Risk-reward ratio, win rate and expectancy: the maths behind a trading edge

Two numbers decide whether a trading method makes money over time: how often it wins, and how much it wins compared with how much it loses. Either number on its own is misleading.

Measuring trades in R

Expressing results as multiples of the amount risked makes trades comparable. Risk $50 and lose it, and the result is −1R. Make $100 on the same risk, and it's +2R. A method's win rate, average win and average loss in R describe it better than its dollar profits, because they don't change when position size does.

Expectancy

Expectancy is the average result per trade:

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

Two examples in R:

• 40% winners averaging 2R, losers averaging 1R: (0.40 × 2) − (0.60 × 1) = +0.2R per trade. Over 100 trades risking $50 each, that's about +$1,000 before costs.
• 60% winners averaging 0.5R, losers averaging 1R: (0.60 × 0.5) − (0.40 × 1) = −0.1R per trade. It wins more often and still loses money.

Break-even win rates

With a fixed reward-to-risk ratio, the win rate needed to break even before costs is 1 ÷ (1 + reward-to-risk):

• 1:1 needs 50% winners
• 1:1.5 needs 40%
• 1:2 needs about 33.3%
• 1:3 needs 25%

A bigger target lowers the win rate you need, but distant targets are reached less often. Ratio and win rate pull against each other, which is why expectancy is the number to track.

Costs change the maths

Spread, commission and swap come out of every trade. On a trade risking 10 pips, a 1-pip spread costs 0.1R, so a method with +0.1R expectancy before costs is roughly break-even after them. The shorter your stops and targets, the more costs matter, which is a big reason scalping is hard.

Getting honest numbers

• Use a large sample. Twenty trades can make a losing method look good by chance. Aim for at least 100 before drawing conclusions.
• Record every trade, including the ones you'd rather forget, in a trading journal.
• Record results in R so changes in position size don't distort the picture.
• Expect losing streaks even with positive expectancy. A method that wins 40% of the time will regularly lose five or more trades in a row; see drawdown and recovery.