Ioannis Ntzoufras

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Analysis of Sports Data Using Bivariate Poisson Models

D. Karlis and I.  Ntzoufras (2003)

Journal of the Royal Statistical Association, D [Statistician], 52, 381-393. 

Abstract

        In this paper, 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 proposed models allow for correlation between the two scores, which is a plausible assumption in sports with two opposing teams competing 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 overdispersion, relative to the simple Poisson distribution, marginal distributions. The properties of the proposed models as well as interpretation and estimation procedures are provided. Illustration of the models is presented using datasets from football and water-polo. 

Keywords: Football; Bivariate Poisson distribution; Difference of random variables; EM algorithm; Zero and Diagonal Inflated Models; water-polo.

[Download paper via Jstor  web-site].

 

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Last revised: 15-11-2001