Expectancy: Win Rate Isn't Everything
A 40% win rate can make money, and an 80% win rate can still blow up. What decides the outcome is win rate combined with payoff ratio.
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Text version · Risk Management & Trading Psychology, lesson 3: “Expectancy: Win Rate Isn't Everything”
A 40% win rate can make money, and an 80% win rate can still blow up. What decides the outcome is win rate combined with payoff ratio.
Win rate × payoff
expectancy = win rate × average win − loss rate × average loss. Measured in R-multiple, trades of different sizes can be compared side by side.
How high a win rate do you need to break even?
Breakeven win rate = 1 ÷ (1 + payoff ratio). With a 2:1 payoff ratio, winning more than 1/3 of the time makes money; at 0.5:1, you need to win more than 2/3. A high-win-rate strategy doesn't necessarily make money.
Expectancy pays off over many trades
+0.2R per trade looks small, but over 100 trades it's about +20R. In the short run the order is random, though: losing money over a few dozen trades is normal. The key is to strictly follow the same trading rule.
Key takeaways
- Expectancy = win rate × average win − loss rate × average loss (measured in units of risk per trade, R).
- Win rate needed to break even = 1 ÷ (1 + payoff ratio): with a payoff ratio of 2, you only need to win more than 1/3 of the time to profit over the long run.
- With a high win rate and a low payoff ratio, one big loss can wipe out dozens of small wins.
- Expectancy only pays off over enough trades. Within a few dozen trades, results are mostly luck.
Try it yourself
You can do these exercises in this lesson's interactive simulation:
- 40% win rate, 2:1 payoff ratio: what's the expectancy per trade? Roughly how many R do you have after 100 trades?
- Raise the win rate to 60% and lower the payoff ratio to 0.5:1: the win rate is higher, but what's the expectancy? What win rate do you need to break even?
- Set the win rate to 25% with a 3:1 payoff ratio: what's the expectancy? Find the cells in the table that show 0.0: what kind of line do they form?
- With the win rate fixed at 40%, what's the minimum payoff ratio to break even? Drag the payoff ratio there to check.
Quiz and explanations
- 1. A 40% win rate, winning 2R and losing 1R. What's the expectancy per trade?
- Answer: +0.2R.0.4 × 2 − 0.6 × 1 = 0.2R.
- 2. A strategy has a 3:1 payoff ratio. What's the minimum win rate to avoid losing money?
- Answer: 25%.1 ÷ (1 + 3) = 25%.
- 3. A 55% win rate, average win 1.2R, average loss 1R, over 200 trades. Roughly what's the expected total?
- Answer: 42R.Per trade: 0.55 × 1.2 − 0.45 × 1 = 0.21R, so about 42R over 200 trades.
Terms in this lesson
- expectancy (Expectancy): What you make per trade on average over the long run: win rate × average win − loss rate × average loss; only worth trading if positive.
- R-multiple (R-Multiple): Measuring results in units of planned risk: the amount you'd lose at your stop is 1R, so making twice that is +2R.
- risk/reward ratio (Risk : Reward): Money you could lose : money you could make; 1:2 means risking $1 to aim for $2.
- trading rule (Trading Rule): Entry, exit and stop-loss conditions fixed in advance that can be checked candle by candle, so they can be tested on historical data.
- win rate (Win Rate): The share of all trades that made money.