Kelly Criterion

Kelly Criterion is a formula used to determine the optimal size when placing bets in sports betting. It is primarily utilized in gambling but is also popular in investing scenarios. It is rumored that successful investors such as Warren Buffett and Bill Gross built much of their fortunes using the strategy. The formula was invented in 1956 by John Larry Kelly, Jr., who was a scientist at Bell Labs.

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Alternative to Flat Betting

In sports betting, Kelly Criterion is a bankroll management strategy and is an alternative a fixed unit staking plan. Kelly Criterion is a variable staking plan with the goal of maximizing bankroll growth by finding the optimal bet size for each wager.

Kelly Formula and Example

These concepts may seem complicated at first, but there is a reason why this formula has been utilized for more than 60 years. Just about anyone can use it, and the math is relatively straightforward.

Kelly Criterion Formula: (xp-q)/x = f

  • X = The odds of your wager converted into a decimal format (decimal odds).
  • P = The probability of success as a percentage converted into a decimal.
  • Q = The probability of losing as a percentage converted into a decimal.
  • F = The solution to the formula in a decimal form which is the suggested percentage of bankroll to bet on the wager.

Let’s look at an example. Say for instance we want to wager on a bet that is +150 in moneyline odds. This is converted to 2.50 in decimal odds. We estimate that we have a 45% chance of winning our bet, which means we have a 55% chance of losing our wager.

(2.50 x 0.45) – 0.55) / 2.50 = 0.23

0.23 = 23%

The formula determines that we should wager 23% of our bankroll on this wager to reach optimal value. This is far from what is recommend by most bettors who subscribe to a flat betting bankroll strategy, which typically tops out of 5% of a player’s bankroll, and even that’s on the high end.

Implied Probability and Finding Value

The formula is simple, but evaluating your chances of success is a bit more complicated. If you look at the example above, you will see that we estimated our win percentage was 45%. Where does that number come from?

Well, each wager has an implied probability. Implied probability is the percentage chance of a particular outcome as it relates to betting odds. The implied probability of a bet at 2.50 (+150 in American odds) is 40%.

In our example, we estimated our edge to bet 45%, which is 5% better than the implied probability for the odds. When using Kelly Criterion, we can only calculate for wagers that are +EV.

The hard part here is quantifying your edge. Most experienced sports bettors have no issues finding value in the lines, but even the best have a hard time figuring out the true edge they have in each bet in many cases.

The Kelly Criterion is excellent if you can accurately predict the probabilities of each bet, thereby correctly calculating your advantage. However, if this is not the case, Kelly betting can be extremely dangerous to your bankroll.

Kelly betting is quite aggressive compared to a flat betting staking plan. If bettors are incorrectly estimating their edge, they will go broke in a hurry. Although the Kelly Criterion is the optimal way to bet if you predict probabilities accurately, some may not prefer it due to the increased risk of ruin.

On one hand, it allows bettors to calculate the size of their wagers, and it makes it easier to decide which amount to bet. On the contrary, if the edge is calculated incorrectly, it can doom their bankrolls.

Fractional Kelly Betting

Kelly Criterion often calls for wagers that exceed 10% or more of your bankroll. As mentioned above, most bettors will never bet more than 5% of their bankroll on a single wager. That’s on the high-end. Many won’t go above 1-2%.

A strategy of some is to utilize the Kelly Criterion but to reduce the bet size by cutting the percentage the formula suggests by ½ or more. This will not only reduce variance but help bettors who have overestimated their advantage on a particular market.

Fractional Kelly betting doesn’t have to be ½ of the calculation. Some may opt for 1/3 of the recommend bet or even less. It all depends on the level of risk you’re willing to endure and how accurate you think your calculations are.

Final Thoughts

Some swear by the Kelly Criterion regarding sports betting while others consider it a waste of time. We’re closer to the latter. It certainly has its uses, but it isn’t something we recommend for beginning bettors or even those at the intermediate level.

If you’re going to go with Kelly betting instead of a fixed staking plan, then we advise you to use some form of fractional Kelly. It is far too likely that you’re not able to quantify your edges correctly and will end up betting over your head.

Remember, the strategy is an aggressive one, if you half your percentage, you can make up for a possible poor calculation. Half-Kelly (1/2) will still typically amount to a higher percentage of your bankroll being bet on each wager compared to a fixed betting bankroll strategy.