Kelly Criterion

The Kelly Criterion is a staking formula published by John L. Kelly Jr. in 1956 that derives the mathematically optimal fraction of a bankroll to commit to a positive expected value bet. It resolves the tension between maximizing compound growth and avoiding the risk of ruin. By scaling each stake to both the measured edge and the price on offer, Kelly produces a faster long-run bankroll growth rate than any competing staking method, while never allocating enough to a single position that one loss proves catastrophic.

The core formula is Kelly % = (bp - q) / b, where b is the decimal odds minus 1, p is the win probability, and q is the loss probability (1 - p). The output is the bankroll fraction to stake. In practice many bettors apply fractional Kelly, wagering one-quarter or one-half of the full figure, to dampen the variance that aggressive sizing introduces. Full Kelly is optimal in theory but generates bankroll swings most bettors find difficult to tolerate.

Example

You assess a team at a 60% win probability, and the book prices it at +120 (decimal 2.20). Feeding the inputs into the formula: b = 1.20, p = 0.60, q = 0.40. Kelly % = (1.20 x 0.60 - 0.40) / 1.20 = (0.72 - 0.40) / 1.20 = 0.267, or 26.7% of bankroll. On a $1,000 bankroll, full Kelly stakes $267. Many bettors would instead apply half Kelly ($133.50) or quarter Kelly ($66.75) to reduce volatility and hedge against the chance their 60% estimate is slightly off.

Key Points

• Maximizes long-term growth: Across all fixed-fraction staking methods, Kelly delivers the highest bankroll growth rate when the probability inputs are accurate.
• Sensitive to probability errors: A small error in your true win-probability estimate can lead Kelly to size positions too large, raising the risk of severe drawdowns.
• Fractional Kelly is standard practice: Most experienced bettors deploy a fraction (commonly 25% to 50%) of full Kelly to lower variance and build a buffer against estimation error.
• Never bets on negative EV: The formula returns zero or a negative value for any bet without an edge, signaling that no stake should be committed.
• Dynamic sizing: Kelly staking recalibrates the stake as the bankroll moves, allocating more after wins and less after losses.