What Is Trading Expectancy?
Expectancy is what a strategy makes per trade on average, combining win rate and payoff size into one number. It is calculated as (win rate × average win) − (loss rate × average loss). If it is negative, no amount of position sizing or discipline makes the strategy profitable.
What is the formula?
Expectancy = (W × average win) − (L × average loss), where W is the win rate and L = 1 − W.
Worked example in dollars. A strategy wins 45% of the time, averaging $620 on winners and $310 on losers. Expectancy = 0.45 × 620 − 0.55 × 310 = 279 − 170.5 = +$108.50 per trade. Over 300 trades that is $32,550, before costs.
Worked example in R, which is the more portable form. A strategy wins 40% of the time and averages +2.5R on winners, −1.0R on losers: 0.4 × 2.5 − 0.6 × 1.0 = +0.40R per trade. Risking 1% of a $50,000 account per trade, that is $200 per trade in expectation.
Why does win rate alone tell you nothing?
Because it is one of the two inputs. Compare:
| Win rate | Avg win : avg loss | Expectancy |
|---|---|---|
| 75% | 0.3 : 1 | 0.75 × 0.3 − 0.25 × 1.0 = −0.025R |
| 60% | 1.0 : 1 | 0.60 × 1.0 − 0.40 × 1.0 = +0.20R |
| 35% | 3.0 : 1 | 0.35 × 3.0 − 0.65 × 1.0 = +0.40R |
The 75% strategy loses money. The 35% strategy is the best of the three. A trader advertising the first row and omitting the second column is not necessarily lying, but the number being advertised is the wrong one.
Where do costs go?
Straight off the top. Subtract the round-trip cost from every trade before computing anything: a +$108.50 expectancy at $12 of commission and spread per round turn is +$96.50, an 11% reduction. For an intraday strategy averaging +$40 per trade, the same $12 removes 30% of the edge and turns a marginal system into a losing one.
How many trades before you believe it?
More than feels reasonable. The standard error on a 45% win rate over 50 trades is sqrt(0.45 × 0.55 ÷ 50) = 7.0 percentage points, so the true rate could plausibly be anywhere from 31% to 59% — which spans profitable and unprofitable at most payoff ratios. At 500 trades the standard error is 2.2 points and the picture is far clearer.
How does this connect to a track record?
One caution about any expectancy computed from a strategy you tuned. The probability that a backtest is overfit rises with the number of configurations tried, and a high simulated performance is easy to reach after testing a modest number of variants[1] — so an expectancy read off a fitted history is an estimate of how well you searched, not of what the method returns.
The bar for believing a measured edge has been raised in the literature too. Reviewing hundreds of published return predictors, Harvey, Liu and Zhu argued that so many had been tested that a new factor should clear a t-statistic above 3.0 rather than the conventional 2.0.[2] An expectancy computed on a few dozen trades is nowhere near that.
A metric is a summary of a record, so it inherits every weakness of that record. Computed from trades selected after the fact, it is a number about the selection. kappi commits each trade before it resolves and publishes it on a Merkle-anchored log, so PnL, RME, correlation to SPX, mean R:R and trade count over 30, 100 and 200-day windows are computed over everything that was committed, losses included. $15/month to keep a record; reading one is free.
Sources
- Bailey, Borwein, López de Prado & Zhu, 'Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance', Notices of the AMS 61(5), 2014, 458 read 2026-08-16
- Harvey, Liu & Zhu, '… and the Cross-Section of Expected Returns', Review of Financial Studies 29(1), 2016, 5–68 — argues a newly claimed factor should clear a t-statistic above 3.0 read 2026-08-16
Frequently asked questions
How do you calculate trading expectancy?
(Win rate × average win) − (loss rate × average loss). A 45% win rate with $620 average wins and $310 average losses gives 0.45 × 620 − 0.55 × 310 = +$108.50 per trade.
What is a good expectancy?
Any positive number that survives realistic costs, measured over enough trades to be distinguishable from luck. Expressed in R, systems in the +0.2R to +0.5R range are common among strategies that persist.
Can a strategy with a 75% win rate lose money?
Easily. At a 0.3:1 payoff ratio, 0.75 × 0.3 − 0.25 × 1.0 = −0.025R per trade. Win rate is only meaningful next to the average win and average loss.
How many trades before expectancy is reliable?
The standard error on a 45% win rate over 50 trades is 7 percentage points, so the true rate could be 31% to 59%. At 500 trades it is 2.2 points. Hundreds, not dozens.