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Next: does the average trade make money?
The win rate and the range say how often. Expected value says how much, with the average win, average loss and costs.
What is included
- The calculator, with your own numbers
- The formula written out
- A worked example you can reproduce
- Where grid, martingale and DCA bots break the maths
Who it is for
- People running or testing a trading bot
- Anyone sizing a position or checking costs
- Readers learning how the numbers work
- Not advice, and not for placing trades
Key facts
- Win rate = wins / (wins + losses). It is an estimate of the true win rate, and the estimate gets better only as trades are added.
- The Wilson score interval gives a range that covers the true win rate about 95 times in 100 repeated samples. It is better than the simple plus or minus formula for small samples.
- Break-even win rate = 1 / (1 + R), where R is average win divided by average loss, ignoring costs. At R = 1 it is 50 percent.
- To narrow the range to about plus or minus 5 points takes roughly 370 to 385 trades. 30 trades prove very little.
- A high win rate is not an edge by itself. A bot with a 90 percent win rate loses money if its losses are more than nine times its wins.
How the calculator works
The win rate is the easy part: wins divided by all trades. The range is the useful part. A win rate comes from a sample of trades, and a sample is a rough picture of the true win rate that sits behind them.
Wilson 95% interval = ( p + z^2/2n +/- z x sqrt( p(1 - p)/n + z^2/4n^2 ) ) / ( 1 + z^2/n ), with z = 1.96
Break-even win rate = 1 / (1 + R), R = average win / average loss
Trades for +/- 5 points = z^2 x p(1 - p) / 0.05^2
The last line is the standard sample size formula for a proportion. It is approximate and uses the win rate you have observed, falling back to 50 percent (the worst case, 385 trades) if the observed rate is very near 0 or 100.
A worked example
Take a made-up record of 18 wins and 12 losses, 30 trades. The win rate is 60.0 percent. The 95 percent Wilson range is 42.3 percent to 75.4 percent. With equal average wins and losses (R = 1) the break-even win rate is 50 percent, and it sits inside that range, so 30 trades cannot say whether this strategy wins more than it loses. To bring the range to about plus or minus 5 points at a 60 percent win rate takes about 369 trades.
Ten times the trades
Keep the same 60 percent but with 180 wins and 120 losses, 300 trades. The range becomes 54.4 percent to 65.4 percent. Now the whole range is above 50 percent. The win rate did not change. What changed is how much we know about it.
| Trades | Wins (60%) | 95% range for the true win rate |
|---|---|---|
| 30 | 18 | 42.3% to 75.4% |
| 100 | 60 | 50.2% to 69.1% |
| 300 | 180 | 54.4% to 65.4% |
| 1,000 | 600 | 56.9% to 63.0% |
Wilson score interval for a 60 percent win rate. Calculated by us on 27 Oct 2026, rounded to one decimal.
Where bots break the maths
- Win rate is high by design. Grid and martingale bots win most cycles by construction, so the observed win rate can be 90 percent or more. The break-even win rate for a payoff ratio of 0.1 (wins a tenth of the losses) is 1 / 1.1 = 90.9 percent. A bot at 90 percent is below break-even. The expected value calculator combines both numbers.
- Trades are not independent. A grid with ten open positions that all close together is one event counted ten times. The calculator treats every trade as separate, so the range is too narrow for such a record. Count cycles or days, not orders.
- The sample may not include the bad regime. A bot with 300 winning trades in a calm market has a tight win rate range and no information about the day the market moves hard against it.
- Selecting the sample. A range from the best-looking period is biased high. See survivorship bias.
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FAQ
Frequently Asked Questions
What is a good win rate?
There is no good number on its own. The win rate means something only next to the average win and average loss. A 35 percent win rate is fine if wins are three times losses, and a 90 percent win rate is not if losses are ten times wins.
What is the Wilson interval?
It is a way to give a range for a true proportion from a sample. It behaves better than the simple plus or minus formula when the sample is small or the win rate is near 0 or 100 percent.
How many trades do I need?
It depends on how tight a range you want. About 385 trades gets a range of plus or minus 5 points in the worst case, and about 1,540 gets plus or minus 2.5 points. Trades that happen together count as fewer than they look.
Does the break-even win rate include costs?
No. It uses only the payoff ratio. Costs raise the break-even, so a strategy that is just above it before costs may be below it after them.
Why does the range look so wide?
Because a small sample cannot narrow it. The range shrinks with the square root of the number of trades, so four times the trades halves it.
Are the numbers on this page real?
Example numbers are made up to show how the maths works, and the page says so. A figure only counts as exact when the page says it was calculated on a stated date. Nothing you enter in a calculator leaves your browser.
Can I use this to decide whether to run a bot?
It can show whether a bot's numbers hold together and how much an account can lose. It cannot say what the market will do, and it is not advice. Use it to ask better questions, then read the terms of your own broker or exchange.
Is this financial advice?
No. It is a calculator and general education. It does not consider your situation, and its output is only as good as the numbers you enter.
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