Hit Rate Versus Payoff Ratio

A strategy that wins on only 35% of its trades sounds like a bad strategy — until you learn the winners average $3,000 and the losers average $1,000. Run the numbers and it's comfortably profitable, despite losing more often than it wins. Two figures determine whether a strategy makes money on average: the hit rate (the fraction of trades that are winners) and the payoff ratio (average win size divided by average loss size). Neither number means anything on its own — a strategy report that leads with "68% win rate" and stops there has told you almost nothing.

Expectancy ties the two together

The per-trade expected profit is

$$E = p \cdot W - (1-p) \cdot L ,$$

where $p$ is the hit rate, $W$ is the average size of a winning trade, and $L$ is the average size (as a positive number) of a losing trade. In plain English: expected profit per trade is a probability-weighted blend of what you typically make when you're right and what you typically give back when you're wrong.

Setting $E = 0$ and solving gives the breakeven hit rate a strategy needs for a given payoff ratio:

$$p^{*} = \frac{L}{W + L} .$$

In plain English: the bigger your average win relative to your average loss, the lower a hit rate you can tolerate and still turn a profit. A strategy with a 3-to-1 payoff ratio only needs to win 25% of the time to break even; a strategy with a 1-to-2 payoff ratio needs to win two-thirds of the time.

Worked example 1: a trend-following strategy

Hit rate $p = 0.35$, average win W = \3{,}000$, average loss$L = $1{,}000$. Expectancy:$E = 0.35 \times 3000 - 0.65 \times 1000 = 1050 - 650 = $400$ per trade — solidly profitable on a low hit rate, because the rare winners run far and the frequent losers are cut small. This is the classic shape of a trend follower: lots of small stop-outs, occasional large trends that pay for all of them.

Worked example 2: a mean-reversion strategy

Hit rate $p = 0.65$, average win W = \800$, average loss$L = $1{,}000$(payoff ratio below 1). Expectancy:$E = 0.65 \times 800 - 0.35 \times 1000 = 520 - 350 = $170$per trade — also profitable, but far thinner, and much more sensitive to the hit rate. Drop$p$to 0.55 and expectancy turns negative:$0.55 \times 800 - 0.45 \times 1000 = 440 - 450 = -$10$. A high-hit-rate strategy has less room to absorb a regime where it stops winning as often.

What this means in practice

Never quote a hit rate without a payoff ratio, and never quote a payoff ratio without a hit rate — a due-diligence reviewer should ask for both in the same sentence. The two also carry different fragility: a high-hit-rate, low-payoff strategy (typical of market making or short-dated mean reversion) can be wiped out by a small drop in hit rate, while a low-hit-rate, high-payoff strategy (typical of trend following) can tolerate long losing streaks as long as the occasional big winner keeps arriving on schedule. Position sizing and stop discipline usually matter more for the first kind; patience and the ability to sit through drawdowns matter more for the second.