Random variable

Sociology

Bivariate data

Marginal distribution

Archaeology

Population

Count data

Mathematics

Poisson distribution

Statistics

Overdispersion

Demography

Econometrics

Joint probability distribution

Geography

Football

Bivariate analysis

Independence (probability theory)

Poisson regression

Zero-inflated model

Journal of the Royal Statistical Society Series D (The Statistician)

Summary. Models based on the bivariate Poisson distribution are used for modelling sports data. Independent Poisson distributions are usually adopted to model the number of goals of two competing teams. We replace the independence assumption by considering a bivariate Poisson model and its extensions. The models proposed allow for correlation between the two scores, which is a plausible assumption in sports with two opposing teams competing against each other. The effect of introducing even slight correlation is discussed. Using just a bivariate Poisson distribution can improve model fit and prediction of the number of draws in football games. The model is extended by considering an inflation factor for diagonal terms in the bivariate joint distribution. This inflation improves in precision the estimation of draws and, at the same time, allows for overdispersed, relative to the simple Poisson distribution, marginal distributions. The properties of the models proposed as well as interpretation and estimation procedures are provided. An illustration of the models is presented by using data sets from football and water-polo.

Analysis of sports data by using bivariate Poisson models