rate?
Use the Wilson score interval: add z² / 2n to the win rate, divide by 1 + z² / n for the centre, then move out by z divided by 1 + z² / n times the square root of p × (1 − p) / n + z² / 4n². The formula is written out above, with z of 1.96 for 95% confidence. The calculator does the arithmetic for you.
What does 95% confidence mean for a win rate?
It describes the method, not one range. If you repeated the same kind of sample many times and built a 95% interval each time, about 95 of every 100 intervals would contain the true win rate. In practice, read the range as the win rates your data cannot rule out.
Why use the Wilson interval instead of the normal approximation?
The Wilson interval works where the simple formula fails. The simple version gives a zero-width range at 0% or 100% and can stray outside 0 to 100% with few trades, while the Wilson interval stays on the scale and is more accurate for small samples. For large samples the two nearly agree.
Is a 55% win rate over 100 trades statistically significant?
Not against a 50% win rate. The 95% range runs from 45.2% to 64.4%, so 50% is still a plausible true win rate. The lower end of the range first rises above 50% at 385 trades.
Does a higher confidence level make the range wider?
Yes. For 55 wins in 100 trades the range is 46.8% to 62.9% at 90% confidence, 45.2% to 64.4% at 95% and 42.3% to 67.1% at 99%. A higher level means more certainty that the range holds the truth, and the price is a wider range.
What is the margin of error of a win rate?
It is half the width of the confidence interval, in percentage points. For 55 wins in 100 trades at 95% confidence it is about 9.6 points. It shrinks with the square root of the number of trades.
Does a wide interval mean my strategy is bad?
No. A wide range means you do not yet know, in either direction. It says the sample is too small to judge, and more trades from the same strategy are what narrow it.