The formula, and what it is really saying
expectancy = (win rate × average win) − (loss rate × average loss)
The output is the amount an average trade is worth. Positive means the method pays; negative means it costs, no matter how good the winners feel.
It also gives the break-even win rate for your particular win and loss sizes:
break-even win rate = average loss ÷ (average win + average loss) × 100
If your average win is 320 and your average loss is 200, break-even sits at 38.5%. Below that the method loses money however disciplined you are, and no amount of screen time changes the arithmetic.
The part almost every calculator leaves out
Expectancy is computed from a sample, so it is an estimate, and estimates have error bars. Nearly every tool that returns this number returns it as if it were measured.
The uncertainty in the win rate follows the standard error of a proportion:
SE = √( p(1 − p) / n ) 95% range ≈ p ± 1.96 × SE
Put a real case through it. Forty-five percent win rate, average win 320, average loss 200 — expectancy is +34 per trade, which looks like a business. Now say those numbers came from 30 trades. The 95% range on the win rate is roughly 27% to 63%, which puts expectancy somewhere between −59 and +127. The honest reading is not "I make 34 a trade". It is "I cannot yet tell whether I make money."
At 200 trades the same win rate narrows to about 38%–52%, and expectancy to roughly −2 to +70. Still wide, and still worth knowing before you scale size.
| Trades | 95% range on a 45% win rate |
|---|---|
| 30 | 27% – 63% |
| 60 | 32% – 58% |
| 100 | 35% – 55% |
| 200 | 38% – 52% |
| 500 | 41% – 49% |
The range narrows with the square root of the sample, which is why it shrinks so slowly: to halve the uncertainty you need four times the trades. There is no shortcut, and a confident number produced from a short sample is not confidence, it is arithmetic performed on noise.
Two levers, and only two
When expectancy is negative there are exactly two things that can move it, and naming them prevents a lot of wasted effort:
- Win more often — better selection, fewer marginal setups, avoiding the sessions or instruments where your record is worst.
- Change the sizes — bigger winners relative to losers, which usually means holding to plan rather than closing early, and cutting at the stop rather than past it.
Everything else people try — new indicators, a different platform, trading more — acts on one of these two or on neither. Most acts on neither. If a change cannot be described as "this raises my win rate" or "this improves my win-to-loss size ratio", it is not a fix, and the calculator will say so when the numbers come back the same.
Why the averages hide as much as they show
Two accounts can produce identical expectancy and behave nothing alike. One earns +30 per trade steadily; the other earns it through a single enormous win among many small losses. The average is the same, the survivability is not — the second account spends most of its life in drawdown, and drawdown is where rules get abandoned.
So read expectancy with the distribution beside it, not instead of it. Grading trades in R-multiples makes the shape visible: a healthy record has several winners above 2R, not one above 8R. And the depth of the drawdowns the shape produces is what decides whether the expectancy ever gets collected, because recovery is not symmetrical.