Kelly Criterion for Sports Betting: How to Calculate Bet Size
The Kelly Criterion is a mathematical formula used to determine a theoretical stake size when you believe the probability of an outcome is different from the probability implied by the available odds.
A Kelly calculator can help estimate the percentage of a bankroll that the formula would allocate to a particular wager.
What Is the Kelly Criterion?
The Kelly Criterion was developed as a mathematical approach to determining how much capital to allocate when there is a measurable advantage.
In sports betting, the formula uses your estimated probability of winning and the odds available for the bet.
Kelly Criterion Formula
For decimal odds, the formula can be expressed using the net odds and your estimated probability:
Kelly % = (bp - q) ÷ b
- b = net decimal odds (decimal odds minus 1)
- p = your estimated probability of winning
- q = probability of losing (1 - p)
Example
Suppose a sportsbook offers decimal odds of 2.50, while you estimate that the selection has a 45% chance of winning.
The net odds are:
2.50 - 1 = 1.50
Your estimated losing probability is:
1 - 0.45 = 0.55
These values can then be entered into the Kelly formula to determine the theoretical bankroll percentage.
Full Kelly vs Fractional Kelly
Full Kelly uses the complete percentage calculated by the formula. Fractional Kelly uses only part of that amount.
For example, a half-Kelly approach uses 50% of the full Kelly stake, while quarter-Kelly uses 25%.
Using a fractional approach changes the amount staked and the resulting risk profile.
Why Your Probability Estimate Matters
The Kelly calculation depends heavily on the probability estimate entered into the formula. An inaccurate probability estimate can produce an inappropriate theoretical stake.
Why Use a Kelly Calculator?
A Kelly calculator removes much of the manual arithmetic. Enter your bankroll, odds, and estimated probability to see the theoretical Kelly stake and compare full or fractional Kelly approaches.