If you do not have an almanac with the results of matches, mistakes are inevitable. But you can judge the odds better than the bookmakers.
The theory of probability in betting helps professionals outplay the bookmakers. A correct assessment of the outcome increases the chances of a long-term profit. In this article, we will explore the theory of probability in sports betting and also discuss how to calculate the bookmaker's margin and determine the value of a bet.
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Probability theory in sports betting
Probability theory is a branch of mathematics that studies the patterns of random events and quantities, as well as their properties and operations on them. It allows you to assess the likelihood of an event in comparison with another.
There are three approaches to determining the probability:
A priori. Also called Bayesian method.
With the a priori approach, the probability of each event is determined in advance. For example, when flipping a perfectly symmetrical coin, the probability of getting heads or tails is 50%.
According to the Bayesian method, each flip will alternate between heads and tails. In practice, this is unlikely. Heads or tails can come up several times in a row, but with multiple tossing of a coin, the ratio evens out. This uneven distribution is called variance.
An empirical approach
According to the empirical method, the probability of an event is determined by the formula:
P = N / X, where N is the number of suitable outcomes, X is the number of all possible outcomes.
For example, PFC CSKA in the 21st century won 13 out of 24 home games against Spartak. The probability of a victory for the "army" in the next match with the red and white in their field is 54.16%.
Determined based on the experience of the observer, public opinion or analysis of a specific situation. When assessing the likelihood, take into account as many factors as possible.
Variance is the spread of a random variable relative to its mathematical expectation.
Determine the probabilities of a series of defeats using the formula:
D = (1 - 1 / coefficient) to the power of S, where S is the number of losses in a row.
For example, in the hockey match "Ak Bars" - "Siberia" analysts give a coefficient of 1.25 for the home win. The probability of winning for Kazan is 0.80: 1 / 1.25. In theory, Ak Bars should win eight out of ten matches. In reality, Kazan may lose in three meetings in a row, but at a distance the results will approach the mathematical expectation.
The probability of three defeats in a row is 0.008: (1 - 1 / 1.25) ^ 3.
Monte Carlo method
Monte Carlo method - modeling all possible outcomes for given parameters. The more factors you consider, the more accurately you get the probability for each choice.
When placing bets on sports at bookmakers, consider not only the odds in the line, but also your own estimate of the probability. To be profitable in the distance you need value bets.
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