Kelly Criterion

Developed by John Kelly at Bell Labs in 1956 to model information-theory bets, the Kelly Criterion gives the fraction of capital to risk on a single trade that maximizes the expected logarithm of wealth. The classic formula is Kelly% = W − (1 − W) / R, where W is win rate and R is the average win divided by the average loss.

Full Kelly assumes the inputs are perfectly known. Real trading inputs are noisy: a 55% win rate measured over 50 trades has a wide confidence interval, and a true rate of 48% would push the Kelly fraction sharply lower or even negative. Acting on full Kelly with estimation error produces drawdowns that can be 40-60% deep — most traders abandon a system long before that.

The professional standard is fractional Kelly, typically a quarter (0.25× full Kelly). Quarter-Kelly captures roughly 75% of the long-run growth rate of full Kelly while halving expected drawdown. Adding Bayesian shrinkage — blending a setup-specific win rate toward a global prior when sample size is small — further protects against over-sizing on noisy data.

Formula

Kelly% = W − (1 − W) / R
W = win rate (e.g. 0.55)
R = avg win / avg loss

How PerpLog uses Kelly Criterion

PerpLog's Adaptive Sizing engine implements quarter-Kelly with Bayesian shrinkage across segmented trader stats (session, playbook, day-of-week, streak). Drawdown-constrained Kelly caps recommendations when historical drawdown exceeds the trader's tolerance.

Related reading

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