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How to calculate the market margin and profit of a bookmaker

In sports betting the theory of earnings breaks down to probability and from there builds up to a number called Market Margin, Payout or Profit. The 3 names stand for the same number looked at from different angles. Since sports betting is about probabilities, the number is nothing fixed or guaranteed but rather an expected statistical value. It shows how much of the stake amount is the bookmaker in the long run expected to keep.

The best way to explain and understand the math in the background is to look at a concrete example where Team 1 meets Team 2.

 1 X 2 2.4 3.2 3

From the numbers you might have guessed straight away, the bookmaker considers the teams pretty much the same strength. Now let’s take a look at how much is the bookmaker expected to earn on this one.

First of all we look at the probabilities

• Probability of home team wins: 1/2.4 = 0.41667 (41,67%)
• Probability of the draw result: 1/3.2 = 0.3125 (31,25%)
• Probability of home team wins:  1/3.0 = 0.3333 (33,33%)

Sum of the 3 numbers gives us the Market Margin 1,0625 – which is 106,25%.

Now the bookmaker’s market margin helps us to calculate the earnings expected to be kept by the bookmaker.

Expected Earnings = (1 – (1 / Market Margin)) * 100% = (1 – (1 / 1,0625)) * 100% = (1 – (0.94118)) * 100% = (0.0588) * 100% = 5.88%

In this case from each £100 stake the bookmaker receives, on average £5.88 is expected to be kept as his profit. You might see the same information displayed differently. It is called Payout and in this case it would be 100% – 5.88% = 94.12%. That means 94.12% is being paid back as punters winnings.

You might want to find out more about how bookmakers earn and we advise you to learn that. If you think they are making money mostly when the underdog wins, you might end up surprised.

The best way to understand the math behind market margin and profit of a bookmaker is a concrete example, where you follow the process step by step