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IMA Journal of Management Mathematics Advance Access originally published online on September 26, 2008
IMA Journal of Management Mathematics 2009 20(2):133-145; doi:10.1093/imaman/dpn026
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© The authors 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

This article appears in the following IMA Journal of Management Mathematics issue: Special Issue Mathematics in Sport [View the issue table of contents]

Bayesian modelling of football outcomes: using the Skellam's distribution for the goal difference

Dimitris Karlis{dagger} and Ioannis Ntzoufras{ddagger}

Department of Statistics, Athens University of Economics and Business, 76 Patission Street, 10434 Athens, Greece

{dagger} Corresponding author. Email: karlis{at}aueb.gr

{ddagger} Email: ntzoufras{at}aueb.gr

Received on 26 July 2007. Accepted on 14 August 2008.

Modelling football match outcomes is becoming increasingly popular nowadays for both team managers and betting funs. Most of the existing literature deals with modelling the number of goals scored by each team. In this paper, we work in a different direction. Instead of modelling the number of goals directly, we focus on the difference of the number of goals, i.e. the margin of victory. Modelling the differences instead of the scores themselves has some major advantages. Firstly, we eliminate correlation imposed by the fact that the two opponent teams compete each other, and secondly, we do not assume that the scored goals by each team are marginally Poisson distributed. Application of the Bayesian methodology for the Skellam's distribution using covariates is discussed. Illustrations using real data from the English Premiership for the season 2006–2007 are provided. The advantages of the proposed approach are also discussed.

Keywords: goal difference; overdispersion; Poisson difference; Skellam's distribution; soccer; zero-inflated models


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