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An application of the generalized Poisson difference distribution to the Bayesian modelling of football scores
Author(s) -
Shahtahmassebi Golnaz,
Moyeed Rana
Publication year - 2016
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12087
Subject(s) - football , poisson distribution , variance (accounting) , mathematics , flexibility (engineering) , poisson regression , bayesian probability , statistics , econometrics , distribution (mathematics) , computer science , geography , mathematical analysis , population , archaeology , demography , accounting , sociology , business
The analysis of sports data, in particular football match outcomes, has always produced an immense interest among the statisticians. In this paper, we adopt the generalized Poisson difference distribution (GPDD) to model the goal difference of football matches. We discuss the advantages of the proposed model over the Poisson difference (PD) model, which was also used for the same purpose. The GPDD model, like the PD model, is based on the goal difference in each game that allows us to account for the correlation without explicitly modelling it. The main advantage of the GPDD model is its flexibility in the tails by considering shorter as well as longer tails than the PD distribution. We carry out the analysis in a Bayesian framework in order to incorporate external information, such as historical knowledge or data, through the prior distributions. We model both the mean and the variance of the goal difference and show that such a model performs considerably better than a model with a fixed variance. Finally, the proposed model is fitted to the 2012–2013 Italian Serie A football data, and various model diagnostics are carried out to evaluate the performance of the model.