Definition
Expectancy
Expectancy is the average result per unit risked. Definition, formula, the break-even win rate, and why win rate alone tells you nothing.
Expectancy is the average outcome of a trade expressed per unit of risk: win rate multiplied by payoff ratio, minus the loss rate. A strategy with a 45% win rate and a 2:1 payoff has an expectancy of +0.35, meaning it earns 0.35 units for every unit risked over a long series. When expectancy is zero or negative, no amount of position sizing, leverage, or discipline makes the strategy profitable.
- Also known as
- expected value per trade · edge
How it is calculated
Expectancy per unit risked = (Win rate × Payoff ratio) − Loss rate
Break-even win rate = 1 ÷ (Payoff ratio + 1)
Expectancy ≤ 0 means no position size makes the strategy profitable.
Worked example: 45% win rate, 2:1 payoff → (0.45 × 2) − 0.55 = +0.35 per unit risked.
Win rate on its own is meaningless
A 90% win rate is a losing strategy if the single loss is larger than the nine wins combined, and a 35% win rate is highly profitable at a 3:1 payoff. Expectancy is the smallest number that combines both, which is why it is the first statistic to compute and the last one to discard when a strategy is being evaluated.
Costs come out of expectancy, not out of profits
Fees, slippage, and funding are subtracted per trade, so they reduce the payoff ratio directly. A strategy with a gross expectancy of +0.1 units and a round-trip cost of 0.12 units is a losing strategy that looks like a winning one in every backtest that omits friction.
How it gets misread
Expectancy computed on a short sample is treated as a property of the strategy. It is an estimate, and it is unstable: a few dozen trades are not enough to distinguish a genuine edge from a favourable run, which is how overfitted systems reach production with confident-looking statistics.
Sources
- A New Interpretation of Information Rate — J. L. Kelly, Jr., Bell System Technical Journal (hosted by Princeton University)
- Optimal Gambling Systems for Favorable Games — L. Breiman, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (UC Berkeley Library Digital Collections)
- Good and bad properties of the Kelly criterion — L. C. MacLean, E. O. Thorp, W. T. Ziemba (hosted by UC Berkeley Department of Statistics)
Definitions are educational. Nothing here is investment advice, and no metric described on this page predicts future results.
Definitions are the easy part
Knowing what drawdown means is not the same as having a system that halts on it. QANTERION applies these limits while a strategy runs.