What Is the Kelly Criterion?
The Kelly Criterion is a mathematical formula developed by John Kelly at Bell Labs in 1956 for optimizing the size of bets. It calculates the exact percentage of your bankroll to stake on each bet to maximize the long-term growth rate of your wealth. It has been used by legendary investors like Warren Buffett and by professional gambling syndicates worldwide.
In the context of football betting, the Kelly Criterion tells you how much to stake based on two inputs: your estimated probability of winning and the odds offered by the bookmaker. The bigger your edge (the gap between your probability and the odds-implied probability), the larger the Kelly stake.
The Kelly Formula
The formula for decimal odds is:
Kelly % = (bp − q) ÷ b
Where:
- b = decimal odds minus 1 (the net profit per unit staked)
- p = your estimated probability of winning
- q = probability of losing (1 − p)
Worked Example 1: Clear Value
Your model estimates a 55% chance of a home win. The bookmaker offers odds of 2.10.
- b = 2.10 − 1 = 1.10
- p = 0.55
- q = 0.45
- Kelly % = (1.10 × 0.55 − 0.45) ÷ 1.10 = (0.605 − 0.45) ÷ 1.10 = 0.155 ÷ 1.10 = 14.1%
Full Kelly recommends staking 14.1% of your bankroll on this bet.
Worked Example 2: Marginal Value
Your model estimates a 45% chance of an away win. The bookmaker offers odds of 2.30.
- b = 2.30 − 1 = 1.30
- p = 0.45
- q = 0.55
- Kelly % = (1.30 × 0.45 − 0.55) ÷ 1.30 = (0.585 − 0.55) ÷ 1.30 = 0.035 ÷ 1.30 = 2.7%
When the edge is small, Kelly recommends a much smaller stake.
Worked Example 3: No Value
Your model estimates a 50% chance of a home win. The bookmaker offers odds of 1.90.
- b = 1.90 − 1 = 0.90
- p = 0.50
- q = 0.50
- Kelly % = (0.90 × 0.50 − 0.50) ÷ 0.90 = (0.45 − 0.50) ÷ 0.90 = −0.05 ÷ 0.90 = −5.6%
A negative Kelly value means there is no value in the bet. Do not stake anything. This is one of Kelly's most valuable features: it automatically tells you when to pass on a bet.
Why Full Kelly Is Dangerous
Full Kelly is mathematically optimal for maximizing long-term growth, but it assumes that your probability estimates are perfectly accurate. In the real world, they are not. Even the best prediction models have uncertainty in their probability outputs. If you overestimate your edge by even a small amount, full Kelly will dramatically over-stake.
The practical consequences of full Kelly are severe drawdowns. Simulations show that full Kelly produces drawdowns of 50% or more from peak bankroll approximately every 100-200 bets. While the mathematical theory says you will recover, the psychological and practical reality is that most bettors cannot survive a 50% drawdown without abandoning their system.
Maximum Drawdown Risk
Full Kelly staking on a 55% edge at typical football odds (around 2.00) produces the following expected drawdown profile:
- 20% drawdown: expected every 20-30 bets
- 40% drawdown: expected every 80-120 bets
- 60% drawdown: expected every 300-500 bets
These drawdowns are mathematically survivable but psychologically devastating for most people.
Fractional Kelly: The Practical Solution
The standard professional practice is to use a fraction of the full Kelly stake:
- Half Kelly (50%): Reduces growth rate by about 25% but cuts maximum drawdowns roughly in half. This is the most commonly recommended fraction for experienced bettors.
- Quarter Kelly (25%): Very conservative. Growth is slower but drawdowns are manageable even with imperfect probability estimates. Ideal for bettors who are still validating their model's edge.
- Eighth Kelly (12.5%): Ultra-conservative. Suitable for very large bankrolls where capital preservation is the priority.
The beauty of fractional Kelly is that you retain the core benefit of Kelly staking — betting more when you have more edge and less when you have less edge — while reducing the risk of catastrophic drawdowns.
Kelly Criterion vs. Flat Staking
How does Kelly compare to simple flat staking? The key differences:
- Growth rate: Kelly (even fractional) produces faster bankroll growth than flat staking when your probability estimates are accurate.
- Drawdowns: Kelly produces deeper drawdowns than conservative flat staking because it concentrates more capital on individual bets.
- Simplicity: Flat staking requires no probability estimates — just set 2-3% and bet. Kelly requires accurate probabilities for every bet.
- Error tolerance: Flat staking is more forgiving of inaccurate probability estimates because the stake does not vary.
For most recreational bettors, flat staking at 2-3% is the better choice. For serious bettors with a validated prediction model, fractional Kelly (quarter to half) offers superior long-term results.
Implementing Kelly with PredictPitch
Our prediction engine provides probability estimates for every match, which you can plug directly into the Kelly formula. Here is the process:
- Check our daily predictions for matches with positive expected value.
- Note the model's estimated win probability for your chosen selection.
- Find the best available odds at your bookmaker.
- Apply the Kelly formula (we recommend quarter Kelly for most users).
- If the Kelly percentage is negative, do not bet. If it is positive, stake that percentage of your current bankroll.
Over time, this approach allocates more capital to your highest-edge predictions and less to marginal ones, optimizing your growth rate while managing risk.
To see how our probability estimates translate into real-world accuracy, visit our system performance dashboard. For premium access to full probability breakdowns and recommended stakes, explore our subscription plans.