Confidence Intervals for Your Win Rate

[Fairman]

Confidence Intervals for Your Win Rate

You won 55 of 100 trades. Does that mean your true win rate is 55 percent? Not necessarily. A confidence interval shows the range of values consistent with what you observed.

A rough formula for the margin of error on a win rate uses the square root of the win rate times the loss rate, divided by the number of trades, multiplied by about 1.96 for a 95 percent interval. With a win rate of 0.55 and 100 trades, the standard error is the square root of 0.55 times 0.45 divided by 100, which is about 0.05. Multiply by 1.96 to get roughly 0.10. So the 95 percent interval runs from about 45 to 65 percent.

That range is wide. A true win rate of 47 percent fits the data just as well as 62 percent. For a strategy that needs 50 percent to break even, you cannot yet tell whether you are above or below.

With 400 trades, the margin shrinks to about 5 percentage points, which is much more informative.

The practical lesson is humility. Early results cannot distinguish good strategies from lucky ones, and the numbers need time to mean anything.

It also guides expectations: if your plan requires a 40 percent win rate to be profitable, and your interval after 100 trades covers 32 to 48 percent, wait for more data.

Practical step: compute the interval for your current win rate and see whether it includes your break-even level.

[Fairman]

This maths is a nice cure for getting excited after a hot month. 45 to 65 percent is a huge range, and your break even might be sitting right inside it. With only 30 trades it's even worse. A 60 percent win rate on 30 trades has a 95 percent interval of roughly 42 to 78 percent, which basically means you know almost nothing yet. That's not a reason to give up, just a reason to keep size small and keep collecting trades. I find it calming, actually. A bad month also tells you less than it feels like, so you can stop reacting to every short run of results.

[Fairman]

Worth doing the same for average R per trade, not only win rate. The spread of results matters as much as how often you win. The rough version is the standard deviation of your R results divided by the square root of the number of trades, times about two. If your average is 0.2R, the standard deviation is 1.3R and you have 100 trades, the margin is about 0.26R either way. So the true average could be slightly negative. That's common for strategies with occasional big winners, where a couple of trades carry the result. It's another reason to be patient before scaling up, even with a decent looking average.