Model of the Soccer Prediction app

The app returns the expected result (rounded) and the probability of each possible outcome given the guess of the user, the certainty of his/her guess and the results of the Bundesliga matches of the seasons 2010/11 until 2016/17. Let be the number of goals of the home team and the number of goals of the guest . As underlying probability distribution I assumed Here, is the probability measure of the model, that one of the users guess and is the certainty of the users guess. We assume conditional independence of and given and , i.e. and . To model the users guess it is convenient to choose a dirac distribution, i.e. if the user guesses to score goals against and so on. To model the data I assumed the goals to by Poisson distributed, i.e. and so on. This is reasonable since the number of occurences of events happening with a constant rate are Poisson distributed. The model coefficients are obtained by a generalized linear model using the team and the opponent as features. Each match is weighted by where is the time when the match happend and a constant. This constant is obtained by trying different values and choosing the one with the highest accuracy on a test set.