Kelly Criterion Explained: How to Size Your Sports Bets
The Kelly Criterion is the mathematically optimal bet sizing formula for maximizing long-run bankroll growth. Understanding it — and why most sharp bettors deliberately use less than it recommends — is essential to sustainable bankroll management.
The Kelly Formula
Kelly = (bp − q) / b
- b = decimal odds − 1 (net profit on a winning $1 bet)
- p = your estimated probability of winning
- q = 1 − p (probability of losing)
Example: 55% win probability, +110 (decimal 2.10).
b = 1.10, p = 0.55, q = 0.45
Kelly = (1.10 × 0.55 − 0.45) / 1.10 = 0.155 / 1.10 = 14.1% of bankroll
At standard −110, you need ~53% win rate to break even. At 55%, Kelly recommends about 4.5% of bankroll.
Why Most Sharps Use Fractional Kelly
Full Kelly is mathematically optimal but practically brutal for three reasons:
- Your edge estimate is uncertain. Kelly is very sensitive to p — a 2% overestimate of your edge changes bet size dramatically.
- Variance at full Kelly is extreme. A 30% drawdown is mathematically expected even when you're winning long-term. Most bettors abandon strategy at that point.
- You need the full bankroll available. Kelly assumes you can place every bet at exactly the calculated size.
Most professional bettors use 1/4 to 1/2 Kelly — divide the full Kelly result by 2 to 4. Half-Kelly captures about 75% of the optimal growth rate with roughly 25% of the variance.
Kelly in Practice: A Simple Framework
- Estimate your win probability for the bet honestly
- Calculate full Kelly using the formula above
- Bet 1/4 of that amount
- Never bet more than 5% of bankroll on any single game regardless of what Kelly says
Use our Kelly Criterion calculator to run the numbers on any bet.