How To Hit Exact Scores Using The Poisson Distribution

June 02, 2021, by Toby Banks

Hit Exact Scores Using The Poisson Distribution

The Poisson distribution is a mathematical formula used to model discrete events. That is, events whose results can only be whole numbers greater than or equal to 0. This formula gives us the probability that a certain number of events will occur during a period. This distribution is named after its discoverer, who published it in 1838. We will extrapolate the use of this formula to the sports world, specifically football. Based on its definition, we can use it to predict the number of goals in 90 minutes. If you are a bettor, this will surely interest you.

The Poisson distribution works quite well for predicting the number of scores in sporting events, such as soccer matches. Because of this, bookmakers and advanced bettors use this mathematical tool widely. Many statistical experts indicate that the probabilities given by this equation are not very precise for the results of 0 goals and 1 goal. In these cases, these authors point out that it is necessary to adjust the formula. In the example that we will show you below, we will not make adjustments since it is for illustrative purposes only. Using the Poisson Distribution betting formula, we can predict a soccer match outcome. This formula is the following:

P(k) = ((λK)x(e-λ)) / k!

P is the probability that a team scores k goals. The lambda symbol (λ) is the average number of goals scored by a team. The letter "e" is a number called Euler's constant equal to 2,718. Besides, k! is the factorial of k. According to statistics, the results of the major soccer leagues follow the Poisson distribution. Let's see an example:

We want to calculate the probability that the Atalanta - Lazio match result is 2 - 1 using the Poisson distribution. Looking at the Serie A stats, we find that Atalanta's goal average is 2.5 and Lazio's 1.8. We will determine the probability that Atalanta will score two goals as follows:

P (2) = (2.5 ^ 2 * e ^ -2.5) / 2! = 0.26

That is, there is a 26% probability that Atalanta will score 2 goals. Now we calculate the probability that Lazio score 1 goal:

p (1) = 1.8 ^ 1 * e ^ -1.8 / 1! = 0.30

Therefore, Lazio has a 30.0% probability of scoring 1 goal. To calculate the probability that the exact result is Atalanta 2 - Lazio 1 we multiply the two results obtained before:

p (2-1) = p (2) * p (1) = 0.26 * 0.30 = 0.078

Then, according to the Poisson distribution, there would be a 7.8% probability that a 2-1 result would occur in this encounter. It can be confusing and tedious to do this calculation manually. But, we can use tools available on the Internet. For example, there are Poisson distribution calculators that can help us a lot to speed up calculations. With this formula, you can determine possible outcomes probabilities and choose the most likely. You can also calculate the probability that several possible outcomes will occur simultaneously by adding their probabilities. For example, you can obtain the probability of a match ending at under 2.5 goals by adding the probabilities of the 1-0, 0-1, 1-1, 2-0, and 0-2 scores.

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