Kelly Criterion

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As said in our previous article regarding money management (Fixed Bet Size Money Management), how you allocate your wagers in terms of size relative to your entire bankroll is a very important, yet often overlooked, aspect of sports betting that is vital to sustaining long term success.

Both the Kelly Criterion and Fixed Bet Size strategies are similar in that they suggest calculating your wager in terms of a percentage of your entire bankroll.  However, the main difference between the two is that Kelly suggests that you vary your bet size from bet to bet as opposed to sticking with a fixed amount for every wager.  In short, Kelly implies that you increase the amount of your wager when you perceive your advantage to be highest, and vice-versa.  If the probability of winning is high, raise the stakes.  If the probability of winning is low, lower the stakes.

The Kelly Criterion formula goes as follows:

Example:  Let’s assume you have a bankroll of $10,000.  You have decided to bet on the Arsenal-Liverpool match in which the match result odds for a wager on an Arsenal victory is 2.65 and you believe there is a 39% probability that they will win the match (b =2.65, p = .39). 

So this model suggests that we should wager 2.03% of our bankroll, or $203.

Now it is very important to understand that the Kelly Criterion is maximally aggressive which means it aims to increase your bankroll at the maximum rate possible. Its wager size recommendations are highly affected by your estimate of the wager’s chances for success. If you were to raise your probability to p = .4, would equal 3.63% which is a substantial increase. On the other hand, if you lowered your probability to p = .375, would equal -0.38%, which in that case you would not bet at all.

Many feel as if the Kelly Criterion is too risky in that it suggests risking higher stakes which in turn can increase the volatility of your short term results. In order to lessen the severity of the short term lows and highs, many bettors often use a “Half Kelly” or even a “Quarter Kelly” system in which they bet 50% or as little as 25% of what the formula suggests.

For an opposing view on the Kelly Criterion, read J.R. Miller’s Debunking the Kelly Criterion.  He is an extreme advocator for the fixed bet size strategy and explains why he feels that using a fixed bet size can yield better results while taking on less risk.