Risk–reward and win rate: the maths of a profitable strategy
- What risk–reward (R) means, and how to measure it
- The break-even win rate for any risk–reward
- Expectancy: the one number that says whether a strategy makes money
Two numbers, always together
Beginners ask "what's your win rate?". Professionals ask "what's your win rate at what risk–reward?". Neither number means anything alone.
Risk–reward compares what a trade can win to what it can lose. Stop 20 pips away, target 40 pips away: you risk 1 to make 2, a 1:2 trade, or a 2R target. Thinking in R (multiples of what you risked) makes trades comparable whatever their size.
The break-even win rate
For any risk–reward there's a win rate below which you lose money, even before costs:
| Risk–reward | Break-even win rate |
|---|---|
| 2:1 (win 0.5R) | 66.7% |
| 1:1 | 50.0% |
| 1:2 | 33.3% |
| 1:3 | 25.0% |
A strategy that wins only 40% of the time can be very profitable at 1:2. One that wins 80% can lose money if each win is small and each loss is big.
Expectancy: the number that matters
40% wins at 2R, 60% losses at 1R: 0.40 × 2 − 0.60 × 1 = +0.20R per trade. At $100 risked per trade, that's an average of +$20 a trade over many trades.
Positive expectancy is the definition of an edge. It says nothing about the next trade, only about the next hundred.
The high-win-rate trap
Some strategies (and some signal sellers) advertise 90% win rates. Look at the average loss. Grid and martingale systems win small almost every time and then lose huge, often wiping out months of gains in one move. A 90% win rate with wins of 0.1R and losses of 2R has an expectancy of 0.9 × 0.1 − 0.1 × 2 = −0.11R: it loses money slowly, then suddenly.
Try it
- Chasing a high win rate by taking profits early and letting losses run: it ruins the risk–reward.
- Judging a strategy on 10 trades. Expectancy needs a large sample.
- Forgetting costs: on short targets, spread and commission eat into every R.
Check yourself
- Win rate means nothing without risk–reward, and the other way round.
- Break-even win rate = 1 ÷ (1 + reward-to-risk).
- Positive expectancy over many trades is what an edge is.