Estimate expectancy before you accept the trade

Filter the setup before you size

A position should be sized and accepted only after both gain probability and payoff odds are estimated. Expected value depends on both inputs, so a higher Risk-reward ratio can still produce a more negative expectancy than a more frequent but smaller win.

Editorial interpretation: treat the trade as an expectancy filter. If the product of gain probability and payoff odds is not clearly positive, refuse the setup instead of accepting it on payoff size alone.

Short samples do not flip a negative edge

With n around 100, binomial standard error of about 0.49 placed 95% win-count limits near 59 to 61. That spread shows that short-sample variance does not rescue a structurally negative expectancy.

Gain probability is not a coin toss

Gain probability can be estimated from historical frequency, a mathematical model, or simulation. Market closes are not a clean binary process: unchanged days occur, and long-run up-day frequency can sit outside a 50/50 interval.

Over a century of DJIA daily closes, up days were about 53% versus 47% down. A 95% interval under a fair-coin model ran from 49.4% to 50.6%, so a simple 50/50 coin model is a poor input for expectancy.

Read payoff against probability

A 10-day average payoff ratio plotted against the 10-day p/q probability ratio can be read against a zero-expectancy Breakeven line and a focus line that shows whether probability or payoff is dominating the path. The Payoff Index keeps that comparison in view over a defined sampling interval.

In the illustrated 12-month SPY window, the path started below breakeven, crossed on the probability side, then later moved into the payoff-dominant region and away from zero expectancy.