So I'm trying to predict football (soccer) results, using mathematics. I have already made a Poisson model, since at first glance it seems very appropriate; "The Poisson distribution is popular for modelling the number of times an event occurs in an interval of time or space".
I have found, when reading literature on the subject, that Poisson seems to be the route that people most often take. However I can't help but think that the Poisson isn't quite right.
Just for one reason, for the Poisson to be appropriate, we have to assume that goals are independent events. I'm sure anyone who watches football will agree with me when I say that it seems goals are not independent. It seems so frequent in football that a team scores a goal, and has some kind of impetus to quickly score another.
This leads me to believe that there is an element of Bayesian statistics here. That we should consider the probability of a goal, given that there has recently been a goal.
Getting to my question: Does anyone have any suggestions on how to modify a Poisson distribution to account for Bayes' theorem? Or even, does anyone know of a model that is more fitting to goals in football, than the Poisson model?