Ioannis Ntzoufras

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Dimitris Karlis & Ioannis Ntzoufras (2011)

*IMA Journal of Management
Mathematics*, **22**, 171-182.

## SYNOPSIS

Existing methods for the prediction of football games final score focus on modelling the numbers of goals scored by the two competitors while parameter estimation of the assumed model is usually based on the maximum likelihood approach. Although this approach allows for sufficiently accurate prediction of the final score, it does not account for large or surprising final scores which may deteriorate parameter estimates especially in competitions with insufficient number of games compared to the participating teams (for example, world cup or champions league). In this paper we propose a weighted likelihood approach which allows to underweight specific football scores if somebody feels that the result was not typical and falsifies (in any way) our parameter estimates. Hence the aim here is to reduce sensitivity of model parameters on isolated large or surprising scores. The imposed game weights can be defined subjectively or by assuming a model based structure where the parameters can be estimated using usual iterative algorithms. The weight structure usually reflects deviations from the assumed model. Hence observations-game scores that have low probability to be observed under the assumed model will be under weighted while the opposite will happen for highly expected results. This procedure will provide effective estimates which will be robust even if surprising (under the assumed model) scores are observed. Champions league data are used to demonstrate the potential implementation of the proposed approach on football data.

: Weighted Maximum Likelihood; Outliers; Model Deviation; Bivariate Poisson model.Keywords

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IMA Journal of Management Mathematics,22, 171-182.Transparencies of the related presentation in the 2nd Mathematics in Sport IMA Conference. [detailed results are available here].

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Last revised: 23/11/2011