The Kelly criterion for sports betting

The Kelly criterion is a formula that tells you what share of your bankroll to bet, based on the odds you're offered and your estimated chance of winning. It stakes more when your edge is bigger, less when it's smaller, and nothing when there's no edge. Most bettors stake a fraction of the full Kelly amount, because the formula is only as good as the probability you feed it.

How it works

For a bet with an estimated win probability p:

f* = (bp − q) / b

• f* is the share of your bankroll to bet.
• b is the net odds: decimal odds − 1, or what you win per $1 staked.
• p is your estimated chance of winning.
• q is your chance of losing: 1 − p.

Another way to read the same formula: the Kelly stake is your edge divided by the net odds, where the edge is the expected value per dollar, p × decimal odds − 1.

A worked example

You estimate a side wins 55% of the time. A book offers −110. Your bankroll is $1,000.

1. Convert the price: −110 is 1 + 100 ÷ 110 = 1.909 in decimal odds, so b = 0.909.
2. Multiply: bp = 0.909 × 0.55 = 0.50.
3. Find the chance of losing: q = 1 − 0.55 = 0.45.
4. Apply the formula: f* = (0.50 − 0.45) / 0.909 = 0.055, or 5.5% of your bankroll.
5. Full Kelly is $55. Half Kelly is $27.50. Quarter Kelly is $13.75.

Check it the other way: the edge is 0.55 × 1.909 − 1 = 0.05, a 5% expected return, and 0.05 / 0.909 = 0.055. Same answer.

Now change the estimate to 50% at the same −110. The formula gives (0.4545 − 0.50) / 0.909 = −0.05. A zero or negative result means don't bet: at −110 you need better than a 52.4% chance just to break even.

Full Kelly vs fractional Kelly

Full Kelly grows a bankroll fastest over the long run, but only if your probabilities are exactly right, and even then it swings hard. Two facts explain why most bettors use a half or a quarter instead:

• Overbetting costs more than underbetting. Under the standard approximation, half Kelly keeps about three quarters of full Kelly's growth with about half the swings. Bet twice full Kelly and expected growth falls to roughly zero.
• Your estimate is noisy. Go back to the example. If your 55% is really 53%, full Kelly at 53% is 1.3% of your bankroll, or $13. Full Kelly on your 55% estimate stakes $55, more than four times that. Quarter Kelly on the same estimate stakes $13.75, close to the right size.

A fraction shrinks the stake. It does not fix a wrong probability. If your estimates are consistently too high, every fraction of Kelly is still too big.

How to size a bet with Kelly

By hand:

1. Start with a fair probability, not a hunch. Remove the vig from a sharp market with the No-Vig calculator, or use your own model.
2. Check the edge first. Put the price and your probability into the Expected Value calculator. If the expected value isn't positive, stop.
3. Work out full Kelly with f* = (bp − q) / b.
4. Multiply by your fraction (a half or a quarter is common) and by your current bankroll.
5. Recalculate when anything changes: the price, your estimate or your bankroll.

On Unjuiced, the Kelly calculator does steps 3 and 4. Enter your bankroll, the offered odds and your projected win probability, then choose full, half, quarter or another Kelly fraction. Every calculator is free and works without an account.

Positive EV also shows a Kelly stake on each play, from the bankroll and Kelly percent you saved in Settings. Its probability comes from removing the margin from a reference market, which is an estimate, not the true chance. Positive EV is on Pro.

Mistakes to avoid

• Feeding it a guess. Kelly takes your probability literally. An overconfident estimate becomes an oversized bet.
• Using full Kelly on noisy numbers. Unless you're very sure of your probabilities, a fraction is the safer default.
• Sizing bets as if each were alone. Kelly assumes one bet at a time. Several bets on the same game, or bets placed at the same time, add up to more exposure than each stake suggests.
• Using money that isn't really your bankroll. Kelly assumes a bankroll set aside for betting. A share of money you can't afford to lose is still money you can't afford to lose.
• Keeping an old stake after the price moves. A worse price shrinks the edge and the stake. Recalculate at the price you actually get.
• Judging the method by a few results. A correctly sized bet still loses often. Check your prices against the close with CLV instead.

Questions

What is the Kelly criterion in sports betting?

The Kelly criterion is a bet-sizing formula: f* = (bp − q) / b, where b is decimal odds minus 1, p is your estimated chance of winning and q is 1 − p. It returns the share of your bankroll to stake, scaled to the size of your edge.

How much should I bet using the Kelly criterion?

Bet the Kelly fraction of your current bankroll, then scale it down. At −110 with a 55% estimate, full Kelly is 5.5% of your bankroll, so most bettors would stake a half (2.75%) or a quarter (1.375%) of that bankroll instead.

Why do most bettors use fractional Kelly?

Full Kelly assumes your probability is exactly right and still produces large swings. Half or quarter Kelly gives up some growth in exchange for much smaller swings and protection against overestimating your edge.

What does a negative Kelly number mean?

A zero or negative Kelly result means the price doesn't justify a bet under your probability estimate. Skip the bet rather than staking a small amount anyway.

Is a Kelly calculator only as good as its inputs?

Yes. The Kelly criterion turns your probability estimate into a stake, so a wrong estimate gives a wrong stake. Use a fair probability from a devigged sharp market or a tested model, and a fractional setting to absorb the error.