Choosing the right tools

Having now established two of the types of models that can be used for this project, we now turn our attention to choosing one of them. The fundamental difference between the two is that in the case of the logistic regression model of the match outcome, a 5-0 thrashing is considered (for modeling purposes) as the same as an ugly 1-0 win, while an entertaining 3-3 draw does not differ in any way with a boring 0-0 stalemate. Alternatively, modeling the whole probability distribution of match scores (i.e. assigning a probability estimate for each and every one of the scorelines) allows for these differences at the potential cost of higher estimation burden (possibly accompanied by an increased estimation error).

In effect we have a simple model, and a more complex one. We don't know much about their forecasting ability yet, although one could argue that sufficient backtesting should have clarified if one is significantly better than the other. However, one consideration that should be taken into account is the fact that modelling the whole distribution of goals (i.e. using the complex model) would also highlight cases where other types of betting (rather than 1X2 betting) could be profitable such as the "Number of Goals" market, Asian handicap, or even correct score betting.

As stated above, the chosen model tries to mimic the behaviour of two variables, namely the goals scored by the home team and the ones scored by the away team. In the univariate case, goals in a match can be seen to reflect events taking place at an unknown rate within a time-period (in the football scenario, 90 minutes), assumed to be constant throughout. This is called the "Poisson Process". The probability distribution of goals, that is the probability of the number of goals scored by the end of the match being 0, 1 2 , ... is entirely dependent on the unknown scoring rate. The bivariate case is simply an extension of this scenario, with the two teams having possibly differing scoring rates. But since they are playing each other, they interact, hence it's probable that their scoring rates are not independent, so under this scenario some sort of dependence structure is needed.

Anyone reading this blog will excuse me for not divulging further details for now. When adjustments are needed, more information on the type of model used may be given out but for now, allow me to keep some things to myself... Until then we shall be focusing on what may or may not be useful in predicting football scores.