Risk to reward and win rate: what the maths says

Two numbers describe most of a strategy: how often it wins, and how much it makes on a win compared with what it loses on a loss. On their own each is misleading. Together they tell you whether the strategy can make money at all.

Risk to reward in one line

The ratio is the distance from entry to target divided by the distance from entry to stop. If you enter at 1.0850, put the stop at 1.0820 and the target at 1.0940, you risk 30 pips to make 90, a ratio of 1:3.

Win rate in one line

Win rate is the share of trades that close in profit. It says nothing about size. A strategy can win 70% of the time and lose money if its losers are much larger than its winners.

The break-even win rate

For any ratio, there is a win rate below which you lose money over many trades. It equals 1 divided by (1 plus the ratio), before costs:

• 1:1 needs to win 50% of trades.
• 1:2 needs to win about 33%.
• 1:3 needs to win 25%.
• 1:0.5, risking two to make one, needs to win about 67%.

Spreads, commissions and slippage push each of these up, so the real break-even is higher. On short-term trades with tight stops the cost drag can be a large share of the gross result.

Expectancy: putting both together

Expectancy is the average result per trade: the win rate times the average win, minus the loss rate times the average loss. With a 40% win rate, an average win of 300 and an average loss of 100, expectancy is (0.4 times 300) minus (0.6 times 100) = 60 per trade, before costs.

A positive expectancy is necessary, not sufficient. It is estimated from past trades, so it is only as reliable as the sample behind it, and it can change when market conditions change.

Why a high ratio is not a free lunch

It is easy to draw a target far away and call the trade 1:5. But a distant target is reached less often, so the win rate falls as the ratio rises. Good targets sit at levels where price has a reason to pause, such as prior highs and lows, not at whatever number makes the ratio look attractive.

Three example strategies

• Strategy A wins 35% of trades, with an average win of 3R and an average loss of 1R. Expectancy per trade is (0.35 x 3) minus (0.65 x 1) = 0.40R.
• Strategy B wins 60% of trades, with an average win of 1R and an average loss of 1R. Expectancy is (0.6 x 1) minus (0.4 x 1) = 0.20R.
• Strategy C wins 70% of trades, with an average win of 0.5R and an average loss of 1.5R. Expectancy is (0.7 x 0.5) minus (0.3 x 1.5) = -0.10R, a losing strategy despite the high win rate.

Here R means the amount risked on a trade. Measuring results in R makes strategies comparable regardless of account size. Notice that the strategy with the lowest win rate has the best expectancy, and the one with the highest loses money. That is the point of looking at both numbers together.

What costs do to the numbers

Suppose the spread and commission on a trade cost 0.1R. Strategy A's expectancy drops from 0.40R to 0.30R, Strategy B's from 0.20R to 0.10R, and Strategy C's from -0.10R to -0.20R. Strategy B has lost half its edge. Costs scale with how often you trade and how tight your stops are, so high-frequency, tight-stop approaches are the most exposed.

Sample size and honesty

A win rate calculated from 20 trades is very noisy. Fifty trades tell you a little more, and a few hundred a lot more, provided the market conditions were varied. Journal every trade, including the ones you would rather forget, and resist choosing which trades to count. A results table that leaves out the bad days is not measuring your strategy.

Turning it into a rule

1. Define your setup precisely enough that two people would agree whether a trade qualifies.
2. Record every trade of that setup in R, including costs.
3. Review expectancy after a meaningful sample, and reduce size if it turns negative.
4. Only change one variable at a time, so you know what moved the result.

Use it before, and after, the trade

1. Before entering, calculate the ratio from the actual stop and target, including the spread.
2. Skip trades whose ratio does not clear your own minimum, whatever that is for your strategy.
3. After enough trades, calculate your real win rate and average win and loss from your journal.
4. Compare your real expectancy with what you assumed. If they differ, fix the assumption, not the maths.

Key takeaways

• Break-even win rate = 1 / (1 + reward to risk), before costs.
• Expectancy combines win rate with average win and loss.
• Measure results in R so strategies compare fairly.
• Costs cut deepest into tight-stop, high-frequency approaches.
• Small samples mislead, so record every trade.