The margin of error of a win rate
For a win rate p measured on n independent trades, the standard error is the square root of p times 1 minus p, divided by n. A rough 95 percent interval is about twice that value on each side.
If the true win rate is 50 percent, a sample of 30 trades gives an interval of about plus or minus 18 points, so a measured 50 percent could hide a real 32 or a real 68. With 100 trades the interval is about plus or minus 10 points, with 400 trades about 5, and with 1,000 trades about 3. The accuracy improves with the square root of the number of trades, which means that quadrupling the sample only halves the uncertainty.
Expectancy needs even more
The average gain in R is noisier than the win rate, because each trade can be worth very different amounts. Its margin of error depends on the spread of the results, and it is usually wide until the sample reaches several hundred trades.
A strategy with an expectancy of +0.1 R and a typical trade result of plus or minus 1.5 R needs a large sample before that +0.1 R can be told apart from zero.
Overlapping trades are not independent
If a strategy opens several trades at the same time on the same market, those trades are not independent observations. They share the same price path, so they win or lose together, and counting them as separate trades makes the sample look larger than it is.
The statistics in ATLAS replay one position at a time, so that each trade is a separate observation.
Many markets help, but not infinitely
Testing the same rule on several markets increases the sample, and it is a useful check that a result does not depend on one instrument. Markets that move together, such as several dollar pairs, count for less than their number suggests.
How ATLAS handles sample size
The sample size is displayed with every figure inside the platform. On the public pages of this website a measurement appears only when it rests on at least 200 signals. When the signal statistics compare buying with selling, they use a test of two proportions and say so when the gap is below what chance alone could produce.
Frequently asked questions
Is 100 trades enough?
It gives a rough idea of the win rate, with a margin of about 10 points, but it is rarely enough to settle an expectancy. More is better, and independence matters as much as the count.
Why does the margin shrink so slowly?
Because it follows the square root of the number of trades. To halve the uncertainty you need four times as many trades.
See it in ATLAS
Signal Statistics
Buy or sell: which strategy works best, on which timeframe and on which market.
Strategy Lab
Describe a strategy in plain words or paste a Pine Script; ATLAS turns it into rules and measures it.
Signals
Every strategy signal across your markets, with the measured statistics of that exact setup.
Terms used in this guide
More guides
This guide explains methods and arithmetic. It is not financial advice, and past results do not guarantee future ones. Read the risk disclosure.
