The Bivariate Poisson Distribution and its Applications to Football

We look at properties of univariate and bivariate distributions, specifically those involving generating functions. Using these properties we arrive at the bivariate Poisson distribution which we use to simulate football matches. We consider the home effect and the problems involved when estimating our parameters. We view two methods for estimating these parameters and use them to simulate football matches. We simulate the 2009/2010 Premier League, looking at the final results for the season, how the home effect influences the model and how teams compare and differ. We finish by considering how others simulate football matches, specifically the computer games industry.