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The Kelly criterion for sports betting: formula, examples and fractional Kelly
How the Kelly criterion sizes a bet from the odds and your win probability, worked examples, why most bettors use half or quarter Kelly, and how to get the probability from a sharp no-vig price.
The Kelly criterion answers one question: given the odds and your estimate of the chance of winning, what share of your bankroll should you stake? It stakes more when the edge is larger and nothing when there is no edge. This post explains the formula, works through examples, and covers the part that matters most in practice: where the probability comes from. The free Kelly criterion calculator runs the numbers.
The formula
With decimal odds d, the net odds are b = d - 1. If you win with probability p and lose with q = 1 - p, Kelly stakes this share of your bankroll:
f = (b × p - q) / b
If f comes out at zero or below, the price offers no edge for your probability, and Kelly says not to bet.
Example 1: a small edge
Odds of 2.10 and a 52% win probability:
- b = 1.10, p = 0.52, q = 0.48
- f = (1.10 × 0.52 - 0.48) / 1.10 = 0.092 / 1.10 = 8.4% of the bankroll
With a bankroll of 1,000 that is a stake of about 84. The expected value of the bet is p × d - 1 = 0.52 × 2.10 - 1 = +9.2% per unit staked.
Example 2: no edge
Odds of 1.90 and a 50% probability:
- f = (0.90 × 0.50 - 0.50) / 0.90 = -5.6%
Negative, so no bet. At 50% the fair price is 2.00, and 1.90 is below it.
Why almost nobody bets full Kelly
Full Kelly maximises long-run growth only if your probability is exactly right. In practice every estimate has error, and Kelly is unforgiving: overestimate your edge and you over-bet, and over-betting increases drawdowns sharply while lowering growth.
So most bettors stake a fraction of it:
| Kelly fraction | Stake in example 1 | Typical use |
|---|---|---|
| Full | 8.4% | theory, perfect probabilities |
| Half | 4.2% | confident, well-tested models |
| Quarter | 2.1% | the common default |
| Eighth | 1.0% | new or noisy models |
Half Kelly keeps about three quarters of full Kelly's growth with far smaller swings, which is why fractional Kelly is the norm.
Where the probability comes from
Kelly is only as good as p. The two common sources are:
- Your own model. Ratings, simulations or machine learning. Test its calibration before trusting it with real stakes.
- A sharp market's no-vig price. Take a low-margin market such as Pinnacle, remove the margin (see how to calculate no-vig odds), and use that fair probability as
pwhen a softer bookmaker offers a longer price.
An example of the second approach: Pinnacle's fair price on a side is 1.95, which is a probability of 51.28%. A soft book offers 2.10 on the same side.
- EV = 0.5128 × 2.10 - 1 = +7.7%
- Full Kelly = (1.10 × 0.5128 - 0.4872) / 1.10 = 7.0%; quarter Kelly is about 1.7%
The no-vig calculator loads live Pinnacle prices for exactly this, and the odds API delivers the same prices to your code so the calculation can run on every market.
Practical rules
- Cap single stakes. Even with a big edge, many bettors never risk more than 2-5% on one bet.
- Recalculate as the bankroll changes. Kelly is a share of the current bankroll, not the starting one.
- Correlated bets need smaller stakes. Kelly assumes independent bets; several bets on the same match are not.
- Track closing line value. Over hundreds of bets, results are noisy. Whether your prices beat the close says more about whether your probabilities are sharp. See the CLV calculator.
PinnRadar provides odds data, not betting advice. The Kelly criterion is a formula, and it is only as good as the numbers you give it.
Questions readers ask
What is the Kelly criterion formula for betting?
f = (b × p - q) / b, where b is the decimal odds minus 1, p is your win probability and q = 1 - p. The result is the share of your bankroll to stake.
Should I use full or fractional Kelly?
Most bettors use fractional Kelly, usually a quarter or half, because full Kelly over-bets whenever the probability estimate is too high, which leads to large drawdowns.
What if the Kelly result is negative?
A negative result means the odds are below the fair price for your probability, so there is no edge and Kelly says not to bet.
Where can I calculate Kelly stakes?
The free Kelly criterion calculator takes the odds, your probability and bankroll, and shows full and fractional Kelly stakes with the expected value.
Pull Pinnacle prices into your own code
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