Trading Concept
Kelly Criterion
A formula that calculates the optimal fraction of capital to allocate to a bet given the probability of winning and the payoff ratio.
The Kelly criterion answers one question: given a known edge, how much of the bankroll to risk per bet to maximize long-term growth. Bet too little and growth is slow. Bet too much and a losing streak wipes out the account. Kelly finds the mathematically optimal point between the two.
The formula is simple: f = (bp − q) / b, where b is the payoff odds, p is the probability of winning, and q is the probability of losing. This formulation applies to binary outcomes — win or lose, at fixed odds. For continuous returns (equities, forex), the Kelly fraction is μ/σ², where μ is expected excess return and σ² is variance. The math differs, but the principle is the same: size proportionally to edge, inversely to uncertainty. In practice, full Kelly sizing is aggressive — most practitioners use a fraction (quarter-Kelly or half-Kelly) to reduce volatility.
In the botwir3 builder, the Kelly multiplier is a configurable parameter in band configuration. The default is 0.25 (quarter-Kelly). The module uses the multiplier to scale position sizes proposed by the strategy. The gate validates that the resulting position stays within the configured tolerance band.