Risk-Reward Ratio And Win-Rate Math
The relationship between reward-to-risk and how often you need to be right is fixed arithmetic, not a matter of trading philosophy.
The breakeven strike rate for any reward-to-risk ratio R is 1 divided by (1 + R). A 1 to 1 trade needs half the trades to work, a 2 to 1 trade needs one in three, and a 3 to 1 trade needs one in four. A method risking more than it targets needs to be right two times in three just to stand still, before any costs are deducted.
What to remember
- Breakeven is 1 divided by (1 + R). At 2 to 1 that is one win in three, at 3 to 1 it is one in four.
- Expectancy is the probability of winning times the average win, minus the probability of losing times the average loss. It is the number that matters.
- Cutting winners short can flip a method to breakeven without any change to the entry, which makes it the most expensive common habit in trading.
- Eight wins at 10 pips against two losses at 50 pips is a losing sequence that feels like a winning one.
Step 8 of 10 on Strategy Building Blocks
The breakeven table, which settles most arguments
Risk-reward ratio compares what a trade risks against what it targets. Win rate is the proportion of trades that end in profit. Neither number means anything alone, and the relationship between them is fixed arithmetic rather than opinion.
The breakeven point for any reward-to-risk ratio R is 1 divided by (1 + R), expressed as a percentage. That produces this table, which is worth knowing by heart.
| Reward to risk | Breakeven strike rate | Meaning |
|---|---|---|
| 0.5 to 1 | 66.7% | Two out of three must win just to stand still |
| 1 to 1 | 50% | Half, before costs |
| 1.5 to 1 | 40% | Four in ten |
| 2 to 1 | 33.3% | One in three |
| 3 to 1 | 25% | One in four |
| 5 to 1 | 16.7% | One in six |
Read across the 2 to 1 row. A strategy risking 1 to make 2 is at breakeven when one trade in three works, which means being wrong on two thirds of trades and still not losing money. Read the top row the other way: a strategy taking small profits and allowing larger losses needs to win two out of three trades just to stay level, before a single pip of cost is deducted.
Expectancy, in one line
The table is a special case of a more useful formula:
Expectancy per trade = (probability of winning x average win) minus (probability of losing x average loss)
Put numbers in it. A method that makes $60 on winners, loses $30 on losers, and wins four trades in ten: (0.4 x 60) minus (0.6 x 30) = 24 minus 18 = $6 per trade. Over 100 trades that is $600, assuming the averages hold.
Now change one variable. Hold the same four-in-ten strike rate but let the average win slip to $45 because of early exits: (0.4 x 45) minus (0.6 x 30) = 18 minus 18 = 0. The method is now breakeven, and nothing about the analysis changed. The behaviour did. That single sensitivity is why cutting winners short is the most expensive common habit in trading.
Costs move the line, and they move it more than people expect
The table above is before costs. Spread and commission are deducted from every trade, winners and losers alike, which shifts the breakeven point upward.
Consider a 2 to 1 setup risking 20 pips to make 40 on a pair with a 1.5-pip spread. The effective risk is 21.5 pips and the effective reward is 38.5, which is 1.79 to 1 rather than 2 to 1. The required strike rate moves from 33.3% to about 35.8%. On a 50-pip stop and a 100-pip target the same spread costs far less proportionally, which is exactly why short-term methods need a better strike rate than longer-term ones to reach the same result. Work your own numbers through the profit calculator using realistic fills rather than the intended ones.
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Risk-Reward Ratio And Win-Rate Math: questions
What is a good risk-reward ratio?
Can you be profitable with a low win rate?
How do you calculate expectancy in trading?
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