Education

How to Apply Kelly Criterion for Sports Betting – Full Explanation of the Formula

Patrick Lynch
By Patrick Lynch
Sports & Casino Expert
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Updated Jul 8, 2024
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Read time 6 min

The Kelly criterion formula could prove valuable for long-term sports betting profit. To achieve success, you must find a consistent edge over the bookmaker, which means understanding as much as possible about finding value via an event’s true odds.

However, winning also relies on proper staking. You will only earn a steady profit if you consistently bet an accurate amount on events. Kelly criterion is a method of calculating the right amount of money to wager on any given event. This article explains Kelly criterion for sports betting by outlining how it works on real wagers. It also investigates the pros and cons of this method and provides advice on how to utilize it.

What Is Kelly Criterion?

Developed by John Larry Kelly Jr. in 1956, the Kelly criterion can determine how much a person should invest in a given asset to provide optimal growth over time. Today, the most popular use of the Kelly criterion is in sports betting. Gamblers use it to decide what percentage of their bankroll to bet on a wager with a positive expected value.

The two main elements of the Kelly criterion formula in gambling are:

  • The likely winning percentage of the outcome
  • The odds offered by the bookmaker

You are only supposed to make a bet when you have an ‘edge’ over the bookie. This means that by your calculations, the probability of an event happening is greater than the implied probability per the bookmaker’s odds.

Therefore, to get the most out of the Kelly criterion in sports betting, you need to know the expected value of your potential wager.

How to Calculate Expected Value?

A wager’s Expected Value (EV) shows how much you’re likely to win or lose each time. Here is a simple EV formula:

(Winning probability) x (Amount earned per wager) – (Losing probability) x (Amount lost per wager)

Barring a mistake by the bookmaker, the EV of a bet will always be negative, as they have an edge. However, you can generate a positive EV if you find that an event is more likely to happen than the bookmaker anticipates. Doing so will likely involve using software or creating an odds tissue.

Suppose a match between Everton and Manchester City has the following odds:

  • Everton: 7.00
  • Draw: 4.75
  • Manchester City: 1.33

The above corresponds to the following implied probabilities:

  • Everton: 0.143
  • Draw: 0.211
  • Manchester City: 0.752

If you want to bet $10 on Everton, the implied probability of the Toffees winning is 0.143 (14.3%), with a potential profit of $60. The probability of losing is 0.211 + 0.752 = 0.963. Let’s see what the EV of this wager is:

(0.143 x 60) – (0.963 x 10)

8.58 – 9.63 = -1.05

Therefore, your EV is -$1.05 for every $10 staked, a poor return. However, things look very different if your software or system determines that Everton’s real probability of winning is 20% or 0.2.

(0.2 x 60) – (0.963 x 10)

12 – 9.63 = 2.37

Suddenly, you have a robust EV of $2.37 for every $10, a significant edge, and a perfect candidate for the Kelly criterion formula.

If the above seems long-winded, you can make things much easier. You know the bookmaker’s odds on Everton are 7.00, which means they have a 14.3% chance of winning.

If your system shows that the Toffees have a better than 14.3% likelihood of victory, you have a potential edge.

Kelly Criterion Explained

The Kelly criterion formula may look complicated, but it is more straightforward than you realize:

f   = (bp – q)

      _____

     b

  • f = The percentage of your bankroll to wager
  • b = The odds in decimals – 1
  • q = Losing probability which is (1 – p)
  • p = Winning probability

Below are three examples of how to use Kelly criterion in sports betting.

Example 1

Let’s use our Everton versus Manchester City game as our first Kelly criterion example. You want to bet on the Toffees at odds of 7.00 because you believe they are overpriced and represent a value bet. Furthermore, your system suggests Everton has a 20% chance of winning. 

Here’s what the formula looks like:

  • b = 7.00 – 1 = 6
  • q = 1 – 0.2 = 0.8
  • p = 0.2

( (6*0.2) – 0.8) / 6 = 0.066

Multiply that figure by 100, and you’ll find that the Kelly criterion formula suggests risking 6.67% of your bankroll on the above wager.

Example 2

In the second example, we’ll simplify things by focusing on a tennis match. Lucia Bronzetti’s odds of beating Jana Fett are 1.50, with an implied probability of victory of 66.66%. Yet, according to your software, Bronzetti’s true likelihood of winning is 70%. Here is what the Kelly criterion formula looks like in this case:

  • b = 1.5 – 1 = 0.5
  • q = 1 – 0.7 = 0.3
  • p = 0.7

( (0.5*0.7) – 0.3 / 0.5 = 0.1

Once again, multiply that figure by 100. In this case, the Kelly criterion calculator tells you to risk 10% of your bankroll on this wager.

Example 3

We’ll stick with a simple market that has just two outcomes. In the NFL, you think the San Francisco 49ers have a 60% chance of beating the Seahawks and are happy to bet on them at odds of 1.5.

However, this is a mistake because the implied probability of the Niners winning is 66.66%, according to the bookmaker. As your system shows they only have a 60% likelihood of success, you’re giving the crypto betting site the edge.

What happens when you put the above figures into the Kelly criterion calculator?

  • b = 1.5 – 1 = 0.5
  • q = 1 – 0.6 = 0.4
  • p = 0.6

( (0.5*0.6) – 0.4 / 0.5 = -0.2

As you can see, there is a minus value, which means the Kelly criterion recommends no bet. You can save yourself the trouble by avoiding any wager where the crypto site has the edge.

Kelly Criterion Sports Betting Pros and Cons

The use of Kelly criterion in sports betting is widely debated. Some professionals swear by it, while others believe it is much ado about nothing. Let’s investigate some of the advantages and disadvantages of this mathematical staking system.

Pros

  • When used correctly, it maximizes profit as you’re staking the ‘correct’ amount each time.
  • It recommends no bet when there is no statistical edge, ensuring you don’t waste money on poor value wagers.
  • It can lead to steady long-term profits in theory, as it only allows you to wager when you have the advantage.

Ultimately, if you’re mathematically inclined, confident that you have an edge in wagers, and want a long-term staking plan, Kelly criterion betting is potentially ideal.

Cons

  • Using it optimally involves knowing your edge each time, which is almost impossible.
  • Even if you get the edge correct, Kelly tends to overstake, and if you overestimate your edge, your risk of ruin skyrockets.
  • It recommends decreasing your stake as your bankroll decreases; while this means it takes longer to go bankrupt, it also decreases the impact of winning runs.

Calculating your edge is the main issue surrounding using Kelly criterion for sports betting. Even if you have sophisticated software, the chances of it providing a consistently accurate portrayal of your statistical advantage are slim.

Consequently, there is a major risk of overstaking. It won’t take long for your bankroll to collapse in the wake of a few losses. Example #2 is a prime example of overstaking in action. Even if you’re right about the edge, it is fairly small (70% against 66.66%) and certainly not an advantage that warrants risking 10% of your entire bankroll.

If Bronzetti’s odds were 1.80 instead of 1.5, the Kelly criterion formula would recommend risking 32.5% of your bankroll on the wager!

What Is the Best Way to Use Kelly Criterion?

If you insist on using Kelly criterion for sports betting, it is advisable to use a conservative approach. Therefore, it is best to use half or even a quarter Kelly. In example #2, using quarter Kelly means risking just 2.5% of your bankroll instead of 10%, a far more sensible option.

It also makes sense to err on the side of caution when calculating your perceived edge. For instance, if your system says there is a 65% chance of an event occurring and the bookmaker’s odds suggest it is only 40%, you may want to scale down your expectations. Doing so also reduces the amount you risk per wager.

It is unclear whether Kelly is suitable for bets at low odds. There is a possibility of overstaking on relatively small edges for short-priced favorites. At least, that’s what example #2 showed.

Should You Venture Into Kelly Criterion?

The Kelly criterion formula could be useful for calculating stake sizes when you’re convinced that the edge lies with you and not the bookmaker. It enables you to optimize the amount you win with successful wagers theoretically.

However, ‘full’ Kelly criterion bets place you in grave danger of overstaking, even if you calculate your edge correctly. If you overestimate the true odds of an outcome, you could lose your entire bankroll in record time.

Those looking to use Kelly criterion for sports betting should opt for a fractional version as it lowers the overall risk. It is also best to underestimate your perceived risk rather than stake overconfidently.

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Patrick Lynch
Patrick Lynch
Sports & Casino Expert

Patrick has been a professional writer since 2009. He knows the issues players face when trying to find reputable casinos and performs forensic analysis on every site he reviews. Since joining in 2021, Patrick has had his eyes opened by the potential of the cryptocurrency market. With a background in sports betting, he realizes the possibilities afforded to successful bettors when using digital currency.