Win Rate and Payoff Ratio

A trader who wins only 40% of the time sounds like a losing proposition until you learn the wins average twice the size of the losses — at that point the losing majority of trades stops mattering, because each rare win pays for more than two losses combined. Win rate on its own tells you almost nothing about whether a strategy makes money; it only becomes meaningful paired with how big the average win is relative to the average loss.

Two numbers, one expectancy

$$\text{Expectancy} = p_{\text{win}} \times \overline{W} - (1 - p_{\text{win}}) \times \overline{L} ,$$

In words: $p_{\text{win}}$ is the win rate, $\overline{W}$ the average size of a winning trade, $\overline{L}$ the average size of a losing trade (as a positive number). Expectancy — the average profit per trade — is positive whenever the win rate times the average win exceeds the loss rate times the average loss. The payoff ratio $\overline{W}/\overline{L}$ captures how many losses one win pays for, and the breakeven win rate for a given payoff ratio $R$ is $p_{\text{breakeven}} = 1/(1+R)$ — the lower the win rate, the bigger the payoff ratio has to be just to keep expectancy at zero.

Worked example 1 — a 40% win rate that's still profitable

A strategy wins 40% of its trades, averaging a $300 profit on wins and a $150 loss on losers — a payoff ratio of $300/150 = 2$. Expectancy: $0.40 \times 300 - 0.60 \times 150 = 120 - 90 = 30$, i.e. $30 per trade. Despite losing on 60% of trades, the strategy is solidly profitable, because each win is worth exactly twice as much as each loss.

Worked example 2 — finding the breakeven win rate

For that same payoff ratio of 2, the breakeven win rate is $p = 1/(1+2) = 33.3\%$. Any win rate above 33.3% with that payoff ratio produces positive expectancy; the strategy's actual 40% win rate sits comfortably above the 33.3% floor. If the payoff ratio instead dropped to 1 (wins and losses the same average size), the breakeven win rate would jump to $1/(1+1) = 50\%$ — the same 40% win rate that was profitable before would now lose money, at exactly $0.40(150) - 0.60(150) = -30$, i.e. losing $30 per trade.

What this means in practice

This is why trend-following strategies, which often win on well under half their trades but let winners run far longer than losers, can still be reliably profitable — and why a strategy with a very high win rate but a poor payoff ratio (small wins, occasional catastrophic losses, common in strategies that sell tail risk) can look great on a win-rate headline while quietly having negative expectancy.