Expectancy: connecting win frequency and outcome size

How it works

Average trade result equals win frequency times average win minus loss frequency times average loss. Deduct costs separately only when those outcomes are before costs.

Do not deduct costs twice when the journal already records net results. Include breakeven trades consistently, either as a separate share or by averaging all rows directly. Always show sample size. Define R as the initially planned cash risk of each trade and do not change that denominator after seeing the outcome. With different risk amounts, average R and cash profit describe different quantities: cash profit is the sum of each R outcome multiplied by its own initial cash risk. Increasing exposure on losing trades can worsen cash performance even when the R statistics are unchanged. Separately distinguish average percentage return per period from cumulative capital change. With no external cash flows and all expenses already included, let r be the period return as a decimal: C₂ = C₀ × (1 + r₁) × (1 + r₂). This differs from average R or the sum of percentages. The chain below is our own hypothetical calculation, not a strategy result.

A hypothetical example

Ten hypothetical trades: four earn +2R and six lose −1R. Total +2R before costs. Costs of 0.1R per trade leave +1R, or +0.1R per trade. The next sample may differ. More observations, new periods and robustness checks are needed. A separate hypothetical counterexample, without costs, deposits or withdrawals: the first trade risks 10 cash units and earns +1R = +10; the second risks 100 and loses −1R = −100. Win rate is 50% and average (+1 − 1) / 2 = 0R, yet cash profit is +10 − 100 = −90. If both trades risked 10, cash profit would be zero. These invented figures check units of measurement; they do not recommend a position size. Another independent hypothetical example: start with 100 cash units, then earn net returns of +20% and −20%, each measured against capital at the start of its period. Capital becomes 120, then 120 × 0.80 = 96. The arithmetic average is 0%, but cumulative return is −4%. The counterclaim “the percentages cancel” is false because their calculation bases differ. After a separate fall from 100 to 80, recovery to 100 requires (100 / 80 − 1) × 100% = 25%, not 20%. These examples have no deposits or withdrawals; all expenses are assumed already included.

Try it yourself

Use consecutive trades from one version of the rules. Compute win rate and average win/loss in R, then verify against the total result. For each row, divide the net cash result by the initial cash risk. Add cash results directly and reconcile with the sum of R × initial risk. If initial risk is zero or unknown, do not assign an R denominator retrospectively; mark the gap. Do not change risk to improve the statistics. In a separate table, build the chain 100 → 120 → 96. Reconcile final capital, average percentage return and cumulative return. Then calculate recovery from 80 to 100. Do not mix these percentages with R or deduct expenses already included.

Win rate 40%, average win 2R, average loss 1R and average costs 0.1R. What is the estimated average? For the separate pair +1R with initial risk 10 and −1R with initial risk 100, find average R and cash profit. What changes if both initial risks equal 10? In the independent no-flow example, capital of 100 earns net +20%, then −20%. Find final capital and cumulative return. Why does an average of 0% not mean no loss? What gain takes 80 back to 100?