Kelly criterion for sports betting

The Kelly criterion is a formula that tells you what fraction of your bankroll to risk on a bet given your edge and the odds. It maximizes long-run bankroll growth, but full Kelly is too aggressive for most real-world betting. Here is how to use it sensibly.

The formula

Kelly fraction = (bp − q) / b

where b = decimal odds minus 1 (the profit per $1 staked), p = your estimated probability of winning, and q = 1 − p.

Example: bet at +120 (decimal 2.20, so b = 1.20) with estimated 50% win probability: (1.20 × 0.50 − 0.50) / 1.20 = (0.60 − 0.50) / 1.20 = 0.083

Full Kelly says risk 8.3% of bankroll. Almost no one does that.

Why full Kelly is too aggressive

Full Kelly assumes you know your edge exactly. In sports betting, your edge estimate is itself uncertain — the true probability might be lower than you think. Full Kelly with overestimated edge produces enormous drawdowns.

A bankroll using full Kelly on a 5% edge can routinely draw down 50%+ in normal variance.

Fractional Kelly

Most disciplined bettors use quarter Kelly (0.25× the full Kelly fraction) or half Kelly (0.5×). Quarter Kelly produces ~94% of full Kelly's long-run growth rate with dramatically lower drawdowns. It is the practical default.

For the example above (8.3% full Kelly), quarter Kelly would be 2.1% of bankroll.

Caps and floors

Even quarter Kelly can recommend large bets on high-edge opportunities. Most practitioners cap any single bet at 1-3% of bankroll regardless of what Kelly says, and skip bets below a minimum size (typically 0.1-0.25% of bankroll) because the variance reward is too small to bother.