Formula, in Backtesting & Validation
Expectancy Formula
Expectancy is the average profit (or loss) a system produces per trade: the win rate times the average win minus the loss rate times the average loss. It is the single most important number for a trading system, because a positive expectancy traded repeatedly with sound sizing compounds, while a negative one guarantees ruin no matter how exciting the winners look.
5 variables. Published May 26, 2026. By AI Fin Hub Research.
Expectancy = (WinRate x AvgWin) - (LossRate x AvgLoss)
R-multiple form: Expectancy_R = (WinRate x AvgWin_R) - (LossRate x 1)
where LossRate = 1 - WinRate and AvgWin_R is the average win in units of initial risk Variables
WinRate
Win rate
Fraction of trades that close profitably.
AvgWin
Average win
Mean profit of winning trades. Expectancy weights it by how often wins occur.
LossRate
Loss rate
Fraction of trades that close at a loss, equal to 1 minus the win rate.
AvgLoss
Average loss
Mean loss of losing trades, as a positive number. Subtracting the probability-weighted average loss from the probability-weighted average win yields the per-trade edge.
AvgWin_R
Average win in R
Average win measured in multiples of the initial risk (R). Framing expectancy in R-multiples makes it independent of position size and comparable across setups.
Step by step
- 1
Determine the win rate and loss rate.
Win rate 0.40, loss rate 0.60.
- 2
Determine the average win and average loss in currency or in R-multiples.
Average win 250, average loss 100 (so average win is 2.5R if risk per trade is 100).
- 3
Multiply win rate by average win and loss rate by average loss.
0.40 x 250 = 100; 0.60 x 100 = 60.
- 4
Subtract the second from the first for expectancy per trade.
100 - 60 = 40 profit per trade.
Worked example
Breakout system with a 40% win rate, risking 100 per trade
Win rate / loss rate
0.40 / 0.60
Average win / average loss
250 / 100
Expectancy = (0.40 x 250) - (0.60 x 100) = 100 - 60 = 40 per trade. In R-multiples, average win is 250/100 = 2.5R, so Expectancy_R = (0.40 x 2.5) - (0.60 x 1) = 1.0 - 0.6 = 0.4R per trade.
Expectancy of +40 per trade, or +0.4R. Each trade is worth, on average, 40% of the amount risked. Over 200 trades that is roughly 80R of expected edge before compounding, which is what makes the system worth trading despite losing 60% of individual trades. Expectancy says nothing about the path, so pair it with drawdown and Kelly sizing.
Common variations
Run the numbers next
- Calculators Kelly Criterion Calculator
Size positions with full, half, quarter, or eighth Kelly and stress-test the choice with a drawdown Monte Carlo simulator. Client-side. Private by default.
- Playgrounds Execution Simulator
Estimate execution cost in closed form — square-root permanent impact, linear temporary impact, half-spread, and a latency-drift band. See the slippage a naive backtest hides.
Sources
- Trade Your Way to Financial Freedom , Van K. Tharp, McGraw-Hill (2006)
- The Mathematics of Money Management , Ralph Vince, Wiley (1992)
Keep the topic connected
- Formula Win Rate Formula
The win rate formula: winning trades divided by total trades. Why win rate alone is meaningless without the payoff ratio, with a breakeven example.
- Formula Profit Factor Formula
The profit factor formula: gross profit divided by gross loss. A single number summarizing a strategy's edge, what values mean, with a worked example.
- Formula Kelly Criterion Formula
The Kelly criterion formula: the bet fraction maximizing long-run log growth from win probability and payoff odds. The optimal sizing rule.
- Learn Kelly Criterion
What the Kelly criterion is, when full Kelly blows up, and why most working quants size at half- or quarter-Kelly.