The Kelly criterion answers one narrow question: what fraction of a bankroll maximises its long-run growth rate, given an edge you believe in. It is a staking rule, not a way of finding value, and it is unforgiving of overconfidence.
The formula
- Kelly fraction:
f* = (bp − q) / b b= decimal odds − 1 (profit per unit staked)p= your estimated probability,q = 1 − p- A negative result means no bet — the formula is telling you the edge is against you.
Worked example
At decimal odds of 2.20 you believe the true probability is 50%. Then b = 1.20, p = 0.50, q = 0.50, giving f* = (1.20 × 0.50 − 0.50) / 1.20 = 8.3% of bankroll. On a 1,000 bankroll that is 83. At half Kelly it is 42. Note how aggressive full Kelly is for an edge of only 10%.
Why almost nobody uses full Kelly
Kelly assumes p is correct. It is not — it is an estimate, and the formula is far more sensitive to overestimating your edge than to underestimating it. Overstating probability by a few points can turn optimal growth into steady ruin, and even a correctly specified full-Kelly strategy routinely draws down 50% or more. Half or quarter Kelly sacrifices a little theoretical growth for a large reduction in variance, which is why practitioners overwhelmingly use fractions.
Doing this at scale
Kelly consumes a probability estimate, and a probability estimate consumes history: results, fixture congestion, home and away splits. Stats API provides that history through one contract, so the input to your staking rule is not itself a data-quality risk.
Common questions
What if the calculator returns a negative stake?
It means the price implies a higher probability than you assigned, so there is no edge. The correct stake is zero. Kelly never recommends betting against your own estimate.
Should I use my probability or the market's?
Yours — that is the entire point. If you use the market's implied probability, the formula returns approximately zero, because a fair price offers no growth.