Trading expectancy: win rate, R multiples and costs

What expectancy measures

For a simplified two-outcome model, expectancy is win probability times average win minus loss probability times average loss, then minus average costs if those costs are not already included. Use realized average outcomes for a retrospective calculation. A planned target is not the same as an average achieved win, and a historical average is not a forecast.

Use a common unit

An R multiple expresses an outcome relative to a defined initial risk amount. A $150 gain with $100 initial risk is +1.5R; a $120 loss is −1.2R. State whether the reference risk includes fees. Using a different denominator for winners and losers makes the average difficult to interpret. If each trade has different dollar risk, average R and average dollars are different summaries.

A worked two-outcome example

Hypothetical win rate 40%, average winner 2R and average loser 1R give 0.4 × 2 − 0.6 × 1 = +0.2R before costs. At 0.1R average cost per trade, net modeled expectancy is +0.1R. With 100 equal-risk $10 trades, the model average is $1 per trade, not a promise of a $100 final profit or a smooth path.

Break-even depends on costs

With fixed win W, loss L and per-trade cost C, break-even win probability is (L + C) / (W + L). For W = 2R, L = 1R and C = 0.1R it is 36.67%. The cost must use the same unit and apply to each trade. When net wins and losses already contain costs, subtracting C again would count the same cost twice.

Planned risk/reward is only a payoff shape

A 3R target says how the planned reward compares with planned risk. It does not supply a win probability or show what partial exits achieve. Stop slippage, early exits and failed targets change realized outcomes. Compare the risk/reward calculator with actual or explicitly hypothetical averages rather than converting a target ratio into a success claim.

Averages do not describe the whole distribution

Two sets can share the same expectancy and have very different drawdowns, tail losses and dependence between trades. A few unusually large winners can dominate a small sample. Recording 20 trades does not establish a stable probability. Include sample size, date range, costs, selection rules and missing results; do not discard losing trades after seeing them.

Test assumptions rather than tune a result

Use the scenario calculator to vary win rate, average loss and costs. Keep the same definitions across cases. Backtesting, out-of-sample checks and forward observation address different questions, and none proves that future conditions will match. A mathematical positive expectation is not a recommendation to trade or a validation of a strategy.

Practice with an explicit counterexample

Compare a high-win-rate case with large occasional losses against a lower-win-rate case with larger average wins. Then add the same costs to both. Explain which input changed the sign and why. This exercise is entirely local and uses user-entered numbers; it does not import performance results or invent a trading history.