# Expectancy

> 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.

Canonical HTML page: https://qanterion.com/glossary/expectancy
Updated: 2026-08-18
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.

## Calculate it

- Kelly Criterion Calculator: https://qanterion.com/tools/kelly-criterion-calculator
- Risk of Ruin Calculator: https://qanterion.com/tools/risk-of-ruin-calculator

## See also

- Risk of ruin: https://qanterion.com/glossary/risk-of-ruin
- Position sizing: https://qanterion.com/glossary/position-sizing
- Slippage: https://qanterion.com/glossary/slippage

## Sources

- [A New Interpretation of Information Rate](https://www.princeton.edu/~wbialek/rome/refs/kelly_56.pdf) — J. L. Kelly, Jr., Bell System Technical Journal (hosted by Princeton University)
- [Optimal Gambling Systems for Favorable Games](https://digicoll.lib.berkeley.edu/record/112884) — 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](https://www.stat.berkeley.edu/~aldous/157/Papers/Good_Bad_Kelly.pdf) — L. C. MacLean, E. O. Thorp, W. T. Ziemba (hosted by UC Berkeley Department of Statistics)

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## Risk notice

Definitions are educational. Nothing here is investment advice, and no metric described on this page predicts future results.