Kelly Criterion, the value of value bets

The most cited tool for achieving success in football betting (or any type of betting for that matter) is "value betting". The concept of "value betting" is pretty simple: do not bet on the most likely outcome but on the most valuable outcome. We'll see what "valuable outcome" means and, since we're in the business of providing football stats for betting, I am going to use a football game as an example.

Let's take the match between Manchester City and Manchester United. The bookmaker's payouts were these: 1.83 (Manchester City wins) / 3.65 (draw) / 4.32 (Manchester United wins). This converts to match result probabilities like this: 52% (Manchester City wins) / 26% (draw) / 22% (Manchester United wins). Remember, these are the bookmaker's probabilities.

Now, let's assume you have your own method of determining the probability of the result and your method gives you the following probabilities: 46% / 28% / 26%. As you can see, your method tells you that the most likely outcome is for Manchester City to win. However, that's not the bet you must place. Seems counter-intuitive, doesn't it? In order to determine the bet you should place you must determine the "value" of each bet. To compute the value of each bet assume the game is played 100 times and your method is accurate.

  • If you bet 1 euro 100 times on Manchester City winning you will be right 46 the times. Given the 1.83 payout, you will receive 84.18 euros. A net loss of 15.82 euros.
  • If you bet 1 euro 100 times on a draw you will be right 28 the times. Given the 3.65 payout, you will receive 102.2 euros. A profit of 2.2 euros.
  • If you bet 1 euro 100 times on Manchester United winning you will be right 26 the times. Given the 4.32 payout, you will receive 112.32 euros. A profit of 12.32 euros.

As you can see the most valuable bet is Manchester United win. And that's the bet you should place. Now you may say, "Hey, but that game is not played 100 times and I cannot place 100 bets!". It's true but you also don't bet on a single match. Your system will give you different probabilities for 100 matches and based on those you will have placed 100 "value bets". If your system works consistently over those 100 matches, it would be the equivalent of placing the same "value bet" 100 times on a single match.

Once you have determined what's the bet you should place, the next question is "how much I should bet?". And this is where the Kelly Criterion is going to help determine the value of the "value bet" or how much of your betting account you should use for that bet.

The Kelly Criterion is a formula for determining the amount of money to place on an wager (sport betting, investing in stock exchange, forex etc) which looks like this


[Amount to bet] =  [Probability of success] - [Probability of failure] / [Profit in case of success]

Given the data from the above example we get the following the amount to bet Manchester United win: 26% - 74% / 3.32 = 3.7%. For comparison the amount to bet on a Manchester City win is: 52% - 58% / 0.83 = -17.8% (which means DO NOT MAKE THIS BET)

The Kelly Criterion determines the maximum value of the bet you should place. Based on how risk averse you are you might bet a smaller amount, but never go higher.

There is no correlation between the profitability of a bet and the Kelly Criterion. In the Man.City vs Man.United match, if your argorithm would have given you 61% chances for a Manchester City win, the profitability would have been 12.32 euros but the Kelly Criterion would have been 14%. Quite a difference, no? This also means that, if your prediction method gives you two value betting option with the same profitability the Kelly Criterion will help you either determine which bet to place if you want to place only one bet (based on the bet amount to be risked) or, if you want to place both bets, how much to bet for each option.

As you have seen, the holy grail of sports betting, aka "value bets", requires that you have your own method of determining outcome pro babilities for matches. And for this you need to use simple, yet actionable football statistics. If you know programming and you are into machine learning our Legend package offers you the option to download historical data that you can use to create your own models for determining odds for various match results.


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