Win Rate Formula
Win rate is the number of winning trades divided by the total number of trades. On its own it says nothing about profitability: a system can win 90% of the time and still lose money if the losses are large enough. Win rate is only meaningful paired with the payoff ratio, through the breakeven win rate that the payoff implies.
Formula
Copy the exact expression or work through it step by step below.
WinRate = Winners / TotalTrades
Breakeven win rate for payoff ratio R: WR_be = 1 / (1 + R)
where R = average win / average loss Variables
Winners
Number of winning trades
Count of trades that closed with a positive return.
TotalTrades
Total number of trades
All closed trades in the sample, winners plus losers (scratch trades at exactly zero are usually excluded or counted as losers by convention).
R
Payoff ratio
Average winning trade divided by the average losing trade, in absolute terms. It sets the breakeven win rate: high payoff ratios let a system profit with a low win rate, and vice versa.
WR_be
Breakeven win rate
The win rate at which expectancy is exactly zero for a given payoff ratio. A system is profitable only when its actual win rate exceeds this threshold.
Step By Step
- 1
Count the winning trades and the total number of trades.
45 winners out of 100 trades.
- 2
Divide winners by total trades for the win rate.
45 / 100 = 0.45, a 45% win rate.
- 3
Compute the payoff ratio as average win over average loss.
Average win 300, average loss 150, so R = 300/150 = 2.0.
- 4
Compare the win rate to the breakeven win rate 1/(1+R) to judge whether the system is profitable.
WR_be = 1/(1 + 2.0) = 0.333; the 45% win rate clears the 33.3% breakeven, so the system has positive expectancy.
Worked Example
Trend system with a low win rate but a high payoff ratio
Winners / total
45 / 100
Average win / average loss
300 / 150
Win rate = 45/100 = 0.45. Payoff ratio R = 300/150 = 2.0. Breakeven win rate = 1/(1 + R) = 1/3 = 0.3333. Since 0.45 > 0.3333, the system is profitable. Expectancy check: 0.45 x 300 - 0.55 x 150 = 135 - 82.5 = +52.5 per trade.
A 45% win rate that is comfortably profitable because the 2:1 payoff lowers the breakeven to 33.3%. This is the central lesson of the win rate: it cannot be interpreted in isolation. A 45% win rate is excellent here but would be ruinous if the payoff ratio were below 1.22 (the R that makes 0.45 the breakeven).
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Sources & References
- Trade Your Way to Financial Freedom — Van K. Tharp, McGraw-Hill (2006)
- The Mathematics of Money Management — Ralph Vince, Wiley (1992)
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