Win rate on its own tells you nothing. A system that wins 90% of the time and loses 3 dollars for every 1 it makes is a machine for losing money slowly. Expectancy is the version that includes both sides.
expectancy = (win% × average win) − (loss% × average loss). The middle number above is the win rate at which expectancy is exactly zero, and it does not depend on the account size at all. If your EA wins 55% and the break-even is 55.6%, it is losing — and no amount of lot-sizing changes that, because it is a property of the trades, not the stake.
Note what is missing: spread and commission. A calculator that ignores them will happily tell you a 5-pip scalper is profitable. It is not. On a 5-pip target with a 1.5-pip spread, you need a 66.7% win rate before costs and better than that after. That sum is worked out here.
I ran this arithmetic across every EA in the 372 batch that closed a trade. The split has no overlap to explain away:
| Expectancy per trade | EAs | Lost money | Share |
|---|---|---|---|
| Negative | 149 | 145 | 97.3% |
| Positive | 41 | 12 | 29.3% |
That is as clean a result as this dataset produces, and it needed no curve fitting — the formula predates the test. It is also not a guarantee, and the exceptions are worth stating rather than hiding: a handful of EAs with negative expectancy finished positive anyway. Swaper made +205.9% with a 98.8% drawdown; HarVesteR +99% with 64.7%. Both are what a positive result looks like when it is luck, because a negative expectancy can only produce that outcome by taking a risk that was one bad week from zero.
The other direction is the one that costs people money. Of the 41 EAs with positive expectancy, 12 still lost. Expectancy says the arithmetic is on your side over a long run of trades; it says nothing about whether the account survives the run. That is the streak tool, and it is why the two belong together.
Small samples. Twenty trades is noise. The average win and average loss of twenty trades are themselves estimates, and a single outlier moves them by double digits. Below thirty closed trades I do not quote expectancy at all.
The average of averages. This formula uses one average win and one average loss. A real distribution has a tail: if one trade out of sixty was +$900, the formula credits every trade with $15 of it. Take that trade out and re-run the sum. If the sign flips, the edge was one trade.
Compounding. Expectancy in dollars is quoted at a fixed stake. At fixed fractional risk the dollar figure grows with the account, so a positive per-trade expectancy at 0.01 lots is a smaller number than the same expectancy at 0.10 — but so is every loss, and the ratio is what you are measuring here.
Related: position size · losing streaks · all 372 results with expectancy printed