The Kelly Criterion is a mathematical formula developed in 1956 by John L. Kelly Jr. It has since gained recognition for its use in investing, but its first application was for gambling as a method to maximize long-term profits while managing a bankroll.
The Formula
The Kelly Criterion is used to find the optimal bet size by balancing the likelihood of winning and the potential reward. It helps determine the percentage of your bankroll to wager on a specific bet, optimized for growth rate. To find the recommended percentage of your bankroll to wager on a given bet, two factors are considered:
Edge: The bettor's estimated advantage on a given wager
Edge = (Probability of winning * Decimal odds of the bet) - 1
Odds: The odds on a given wager, in decimal odds format
The formula is:
Kelly % = Edge / (Decimal Odds - 1)
For example, if you believe your odds of winning a bet are 60% and the decimal odds are 1.7:
Edge = (.6 * 1.7) - 1 = 1.02 - 1 = 0.02
Kelly % = 0.02 / (1.7 - 1) = 2.86%
So if your bankroll is $10,000, your recommended bet size for this wager would be $285.
Applying Kelly in the Real World
Determining your win probability (and therefore your edge) isn’t easy. It often requires data analysis, expert insights, and/or modeling. It’s important to make sure this probability is as accurate as possible to avoid overestimating your edge. We discuss finding advantages and estimating them extensively in the Advanced Course, so definitely check that out before estimating your edge without anything to support your number.
While the Kelly Criterion is a powerful tool for optimizing bet sizing in sports betting, it also assumes that the bettor has both perfect information and a high risk tolerance. Betting the full Kelly amount WILL lead to significant volatility in bankroll growth, especially when you're dealing with unpredictable outcomes and estimation errors which are inherent to sports betting. Most people opt to use a fraction of the Kelly Criterion, commonly referred to as Fractional Kelly, to reduce volatility and smooth out the ride.
With Fractional Kelly, you bet only a percentage of the recommended Kelly bet size, like 50% (Half-Kelly) or 25% (Quarter-Kelly). I haven’t talked to any sharp bettors who go above Half-Kelly, and I personally use Quarter-Kelly for most applications. If you know your edge with more certainty (like in top-down betting- see more in the Approaches to Winning video in the Basics Course), then you might consider using Half-Kelly.
The swings in your bankroll become less dramatic, providing some much-needed psychological relief and minimizing the chances of going broke in the short term.
The trade-off when using a fractional Kelly strategy is a slower rate of growth. While Fractional Kelly reduces volatility, it also reduces your potential upside. Full Kelly betting maximizes the rate at which your bankroll grows in the long run, but it assumes a high risk tolerance and perfect accuracy in estimating the edge, which just doesn’t exist in sports betting.
Limitations
While the Kelly Criterion can be an effective tool for managing a sports betting bankroll, we’ve seen that it has some serious limitations. Here’s a more complete list:
Requires Accurate Estimation of Probabilities:
The Kelly formula depends on accurate input for win probability. Estimating these values incorrectly can lead to under-betting or over-betting, which can reduce profitability or, more importantly, increase the risk of bankroll depletion.
Assumes Bets are Independent Events*:
The Kelly Criterion assumes that each bet is independent of the others. In real-world sports betting, however, bets might be correlated, and the formula doesn’t account for it.
Does Not Account for Multiple Simultaneous Bets*:
When funds are tied up in several wagers at once, your effective bankroll is reduced, which can lead to over-betting if the Kelly strategy is followed strictly for each individual bet. For example, if you have a bankroll of $1000, and you place 100 bets before any of them result, Kelly might tell you to wager $10 on each one, even though your bankroll is effectively decreasing by $10 for each bet you place.
High Volatility with Full Kelly:
While the Kelly Criterion maximizes long-term growth, it does so with high volatility when using the full Kelly amount. Large swings in the bankroll, both positive and negative, can be psychologically difficult to manage, especially for risk-averse bettors. Some people might not be comfortable with the high-stakes nature or the dramatic ups and downs you experience with the full Kelly Criterion.
Bet Sizes May Exceed Available Liquidity or Limits*:
In some cases, the Kelly Criterion may recommend a bet size that is larger than what is practically available, especially in small markets or with certain sportsbooks where large bets can’t be placed.
Kelly Is Optimal Only in the Long Run:
The Kelly Criterion is designed to maximize wealth over a long series of bets or investments. In the short term, however, even when correctly applied, it may lead to significant losses or drawdowns, which could be challenging to recover from, especially for smaller bankrolls. Kelly is theoretically OK with you going from a $10,000 to a $1 bankroll, because you still have money to bet with and you can still calculate a Kelly %, your bets are just going to be smaller now.
Overestimation of Edge Can Lead to Bankruptcy:
Overestimating your edge can result in over-betting, leading to rapid losses and eventual bankruptcy. Unfortunately, it is extremely easy to overestimate your edge in sports betting, making this a significant limitation.
* We’ll talk about ways around these limitations in the Advanced Course.
Summary
The Kelly Criterion is a valuable tool for sports bettors who want to maximize their potential profits over time. By adjusting the bet size according to the perceived edge, bettors can manage risk and make more efficient use of their bankrolls. However, for this to be a good strategy, you need to be mindful of the limitations, especially overestimating your edge.