What Is the Kelly Criterion?
The Kelly Criterion is a mathematical formula used to determine the optimal size of a bet relative to your bankroll. Developed by mathematician John L. Kelly Jr. in 1956, it was originally applied to information theory but has since become one of the most widely discussed staking systems in sports betting and financial investing.
The core idea is straightforward: bet more when you have a larger edge, bet less (or nothing) when you don't. It's a disciplined framework that aims to maximise long-term bankroll growth while avoiding ruin.
The Kelly Formula
The formula is expressed as:
f* = (bp – q) / b
- f* = the fraction of your bankroll to wager
- b = the decimal odds minus 1 (i.e., the net profit per unit staked)
- p = your estimated probability of winning
- q = your estimated probability of losing (1 – p)
A Worked Example
Suppose you believe a team has a 55% chance of winning, and the bookmaker is offering odds of 2.10 (decimal).
- b = 2.10 – 1 = 1.10
- p = 0.55
- q = 0.45
- f* = (1.10 × 0.55 – 0.45) / 1.10 = (0.605 – 0.45) / 1.10 = 0.155 / 1.10 ≈ 0.141
This means the Kelly Criterion suggests staking approximately 14.1% of your bankroll on this bet. That's a meaningful stake — reflecting a genuine edge at those odds.
Why Kelly Works in Theory
Kelly staking is mathematically proven to maximise the rate of long-term bankroll growth when your probability estimates are accurate. It also inherently protects against ruin — the formula will never recommend betting your entire bankroll (unless you're essentially guaranteed to win), and it will output a negative value (meaning "don't bet") when there's no edge.
The Catch: Your Edge Estimate Must Be Accurate
Here's where most bettors run into trouble. The Kelly formula is only as good as your probability estimate. If you overestimate your edge — which is very easy to do — Kelly staking will recommend oversized bets that can seriously damage your bankroll.
This is why most experienced bettors use Fractional Kelly.
Fractional Kelly: The Safer Approach
Instead of betting the full Kelly amount, most professionals advocate for betting a fraction — commonly half (Half Kelly) or a quarter (Quarter Kelly). This reduces volatility significantly while still capturing most of the long-term growth benefit.
| Approach | Stake (from example) | Risk Level |
|---|---|---|
| Full Kelly | 14.1% of bankroll | High volatility |
| Half Kelly | 7.05% of bankroll | Moderate |
| Quarter Kelly | 3.53% of bankroll | Conservative |
For most recreational bettors, Half Kelly strikes the best balance between growth and protection.
When Not to Use Kelly
- When you're not confident in your ability to estimate true probabilities accurately.
- When betting on events with high variance (e.g., long-shot accumulators).
- When your bankroll is very small and even fractional Kelly stakes are impractical.
Practical Tips
- Always start with Fractional Kelly until you've tracked your edge over a large sample of bets.
- Reassess your probability model regularly — your estimates should improve with experience.
- Use a spreadsheet or betting tracker to apply the formula consistently.
- Never let excitement or emotion override your calculated stake.
The Kelly Criterion won't guarantee wins — no system can. But used carefully, it's one of the most rational frameworks available for growing a betting bankroll over the long run.