The Kelly Criterion
WeBall3 min readUpdated Aug 15, 2026Reviewed Aug 15, 2026
Knowing a bet is good does not tell you how much to put on it. Kelly is the formula that answers that, and understanding why nobody should follow it exactly is as important as the formula itself.
The formula
f* = (b × p − q) ÷ b
Where b is the net decimal odds (decimal minus one), p is your win probability and q is 1 − p.
A 55% chance at even money
- 01Even money is +100, so decimal odds are 2.00 and b = 1.
- 02p = 0.55, so q = 0.45.
- 03f* = (1 × 0.55 − 0.45) ÷ 1 = 0.10.
- 04Full Kelly says stake 10% of your bankroll on this bet.
The Kelly calculator runs it for any bankroll, price and probability, with fractional options.
What Kelly is actually optimising
Not expected profit — expected logarithmic growth of the bankroll. That distinction matters, because it is what makes Kelly refuse to overbet even when the EV is enormous.
Betting your whole bankroll on a 99% favourite has excellent expected value and a 1% chance of ending your betting career. Kelly maximises long-run compounding, and compounding requires surviving.
Why full Kelly is dangerous
The formula assumes p is known exactly. In betting it is estimated, often badly, and the error is not symmetric in its consequences.
Since almost everyone overestimates their edge, and the penalty for overestimating is severe while the penalty for underestimating is mild, the correct response is to deliberately stake below the formula.
Fractional Kelly
Multiply the recommendation by a fraction — commonly 0.25 or 0.5.
| Fraction | Growth retained | Volatility |
|---|---|---|
| Full (1.0×) | 100% | Brutal |
| Half (0.5×) | ~75% | Much calmer |
| Quarter (0.25×) | ~44% | Comfortable |
Quarter Kelly is the common professional default. It gives up more than half the theoretical growth in exchange for drawdowns you can actually live through, and it provides a large margin of safety against your probability estimates being wrong.
Practical guardrails
Even fractional Kelly needs a ceiling. A probability estimate that is badly wrong can produce an enormous recommended stake, and a hard cap prevents any single mistake from being fatal. WeBall's engine defaults to quarter Kelly with a hard cap at 5% of bankroll for exactly this reason.
The other guardrail is honesty about correlation. Kelly assumes bets are independent. Six NFL sides on the same Sunday are not independent — they share weather, they share market conditions, and they can all lose together. Sizing each at quarter Kelly means your true exposure is much higher than it looks.
When not to use Kelly at all
If you cannot state your win probability with any confidence, Kelly has nothing to work with and will amplify whatever you guessed. Under those conditions flat betting is genuinely better: it is impossible to get wrong, and it makes your results interpretable because every bet contributed equally.
Start flat. Move to fractional Kelly only once you have enough history — and enough closing line value — to believe your probability estimates are calibrated.
Common questions
Should I use full Kelly?
Almost certainly not. Full Kelly assumes perfect knowledge of your win probability. Overestimate your edge by a little and you are dramatically overbetting, and the growth curve punishes overbetting far more harshly than underbetting.
Is flat betting worse than Kelly?
Theoretically yes, practically often no. Badly executed Kelly — built on probability estimates that are too confident — underperforms flat betting badly. Flat betting is the correct default until you have evidence your estimates are calibrated.