Composite Poisson Models for Goal Scoring

Goal scoring in sports such as hockey and soccer is often modeled as a Poisson process. We work with a Poisson model where the mean goals scored by the home team is the sum of parameters for the home team's offense, the road team's defense, and a home advantage. The mean goals for the road team is the sum of parameters for the road team's offense and for the home team's defense. The best teams have a large offensive parameter value and a small defensive parameter value. A level-2 model connects the offensive and defensive parameters for the k teams. Parameter inference is made by imagining that goals can be classified as being strictly due to offense, to (lack of) defense, or to home-field advantage. Though not a realistic description, such a breakdown is consistent with our model assumptions and the literature, and we can work out the conditional distributions and generate random partitions to facilitate inference about the team parameters. We use the conditional Binomial distribution, given the Poisson totals and the current parameter values, to partition each observed goal total at each iteration in an MCMC algorithm.