Calculate the Kelly Criterion
26 June 2019
Most people who place a bet are unsure of the best stake to place. Sometimes, the risk and reward doesn’t match up and people end up staking far more money than they should. That’s where the Kelly Criterion is a useful thing to understand, as it helps punters work out the ideal stake in relation to potential returns and their own betting bankroll.
What is the Kelly Criterion?
In 1956, a scientific researcher by the name of J.L Kelly discussed a formula he had come up with which would go on to become a popular staking method among sports bettors and stock market investors.
The aim of the Kelly Criterion is to help place the ideal stake in relation to your bankroll, by using your own probability of an outcome and the actual betting odds available. It sounds rather complicated, but it isn’t when you understand it and see it in action.
Bet Using the Kelly Criterion
Some people will recommend you always stick to staking the same percentage of your betting bankroll regardless of the chances of a particular outcome. So, you would bet say 3% on every bet you place whether you believe the selection has a 50% chance or a 10% chance of winning.
Betting using the Kelly Criterion looks at things a little differently, as using the formula tells you the ideal percentage of your bankroll to stake every time. It is claimed that this method can help you to make a better long term profit and enables better money management.
Kelly Criterion Calculator
The formula for the Kelly Criterion staking system is:
• [(Probability * odds) – 1] / (odds-1)
So, lets take a look at how the Kelly Criterion works using an example of a selection priced at 11/4, which is decimal odds of 3.75 and an implied probability of 26.7%. But, by doing your calculations, you believe the true probability of the selection winning is 30%.
We need to look at everything as a decimal in order for the formula to work. So, 30% is 0.3 and we use decimal odds instead of fractional. Which gives us something which looks like this:
• [(0.3 * 3.75) – 1] / (3.75 – 1)
• Which goes to (1.125 – 1) / 2.75
• Which is then 0.125 / 2.75
• = 0.045
We then multiply the result of the formula, 0.045, by 100. This gives us a recommended ideal stake of around 4.5% of our total bankroll. If our bankroll is £1,000, our ideal stake would be £45.
If the result of the Kelly Criterion formula is 0.00 or a minus number, then it’s recommended to not bet on this selection at all as the risk far outweighs the reward.
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Fractional Kelly Criterion
Obviously, nothing is certain in sports betting and some people may over-estimate the probability of a certain outcome for an event. To the more cautious bettors among us and to those who believe their calculations gives a selection more chance than they actually have, there’s the fractional Kelly staking system.
The fractional Kelly system allows you to bet a fraction of the percentage calculated using the Kelly Criterion formula, as shown above. Most bettors will usually go with a “Half-Kelly”, which is half of the recommended percentage. But any fraction can be used, depending on how cautious a bettor you are.
The formula for this is exactly the same as above but you multiply the total by your chosen fraction, which looks like:
• [(Probability * odds) – 1] / (odds-1) * Your Fraction
If you want to bet half of the total Kelly amount, you would use the fraction 0.5. So, using the same numbers as in the example above, we get a final sum:
• 0.045 * 0.5 = 0.0225
Multiplied by 100 to get a percentage, we get 2.25% of our total bankroll.
This means that we will stake £22.50 from our £1,000 bankroll instead of the £45 from the original formula.
Using the fractional Kelly method lessens the risk of losing a lot of money fast, so gives you more bets from your bankroll. However, it will mean any winnings will be reduced by half as well.
Betting £45 on an 11/4 shot will pay you total winnings of £168.75 if the selection does win, whereas betting £22.50 will only give you total winnings of £84.38.
We recommend looking at it in terms of your total bankroll and how experienced you are at using the Kelly Criterion.
It’s entirely up to you how you bet using this system but if you are starting out using this formula, you should maybe stick to the fractional Kelly system for a while. Keep a note of your bets using this system and how good your calculated probability of a certain outcome is.
If you find that your predictions are good, and you have a decent sized bankroll, then go on to the full Kelly Criterion system.
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