Kelly Criterion Formula: Calculating Optimal Bet Sizing

Flat staking treats every single bet as equal, staking the exact same 1% or 2% of bankroll regardless of whether your calculated edge is slim or substantial. The Kelly Criterion takes a mathematical route, scaling bet size strictly to your assessed advantage and the available sportsbook decimal odds.

First introduced by John L. Kelly Jr. in 1956, the formula determines what fraction of your total bankroll to wager to balance exponential growth against the risk of ruin.

The Mathematical Formula

The standard Kelly Criterion formula for sports betting is:

K% = ((B × P) - Q) / B

Where:

K% = The percentage of your bankroll to stake
B = Decimal odds minus 1 (the decimal profit odds)
P = Your calculated probability of winning (as a decimal)
Q = The probability of losing ($1 - P$)

Calculation Example

Suppose your model projects a home team has a 55% chance of winning ($P = 0.55$). The bookmaker offers decimal odds of 2.00 ($B = 2.00 - 1 = 1.00$).

Calculate probability of losing: $Q = 1 - 0.55 = 0.45$
Apply the formula: K% = ((1.00 × 0.55) - 0.45) / 1.00
Result: $K% = 0.55 - 0.45 = 0.10$ or 10% of bankroll

If your calculated probability drops to 52% ($P = 0.52$) at the same 2.00 odds:

K% = ((1.00 × 0.52) - 0.48) / 1.00 = 0.04 or 4% of bankroll

When your calculated probability equals the implied market probability, the formula returns zero. If your probability is lower than the market implied odds, the result is negative, indicating no wager should be placed.

Full Kelly vs. Fractional Kelly

Staking full Kelly amounts requires precise probability estimations. Overestimating your edge by even 5% under Full Kelly can cause rapid bankroll drawdowns during normal statistical losing streaks.

Because sports outcomes involve unquantifiable variables like late injuries, pitch conditions, and referee calls, most disciplined bettors use Fractional Kelly.

Half Kelly (50% Sizing)

Half Kelly multiplies the Full Kelly percentage by 0.5. In the 55% probability example above, Full Kelly suggested a 10% wager. Half Kelly reduces that stake to 5% of bankroll.

Half Kelly yields roughly 75% of the theoretical growth rate of Full Kelly while reducing bankroll volatility by 50%.

Quarter Kelly (25% Sizing)

Quarter Kelly multiplies the Full Kelly percentage by 0.25. The 10% recommendation becomes a 2.5% stake.

Quarter Kelly offers a smoother equity curve and provides a buffer against errors in probability modeling, keeping stakes close to standard bankroll protection guidelines.

Staking Comparison Matrix

Assumed bankroll of $5,000 with calculated 55% probability at 2.00 odds:

Staking Model	Formula Fraction	Recommended Stake %	Dollar Amount	Risk Profile
Full Kelly	1.00	10.0%	$500	High Volatility
Half Kelly	0.50	5.0%	$250	Moderate Volatility
Quarter Kelly	0.25	2.5%	$125	Low Volatility
Flat Staking	Fixed	2.0%	$100	Zero Edge Sensitivity

Core Rules for Implementing Kelly Sizing

Calculate Bankroll Dynamically: Recalculate your dollar stake before every single bet based on your current bankroll, not your starting deposit.
Never Bet Negative Outcomes: A negative Kelly result indicates the odds offer negative expected value ($EV < 0$).
Cap Maximum Exposure: Set an absolute hard cap (such as 5% of bankroll) regardless of what the Full Kelly formula suggests for an apparent high-edge mismatch.