Applying the Kelly Criterion for Optimal Sports Betting

As sports bettors, we're always trying to get an edge on the house. It's a difficult task, but with help from the Kelly Criterion, you might just be able to get ahead in the sports betting market.  This mathematical formula might just be your ticket to elevating your betting strategy.
Applying the Kelly Criterion for Optimal Sports Betting

What is the Kelly Criterion?

The Kelly Criterion is a mathematical formula used to determine the optimal size of a series of bets. 

Invented by John L. Kelly Jr., a scientist at Bell Labs, in 1956, it’s a strategy that has transcended its origins and found a place in the world of sports betting. 

The core idea is to maximize the growth of your betting bankroll over the long term by determining the ideal stake for each bet.

Sure, that seems simple enough, right? However, there is a bit of math involved.

The Math Behind the Magic

At its heart, the Kelly Criterion involves a formula that might seem daunting at first glance but is pretty straightforward. 

It’s all about calculating the ‘edge’ you have in a bet and then betting a proportion of your bankroll based on that edge. The formula looks like this:

  • k% = (b * p – q) / b

Where—

  • k% is the total percentage of your bankroll you should bet 
  • b is the odds received on the bet (decimal odds minus 1),
  • p is the probability of winning,
  • q is the probability of losing (which is 1 – p).

If your head is about to explode after seeing that, don’t worry. It’s a bit simpler than it seems on its face. Sure, there are Kelly Criterion calculators out there, but you don’t need one.

We’ll get into a real-world example of how you can use it at your favorite online sportsbook.

Applying Kelly in Sports Betting

So, how does this apply to sports betting

Imagine you have a deep understanding of a particular sport, and through your analysis, you can accurately estimate the probabilities of certain outcomes. 

On top of just having a solid understanding of the game, there are tools that will help with some of the numbers we listed above.

By using the Kelly Criterion, you can calculate the optimal amount of your bankroll to wager, ensuring that you’re neither over-betting (risking too much) nor under-betting (not winning as much as you could).

Unlike more simplistic strategies like flat betting or Martingale, the Kelly Criterion is dynamic and adjusts the bet size based on the perceived edge. It’s more sophisticated and tailored to individual bets.

The Benefits for Sports Bettors

The primary benefit of using the Kelly Criterion in sports betting is that it balances the twin goals of maximizing bankroll growth while minimizing the risk of going broke. 

This approach encourages a disciplined betting strategy, which is crucial in the volatile sports betting industry.

We mention this over and over in other posts, but sports betting isn’t just about winning a single bet here or there. It’s about the long-term health of your bankroll. Leveraging the Kelly Criterion helps you stay in the game longer and bring in more money.

Real-world Example

Let’s put this into a real-world context. 

Imagine you’re betting on the Packers and Cowboys wild-card game where you believe the underdog (in this case, the Green Bay Packers) has a 40% chance of winning. 

If the bookmaker offers odds of 3.0 (or 2/1 in fractional odds) for this outcome, you can plug these numbers into the Kelly formula. 

  • The odds are 3.0, so b = 3.0 − 1 = 2
  • The probability of winning (p) is 40% or 0.40,
  • The probability of losing (q) is 60% or 0.60.

Now, if we plug these numbers into our Kelly formula, we get—

  • k% = (2 * 0.40 – 0.60) / 2
  • k% = 0.20 / 2
  • k% = 0.10

With all of that work laid out, the formula states you should bet only 10% of your bankroll on this game.

It’s a balance of the odds the bookie laid out and the chance of winning. Of course, if the chance of winning is higher, you can also expect the k% to be higher.

The Kelly Criterion in Action

One of the best aspects of using the Kelly Criterion is seeing it in action. 

As you apply it consistently to your betting strategies, you’ll notice how it guides your decisions, often preventing emotional or impulsive betting. 

You start to bet smarter, not harder.

Will you win more? Maybe. But the real question is, will you retain your bankroll more? Most likely. 

That’s because you’re placing bigger bets where they need to be placed. It’s a mathematical hedging of your bets.

Limitations and Considerations

While the Kelly Criterion is a powerful tool, it’s not without its limitations. 

  • Risk of overestimation. The Kelly Criterion depends heavily on accurate estimations of winning probability. Overestimating a team’s chances can lead to disproportionately high bets and potentially significant losses.
  • Bankroll volatility. The Kelly Criterion can lead to high bankroll volatility even with correct probability estimates. Large bets on individual events can result in significant swings in the bankroll, which may not be suitable for all bettors.
  • Complexity in multi-outcome events. Sports events often have more than two outcomes (win/lose), especially in games with the possibility of a draw. The Kelly Criterion becomes more complex in these scenarios, requiring adjustments to the formula.
  • Ignoring non-quantitative factors. The Kelly Criterion relies solely on quantitative inputs (odds and probabilities). It doesn’t account for qualitative factors like team morale, weather conditions, or player injuries, which can significantly impact the outcome of sports events.

The biggest challenge is accurately estimating the probability of an event’s outcome.

Estimating the probability of a win involves analyzing the sport, the teams or players involved, historical performance, and other relevant factors. It requires knowledge, research, and, sometimes, statistical models. This can be the most challenging part of the Kelly Criterion.

Also, this strategy can lead to high volatility in your bankroll, and some bettors may find the recommended bet sizes too aggressive.

It’s worth noting that no betting strategy, including the Kelly Criterion, can guarantee profits. Sports betting involves risk, and outcomes are not always predictable. However, the Kelly Criterion can help manage and optimize that risk.

A Game Changer for the Informed Bettor

Incorporating the Kelly Criterion into your sports betting approach could be a game changer, especially if you’re armed with good predictive skills and discipline. 

Remember, it’s not just about your bets but how and why you make them.

Think about your bankroll in a long-term sense, and you can keep playing, getting more chances of hitting the big win.

 

Matt Brown


Head of Sports Betting and DFS

Matt’s love for sports betting and daily fantasy sports, coupled with a deep understanding of football, hockey, and baseball, shapes his innovative thoughts on Hello Rookie. He has a B.S. in Aeronautical Computer Science and a M.S. in Project Management.