Betting analytics glossary
The Kelly Criterion for sports betting
Kelly is the maths behind “how much should I bet?”. It sizes each stake as a fraction of your bankroll based on your edge on that bet. Most sharps use half of what full Kelly recommends, and there’s a good reason for that.
TL;DR
- Kelly fraction = (odds × probability − 1) / (odds − 1). Output is the % of bankroll to stake.
- No edge → Kelly says stake zero. Small edge → small stake. Big edge → big stake. Never bet without a probability estimate.
- Full Kelly maximises long-run growthbut produces 30%+ drawdowns that most punters can’t stomach.
- Half-Kelly is the practical default: keeps most of the growth advantage, roughly a quarter of the variance. Quarter-Kelly is even safer.
- Staking above 2× Kelly turns positive-edge betting into a losing strategy long-run. The maths is unforgiving.
The short definition
The Kelly criterion is a stake-sizing formula developed by John Kelly at Bell Labs in 1956. It takes two inputs — your estimated probability of winning and the odds on offer — and outputs the fraction of bankroll to stake that maximises long-run growth of the bankroll.
For sports bettors, Kelly is the mathematical answer to “how much should I bet on this?”. It says: bet more when you have more edge, less when you have less, and nothing at all when you have none.
The formula
For a decimal-odds bet, the Kelly stake as a fraction of bankroll is:
Kelly % = (Odds × Win Probability − 1) ÷ (Odds − 1)“Win Probability” here is yourestimate of the true win chance, not the bookmaker’s implied probability. If your estimate matches the bookmaker exactly, Kelly outputs zero (no edge). Positive Kelly = the market underprices your selection.
Worked example
Say you back Arsenal to beat Liverpool at odds of 2.20. Your honest estimate of Arsenal’s win probability is 50%.
Kelly % = (2.20 × 0.50 − 1) ÷ (2.20 − 1) = 0.10 ÷ 1.20 = 8.3 %Full Kelly says stake 8.3% of your bankroll. On a £1,000 bankroll that’s £83.
Half-Kelly cuts that to ~4.2%, or £42. This is where most experienced bettors sit. You lose about 25% of the theoretical growth rate but roughly a quarter of the variance, and you protect yourself against overestimating your edge — because your 50% estimate might actually be 47%, and full Kelly on a wrong estimate loses money fast.
Why almost no one uses full Kelly
Full Kelly is theoretically optimal — but only if your edge estimate is exactly right. In practice, two things go wrong:
- Estimation error.Real bettors don’t know their edge exactly. You think Arsenal is 50% but it might actually be 46%. Full Kelly on a 4-percentage-point overestimate loses money long-run even though the maths of full Kelly says otherwise.
- Variance is brutal. Full Kelly produces drawdowns of 30–50% of bankroll routinely. Most punters tilt or quit before the strategy has time to work. Half- Kelly cuts that risk of ruin dramatically.
Fractional Kelly (half, quarter, or even less) is what almost every sharp bettor with a real bankroll actually uses. The academic literature on Kelly explicitly recommends fractional Kelly for anyone whose edge estimate has non-zero error, which is everyone.
The 2× Kelly cliff
A hard mathematical result: if you stake more than 2× the Kelly-recommended amount, your long-run bankroll growth turns negative even if your edge is positive. The variance overwhelms the edge and compounds you into the ground.
This is why “going big on my locks” loses money for confident bettors who dohave edge. Confidence isn’t the same as edge; edge is what Kelly cares about; and Kelly punishes overbetting harder than it rewards correct sizing.
Related terms
Frequently asked questions
What is the Kelly Criterion in sports betting?
The Kelly criterion is a stake-sizing formula that tells you what fraction of your bankroll to bet given your estimated edge and the odds. Its output is the stake that maximises long-run bankroll growth. If you have no edge, Kelly says bet nothing; if you have a huge edge, Kelly says bet a lot; if you have a small edge, Kelly says bet a small fraction.
What is the Kelly formula?
In decimal odds the simplest form is: Kelly fraction = (odds × probability − 1) / (odds − 1). If you estimate a 55% chance on a 2.00 bet, that's (2.00 × 0.55 − 1) / (2.00 − 1) = 0.10, or 10% of bankroll. The classical b·p − q / b form uses fractional odds where b is the decimal odds minus one.
Why do sharp bettors use half-Kelly?
Two reasons. First, full Kelly is aggressive: it maximises the average growth rate but produces gut-wrenching drawdowns of 30%+ that are hard to sit through. Second, full Kelly only works if you know your edge exactly. Real bettors estimate edge with error, and overestimating your edge by even a little makes full Kelly bet too much. Half-Kelly (staking half the recommended amount) keeps most of the growth advantage while roughly quartering the variance.
What happens if you bet more than Kelly?
Long-run bankroll growth turns negative even when your edge is positive. Above roughly 2× Kelly the bankroll is expected to trend down, not up. This is the mathematical proof for why fixed-percentage staking above your edge is a losing strategy, no matter how sure you feel about the pick.
Can you use Kelly with unknown probabilities?
Not directly. Kelly needs a probability estimate as input, and if your estimate is wrong Kelly's output is wrong too. Sharp bettors usually derive probability from the closing odds of a market that takes serious money (Pinnacle, Betfair Exchange), then compare against the price they took. If your entry price implies 45% and Pinnacle's no-vig close implies 50%, your edge on that bet is roughly 5% and Kelly can size accordingly.
How does Kelly compare to flat staking?
Flat staking (same size on every bet) is simpler and lower-variance but leaves growth on the table when the edge is large. Kelly (or a fraction of Kelly) scales stakes with edge, so bigger edges get bigger bets. For a bettor with real edge over many bets, fractional Kelly compounds meaningfully faster than flat staking. For a bettor without real edge, both lose; Kelly just loses faster.