Kelly Criterion & +EV Bankroll Stake Calculator
Compute mathematically optimal wager sizing based on sports betting odds, estimated true win probabilities, and fractional Kelly risk controls.
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Kelly Criterion Mathematical Formulation
Developed by mathematician J. L. Kelly Jr. in 1956 at Bell Labs, the Kelly Criterion calculates the proportion of a bankroll to commit on a favorable bet to maximize logarithmically cumulative long-term capital compounding:
f* = (b * p - q) / b
Where:
- f*: Fraction of the bankroll to wager.
- b: Net odds received on the wager (Decimal Odds minus 1).
- p: Probability of winning (your assessed true likelihood).
- q: Probability of losing (1 - p).
Why Fractional Kelly (1/2 or 1/4) Is Critical
While theoretical Full Kelly achieves the fastest theoretical compounding rate, it subjects sports bettors to severe peak-to-trough drawdowns exceeding 50% due to estimation error in win probability. Practical quantitative sports bettors employ Fractional Kelly (typically 0.5x or 0.25x), which retains 75% to 90% of the maximum growth rate while reducing bankroll volatility by more than half.