Distribuição de Poisson bivariada aplicada à previsão de resultados esportivos

Abstract

The modelling of paired counts data is a topic that has been frequently discussed in several threads of research. In particular, we can cite bivariate counts, such as the analysis of sports scores. As a result, in this work we present the bivariate Poisson distribution to modelling positively correlated scores. The possible independence between counts is also addressed through the double Poisson model, which arises as a special case of the bivariate Poisson model. The main characteristics and properties of these models are presented and a simulation study is conducted to evaluate the behavior of the estimates for different sample sizes. Considering the possibility of modeling parameters by insertion of predictor variables, we present the structure of the bivariate Poisson regression model as a general case as well as the structure of an effects model for application in sports data. Particularly, in this work we will consider applications to Brazilian Championship Serie A 2012 data, in which the effects will be estimated by double Poisson and bivariate Poisson models. Once obtained the fits, the probabilities of scores occurence are estimated and then we obtain forecasts for the outcomes. In order to obtain more accurate forecasts, we present the weighted likelihood method from which it will be possible to quantify the relevance of the data according to the time they were observed.