What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula developed by John Kelly. It helps determine the optimal bet size in order to maximize long-term growth in situations with uncertain outcomes, such as sports betting or investing. It takes into account the probability of winning and the potential return offered by the odds.
The formula suggests that the bet size should be proportional to the edge or advantage you have over the bookmaker. This is determined by comparing your probability estimate with the odds provided. The Kelly Criterion aims to strike a balance between maximizing growth and minimizing the risk of ruin.
In theory, the use of Kelly’s formula maximizes the rate of bankroll growth, but it relies on knowing the exact probabilities. However, in sports events, probability estimates are at the end of they day – estimates. By it’s nature, sports betting involves a lot of uncertainty, randomness and luck inside one game of football.
When considering that betting with a Kelly bet size over two times can mathematically lead to a negative expected return, it is prudent to use a smaller bet size than what Kelly’s formula suggests. This helps protect our bankroll during inevitable losing streaks. Since Kelly Criterion defines the point of maximum growth one should consider it rather the max bet size, not the goal or actual bet size.
A good practice is to add a divisor to Kelly’s formula to reduce risk and avoid ruin.
If you want to take a deeper dive I recommend reading this short paper on the subject
How does the Kelly Criterion Work?
The Kelly Criterion works by considering the probability of an event occurring and the potential return offered by the odds. By using the formula B = (p * o – 1) / (o – 1), the Kelly Criterion calculates the optimal fraction of your bankroll to wager on a specific bet.
The formula determines the bet size based on the difference between the estimated probability of winning (p), and the odds offered by the bookmaker (o). It aims to allocate a larger bet size when you have a higher edge and a smaller bet size when the edge is smaller. The goal is to maximize long-term growth while managing the risk of losing the entire bankroll. We prefer to use Kelly divisor d in the formula to reduce risk, where B = (p * o – 1) / (o – 1) / d:
For example, in a bet where the probability of winning is 45.4% and the odds are 2.37. With a Kelly divisor of 5, the recommended bet size would be as follows: B = (0.454 * 2.37 – 1) / (2.37 – 1) / 5 = 0.011. By playing according to Kelly/5, a bettor would allocate 1.1% of their bankroll to that particular bet. Without the divisor the bet size would be 5.54% of your bankroll balance according to Kelly Criterion, which is way too risky in reality.
What is the ideal Kelly criterion divisor?
The ideal Kelly divisor, is subjective and depends on an individual’s risk profile and confidence in their probability estimates. The choice of the multiplier allows you to adjust the bet size to a level that aligns with your desired risk/reward profile.
You can understand the importance of Kelly divisor when making a calculation with a simple coinflip scenario. The only exception here is that the coin is weighted and lands 60% of the time heads. Therefore your probability of winning betting heads is 60% or 0.6 with 2 odds. By applying the formula this gives us the bet suggestion of 20% without the divisor. Naturally, if this scenario would exist in real world you should bet as such. But in a single match of Football luck plays a part and your estimate of probability of a win is like the name suggests, an estimate. So even if you come up probability estimate of 20% higher than the bookmakers odds, you should consider using the divisor.
The more confident you are with your probability estimate and the bet landing (higher expected value), using larger multiplier can be implemented and with lower expected value (but still positive) a smaller. To learn more about the expected value, you can read this post
A larger divisor reduces the bet size, making it more conservative and less volatile. Smaller divisor decreases the bet size less, which can lead to higher potential returns but also higher risk. It’s essential to choose a multiplier or divisor that allows you to stay within your comfort zone and manage your bankroll effectively. Personally I use bet size anything between 1-5% depending on the expected value and overall confidence on the analysis and bet, however rarely over 3% since I’m most comfortable so.
Betting Graph
We’ve provided you visual graph to help to visualize the problems using Kelly Criterion without any risk. When you are betting over Kelly it’s never logical and considered insane. The smartest way to approach your betting is to stay in the conservative green area. This simply means there needs to be a divisor in use when using Kelly Criterion in sports betting.