Expectancy, win rate and R: which number actually matters

Ask a trader how they are doing and you will usually hear a win rate. It is the most quoted statistic in trading and close to the least informative one, because it deliberately throws away the only thing that decides whether a strategy makes money: how big the wins are compared to the losses.

The three numbers, in order of usefulness

R-multiple

One R is the amount you risked on a trade: the distance from entry to your initial stop, times position size. A trade that makes twice what you risked is +2R. One that hits your stop is −1R. Expressing every result in R rather than currency is what lets you compare a futures trade against an equity trade, or this month against a month when you were sizing differently.

Win rate

The share of trades that finish positive. Useful only next to average win and average loss. On its own it is a number you can raise at will by taking profits earlier, which usually makes you less money while making the statistic look better. That is a genuinely perverse incentive, and one that a lot of traders follow without noticing.

Expectancy

What you expect to make, in R, per trade taken. It is the number that actually answers "is this worth doing", and it folds the other two together.

Expectancy = (win rate × average win in R) − (loss rate × average loss in R)

Why a 35% strategy can beat a 65% one

Two traders, a hundred trades each.

• Trader A wins 65% of the time. Average win 0.5R, average loss 1R. Expectancy = (0.65 × 0.5) − (0.35 × 1) = 0.325 − 0.35 = −0.025R per trade. Losing money, with a win rate most traders would envy.
• Trader B wins 35% of the time. Average win 3R, average loss 1R. Expectancy = (0.35 × 3) − (0.65 × 1) = 1.05 − 0.65 = +0.40R per trade. Over a hundred trades that is +40R.

Trader B loses roughly two out of every three trades and is enormously more profitable. If you only ever look at win rate, A looks like the trader to copy. That is exactly the mistake trend-following traders spend their first two years being talked out of.

How to work yours out

1. Take your last hundred closed trades. Fewer than about thirty and you are measuring noise rather than an edge.
2. Convert each result to R by dividing by the risk you had on at entry, not by the currency amount you ended up with.
3. Average the positive ones. Average the absolute value of the negative ones. Count the share that were positive.
4. Put them in the formula. If the answer is positive, the method makes money at that sample size. If it is near zero, costs and slippage will decide it, and they usually decide against you.

Then do it once more per setup rather than across the book. An overall expectancy of +0.1R often hides one setup at +0.6R and another at −0.3R, and the single most profitable change available to most traders is to stop taking the second one.

The trap in the denominator

Expectancy is per trade taken, so it improves if you take fewer bad trades and also if you simply take fewer trades. Read it beside your trade count. A setup at +0.8R that appears twice a month is a good filter; the same number on a setup that appears twice a year is a statistical accident you should not restructure anything around.