Confidence interval

A range built from a sample by a method that, over many repeated samples, contains the true value in a stated share of them, such as 95%. Small samples give wide intervals.

A rough interval for expectancy is average ± 1.96 × (standard deviation per trade ÷ √n). For a share, such as how often a target is reached, the Wilson interval works better on small samples: 12 of 30 (40%) gives about 25% to 58% (computed, Illustrative). The 95% describes the method, not one particular range.

Losing streaks

Runs of losses follow from the loss rate alone. At a 45% loss rate with independent trades, at least one run of 5 or more losses appears in about 65% of 100-trade blocks (computed, Illustrative). A streak is evidence of change only alongside something checkable, such as rising costs.

Optional stopping

Checking results repeatedly and stopping at the first good-looking one inflates false findings. In a simulated zero-edge process, one check at 100 trades "passed" in about 2% of runs; checking every 10 trades did so in about 11% (computed, Illustrative).

What traders should verify

Fix the sample size before a block, evaluate once at the end and report each figure with its interval and n. Treat clustered trades in the same stock and morning as fewer independent observations.

Do not conflate

The formulas assume independent trades; correlated scalps make intervals look narrower than they are. An interval that covers zero or breakeven has not shown an edge, and one that excludes it can still be a chance result.

Primary source

Wilson, 1927