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Standard error of expectancy

The uncertainty around your measured edge, computed from the spread of trade results and the number of trades.

Standard error = standard deviation of R multiples / sqrt(n). If your trades have a standard deviation of 1.6R and you have 100 of them, the standard error of your mean is 0.16R.

Put that next to a measured expectancy-per-trade of plus 0.22R. Two standard errors is 0.32R, so the 95% interval runs from minus 0.10R to plus 0.54R - it includes zero. After 100 trades, a seemingly solid edge has not been demonstrated at all. To get the interval clear of zero you need roughly n > (2 x 1.6 / 0.22)^2 ≈ 212 trades, and that assumes the edge is stable throughout.

This single calculation resolves most arguments about whether a strategy is working. It also explains why outlier-dependent systems need enormous samples: their R standard deviation is large, so the numerator of the standard error stays high.

Related: sample-size-for-edge, expectancy-per-trade, win-rate-confidence-interval, outlier-dependence

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

The spread of outcomes behind an expectancyA histogram of forty trades: a tall block of small losses on the left, a low spread of larger wins on the right, and a line marking the average outcome.NUMBER OF TRADES051024 LOSSES, AVG −$20016 WINS, AVG +$600EXPECTANCY +$120−$400−$200$0+$200+$400+$600+$800PROFIT OR LOSS PER TRADEexpectancy = (40% × $600) − (60% × $200) = +$120 per trade
Expectancy: the average trade. Forty trades sorted by outcome: 24 small losses and 16 larger wins. Weighting each side by how often it happens gives the average result per trade, marked here by the dashed line at +$120.

Educational only, not advice. Spotted an error? Post in Site Feedback.