Statistics from the major European leagues over several years show that the number of goals scored in a soccer game is poission distributed.
If we stick to soccer, this can be read like: “The probability of a team scoring X goals” where Lambda (upside down ‘y’) is the average number of goals scored by the team, ‘e’ is a mathematical constant (2,718) and X! is X factorial (X multiplied with all real numbers between 1 and X – e.g. 5 factorial = 5*4*3*2*1 or 7 factorial = 7*6*5*4*3*2*1)
Example Football predictions:
Let’s say that the average number of goals scored by Barcelona is 3,1, and we want to calculate the probability of them scoring 2 goals:
p(2) = 3,1^2 * e^-3,1 / 2! = 0,216
The probability is then 21,6%.
The fact that we are able to calculate probabilities of a team scoring x goals gives us the opportunity to predict the exact goal scoring for each team. Let’s do another example soccer predictions:
Arsenal meet Liverpool at Highbury:
Arsenal lambda (average goals per game) = 1,8
Liverpool lambda = 1,6
We want to calculate the probability of the result 1-1:
First we calculate the probability of Arsenal scoring 1 goal using the poisson formula showed above = 29,8 %
We do the same with Liverpool, and find 32,3 %
We now multiply these two numbers = 9,6 %
In order to predict for instance the home win probability, you simply add up the percentage of all probable home win results (1-0, 2-0, 2-1 etc.).
The main problem is to calculate the lambda value, i.e. the average number of goals scored by the team. It must be an average value of goals scored by the team and goals conceded by the opponent.