How bookmakers calculate the probability

Many people know that bookmakers employ a whole staff of analysts who determine the probability of outcomes and then place them in the listings. This indicator directly affects the odds. 

Mathematical analysis: what it is and why a bettor needs it

Mathematics plays a significant role in the activities of bookmakers and players. Therefore, mathematical analysis can be called a set of activities, which includes the following elements:

  • Analysts need to calculate the percentage probability to form bookmaker quotes then.
  • The gambler should do the same thing – determine the probability, but only better than the analysts.
  • Also, the bettor should determine such an important indicator as the bet amount.
  • Let’s consider the first point in detail. Suppose, based on their experience and statistics. The analysts found out that the probability of Chelsea winning against Villarreal is 59%. To get the odds, they divide 100 by the likelihood of winning, i.e., 100/59=1.69. From the player’s perspective, this means that if he decides to bet $100 and the Londoners do best, he will get 100*1.69=169. And the net profit from such a bet would be $169-100=69. 

Valuation bets as a part of metanalysis

The second item in the above list describes a straightforward explanation of gross bets. The bottom line is that you need to find the underestimated events, the odds the bookmaker has higher than they really should be. But, of course, this is only possible if there is an error in the bookmakers’ analysis. The difference between the absolute values and those given by the bookmakers’ experts, for example Betwinner app.

What is the mathematical expectation?

In sports betting, the mathematical expectation can be described as the number of possible winnings if the player constantly bet on the same odds. The term can refer not only to the odds but also to the strategy. 

Dispersion in sports betting

Dispersion is the deviation of the actual results from the expected results. For example, you bet on A player is expected to get $59.3 for every $100 invested. With 1,000, it will be 593 but got 200. Thus, the deviation, i.e., variance, will be $393, or $100/593*200=33.72%, which is quite a lot. We need to improve the probability by analyzing it more thoroughly! Chance has nothing to do with it. 

Bayesian method

Next, let’s look at several methods bookmakers’ analysts use to determine the probabilities and then the quotes. First, the Bayesian approach considers the meaning of probability theory and the dependencies of one event on another. 

Empirical Approach

This determining probability considers the number of possible outcomes out of all possible products – the first divided by the second. 

Monte Carlo method

Bookmakers analysts make a list of criteria and give each of them according to their importance. Then the average value and the quote are determined. 

Subjective probability

Some bettors mix their own opinion into one of the methods described above. It is not based on any numbers.

Strategies when betting “scientifically”

Such strategies are not about determining probability but about managing the playing bank. Their point is that if customers use such approaches, they will stay in profit. 

How to calculate the bookmaker’s margin and probability of an outcome

In addition to calculating the probability and odds, it is also essential to consider the margin, that is, the markup. To sum it, you need to divide 100 by the opposite quotes and add up the resulting values. To calculate the probability yourself, follow these steps:

  • Make a list of criteria based on which the prediction will be made. In soccer, for example, it may be personal meetings, the number of injuries, scoring and conceding home and away, adjusting for the class of opponents and tactics. If it is other sports, the criteria may be different.
  • Study statistics and make a prediction based on them. There is no single formula to calculate the probability. You have to come up with it yourself; it will be challenging for beginners. But gradually, you can come to determine the likelihood more accurately than recognized experts do. Perhaps you will even be hired in the probability calculation department.
  • Try different approaches and different criteria, and improve yourself.


Bookmakers use statistical data to determine the odds. The player’s task is to calculate the odds better than the BC analysts and find underestimated events. Mathematics in betting is also used when determining odds and betting amounts.


Why is it important for the bookmaker to calculate the odds accurately? 

Because his profits depend on it. 

Are the betting odds always correct? 

No, because it is physically impossible to calculate the exact probability of the outcome of so many matches. Bookmakers also make mistakes. 

What factors influence the probability of a match outcome? 

Statistics, the current state of players, place in the standings and other factors. 

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