Kelly Criterion: Stake Calculator, Definition, Formula

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How does this Kelly Criterion Calculator work?

The majority of Kelly’s criterion stake calculators on the market ask you to insert four types of data:

• Your actual betting account balance
• The odds you want to place a bet on
• Probability of winning in %
• The fraction of Kelly you want to use

This approach to calculating the right stakes might seem the simplest until you need to insert the true statistical probability of the betting outcome you chose.

To have the correct stakes with the Kelly criterion calculation, the true statistical probability of the outcome is mandatory.

The odds you want to place a bet on are hopefully overpriced, so calculating the probability from that is impossible.

This is why I developed a new approach, the Kelly criterion stake calculator, that allows you to easily find out the statistical probability.

How is this performed?

• You find the same betting market at sharp/accurate sportsbooks such as Pinnacle
• Insert these sharp odds in the right fields (sharp odds same & other outcome)

Definition of Kelly Criterion staking in sports betting

The Kelly Criterion is a mathematical formula that can be applied in sports betting to help bettors calculate the most optimal stakes. This formula was initially developed by J.L. Kelly in 1956.

The original goal of this formula was to increase wealth by optimizing financial portfolios. Fortunately, later bettors started using the formula to achieve a more effective stake-sizing strategy.

The Kelly Criterion money management method in sports betting has the role of reducing the risk and increasing the long-term winnings in the most optimal way.

It has the biggest role in value betting strategies, where the goal is to generate long-term profits by beating statistical probability with the help of overpriced markets.

The formula takes into consideration factors such as the size of your actual betting balance, the odds you want to bet on, and the true probability of the outcome to win.

The goal of the Kelly Criterion staking system in sports betting is to reduce the effect of long losing streaks to avoid losing the whole betting balance.

It also has the role of enhancing the winnings when facing longer winning streaks. Both roles of the Kelly staking method are applied with the final goal of getting the most optimized results in the long run.

Relevant article -> Check my list and guide on the best EV betting tools.

How is statistical probability calculated?

To make sure you understand how the true probability is calculated by this Kelly Criterion calculator, here is the full process:

• Both outcomes are used to figure out the house edge of the bookie
• The true odds are calculated with the help of the house edge
• The true statistical probability is calculated from these true odds

Fractional Kelly and its role

The Fractional Kelly data is 1 as a default; you do not need to include anything if you don’t want to.

Letting it be 1 means you follow the optimal staking method recommended by the original formula.

Reducing this number will result in using a lower % of the actual betting account balance as a stake.

Bettors with a low risk tolerance tend to use a fraction of the stake recommended by the calculator to lower the risks of losing the whole betting balance.

Using a smaller value than 1, such as 0.5 or 0.7 for Fractional Kelly data will also decrease the effect of variance.

While this sounds great, it has the downside of slowing down lowering the winning process and profitability.

If you need additional info on how this money management strategy works, check my dedicated Kelly Criterion stake sizing article.

What is the formula for Kelly Criterion in betting?

The Kelly Criterion formula in sports betting can be summarized as follows:

f = (bp-q)/b

The explanation of this formula:

• f  is the fraction of your actual balance you need to use as a stake
• b is the odds you need to place a bet on in decimal format – 1. (For example, if the bet pays 3 to 1, then b=3)
• p is the probability of winning the bet
• q is the probability of losing the bet (which is 1−p)

The components of the Kelly Criterion formula in betting:

– The numerator (bp – q) calculates your ‘edge’, which is the expected profit per dollar wagered.

– The denominator b is the odds you’re getting on the bet, adjusted for the fact that odds are typically quoted including the return of the stake.

The result, f, represents the optimal proportion of your bankroll that you should wager on a given bet to maximize your long-term growth rate.

How can Kelly’s criterion be used in sports betting?

To use the Kelly Criterion in sports betting, you need to calculate your positive EV (expected value), also mentioned as edge, determine the odds, and apply the formula.

1. Calculate Your Edge

Calculating the positive expected value/edge over the bookmaker is the first and essential part of applying the Kelly Criterion staking method properly.

This calculation is done by estimating the statistical probability of a sports outcome you want to bet on (signed as p in the formula) and comparing it with the probability implied by the odds offered by the bookie. 

As an example, if you calculate that a football team has a true 50% chance of winning, but the sportsbook offers odds that reflect a 40% chance, you have an edge.

2. Determine the odds

The easiest way to calculate the Kelly Criterion stake for your bet is by using odds in decimal format. In case your odds are in Moneyline or Fractional format you can use a simple odds converter and you can take the next step.

3. Apply the Formula

In the next step, you need to substitute each data/info about your betting opportunity into the Kelly Criterion formula. The result will be the percentage of your bankroll you need to use in that specific betting opportunity.

4. Calculate Your Bet Size

If you multiply the fraction obtained in the previous set from the Kelly formula by your total betting bankroll you will get the exact stake you need to use. 

Your total bankroll when using the Kelly Criterion formula for betting can be your actual balance on your bookie account or the overall money you allocate for wagering.

5. Consider Using Fractional Kelly

Sports bettors face variances daily. This betting-related phenomenon can destroy your balance even when using the Kelly Criterion staking strategy.

For this reason, many bettors choose to use the so-called Fractional Kelly staking method. 

It means instead of using the whole stake advised by this formula, you can reduce the risked money by using half or a quarter of the recommended stake.

This fractional Kelly staking method reduces the effect of long losing streaks. It also has the advantage of reducing the effects of a wrongly calculated positive EV of a bet.

Make sure to check the betting stake calculator/simulator and find out which stake sizing generates the most profits for your strategy.

6. Monitor and adjust the staking

Many times, bettors don’t have the desired results even when using the most effective Kelly Criterion staking strategy. There can be many reasons why you fail, such as not being able to define the true probability of an outcome accurately.

By monitoring your results with a spreadsheet or an automated tracking system like RebelBetting, you can spot mistakes.

Adjusting the fraction of your Kelly staking or the markets/odds ranges used in your strategy can significantly increase your long-term results.

What is an example of a Kelly criterion stake sizing in betting?

Football example:

– Event: A football match between Team A and Team B.

– Your Assessment: You estimate that Team A has a 50% chance of winning the event.

– Bookmaker’s Odds: the sportsbook offers odds of 2.15 for Team A’s win.

Making early calculations:

1. Determining the Variables for the formula:

– p (Your Estimated Probability of Winning): 50% or 0.50.

– q (Probability of Losing): The complement of p, which is 50% or 0.5 (1 – 0.50).

– b (Decimal Odds – 1): For odds of 2.15, b is 1.15 (since 2.15 – 1 = 1.15).

2. Calculation:

– The formula is (bp-q)/b).

– Plugging in the values: (1.150.5-0.5)*1.15.

– The calculation becomes 0.075*1.15 = 0.0825

– So, the Kelly Criterion formula suggests you should wager 8.25% of your bankroll.

3. Determining Bet Size:

– If your total betting balance is $500, then according to the Kelly Criterion staking formula, you should bet 8.25% of $500, which is $41.25.

Example summary:

As mentioned above, the stake size advised by the Kelly Criterion formula can seem high.

For this reason, many bettors should use a fraction of this stake. In this example using a stake of $20 or even $10 would generate significantly less profits in the long run. 

But proportionally decreasing the Kelly stake will guarantee facing fewer risks of losing the whole betting balance when losing many bets in a row.

Is the Kelly Criterion or flat staking better?

Using the right stake sizing strategy between Kelly Criterion and flat staking for betting depends on multiple factors, such as your balance size, risk tolerance, and the strategy you use.

We already know how the Kelly-style staking method works, so here is a little info on flat staking.

The flat staking sports betting staking method involves wagering the same amount on every bet, regardless of your edge and odds used. 

1. Risk Management: While using the flat staking method, the risk gets lower as your bankroll grows. The Kelly Criterion can result in huge stakes when your betting balance grows.

The risk of using the Kelly method does not grow when the balance is bigger. With flat staking, on the other hand, the risk level changes all the time.

2. Profit Potential: Using Kelly style staking has a higher profit potential in the long run than flat staking.

3. Usability/complexity: The Kelly Criterion stake sizing method requires more effort and time investment compared to flat staking.

While following a value betting strategy, the odds are dropping fast, which makes the manual Kelly stake calculation almost impossible. Flat staking, on the other hand, does not require effort or time investment.

In summary, flat staking is a more beginner-friendly method, with the downside of lower profit potential.

The Kelly Criterion [1] sports betting stake sizing strategy is more profitable in the long run but it requires more skills, time, or an automated in-built stake calculator to use it effectively.

Is the Kelly Criterion stake management the best for football betting?

The Kelly Criterion [2] stake size management strategy is the best for football betting only if it is included in value betting software. An in-built calculator automatically includes the edge over bookies and displays the desired stake instantly.