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Key Takeaways
- Expectancy combines win rate with the average size of wins and losses, so no single input determines profitability.
- A strategy can have positive expectancy with a low win rate when winners are sufficiently larger than losers.
- Measure expectancy on completed trades, each at its full net result after costs; signals that never filled belong in a separate per-signal count.
- Compare expectancy setup by setup and holding period by holding period to find where the edge lives.
- Express each net outcome in units of its own initial planned risk to calculate R-multiple expectancy.
What is trading expectancy?
Trading expectancy is the probability-weighted average payoff of a defined trade: the amount a strategy earns or loses per trade on average once wins, losses and their frequencies are combined. From a completed record, its sample estimate is total net profit or loss divided by the number of completed trades. Positive expectancy means the average net outcome is above zero.
The same estimate comes from weighting average wins and losses by their frequencies. Include exact zero-net scratches as a separate category when present.
Formula
Expectancy = (win probability × average net win) − (loss probability × average net loss magnitude)- Average loss is entered as a positive magnitude in this version of the formula.
- Give zero-net scratches their own probability, so win, loss and scratch probabilities sum to 1; with no scratches, loss probability is 1 minus win probability.
Trading expectancy example: 120 trades
A strategy records 120 completed trades, each with $180 initial planned risk: 48 net winners averaging $360 and 72 net losers averaging $180.
- 48 / 120 = 40% win rate and 72 / 120 = 60% loss rate
- 0.40 × $360 = $144 weighted average win
- 0.60 × $180 = $108 weighted average loss
- $144 − $108 = $36 expectancy per trade
The historical expectancy is positive $36 per trade even though the strategy loses more often than it wins because its average winner is twice its average loser.
The 48 winners average $360, contributing $17,280. The 72 losers average $180 in loss magnitude, subtracting $12,960. Net profit is $4,320, or $36 per completed trade.
The chart gives every trade $180 initial planned risk. Winners average +2R and losers average −1R, producing 0.40 × 2R − 0.60 × 1R = +0.20R.
The chart shows the path to the $36: 40 of the 72 losers stop out at −1R and 16 run past the stop to −1.5R, while the winners stretch from +0.5R to +4.0R.
How to count trades, costs and unfilled orders
Treat each position as one trade: entries, partial exits and any exercise or assignment that follows roll into a single net result.
Fills already carry the spread and slippage, so subtract only the separately charged fees and financing, once each. To see what execution cost, compare the fills with a reference price such as the midpoint at order time.
Leave unfilled orders out of the trade count. Track them in a separate per-signal figure, which shows how many setups the execution rules let through.
Expectancy in R multiples
Divide each trade’s net result by its own initial planned dollar risk. A $400 gain on $200 planned risk is +2R; a $250 loss on $500 planned risk is −0.5R.
Average those individual R outcomes. Dividing the average dollar result by the average risk gives a different, risk-weighted figure whenever initial risks vary, so pick one method and keep it.
Expectancy vs win rate, drawdown and compounding
Review win rate, average gain, average loss and costs by the selected setup. Compare holding time, drawdown and capital usage alongside expectancy, and use the completed trade record to compare planned payoffs with actual net outcomes.
For a fixed number of trades with the same expected dollar payoff, expected total profit is trade count times that payoff: 120 trades at $36 is $4,320. Once position sizes change with the account, model the account path instead.
Limitations of trading expectancy
- Trust the number in proportion to the sample. A short record leaves wide uncertainty, and a new period or market regime can move it, so keep updating it as trades complete.
- The average hides the path. Two strategies with the same expectancy can have very different drawdowns and losing streaks, so size for the streak.
- Match the trade definition and cost accounting before you compare two samples.
- Use R when risk varies from trade to trade, because dollar expectancy then overweights the biggest positions.
- Multiply expectancy by trade count only at a fixed size: 120 trades at $36 is $4,320. With compounding or changing sizes, model the account instead.
Bottom line
Trading expectancy shows what a strategy earns or loses per trade on average once win rate and the size of wins and losses are combined. Calculate it from complete net results, express it in R to compare setups, and read it with the trade count, drawdown and full outcome distribution.
Clear answers
Frequently Asked Questions
Sources and Further Reading
How entries are sourced, calculated and updated: editorial methodology.