A Comparative Study of Logistic Models Using an Asymmetric Link: Modelling the Away Victories in Football

José Pérez–Sánchez,Nancy Dávila–Cárdenes,Emilio Gómez–Déniz

doi:10.3390/sym10060224

José Pérez–Sánchez, Nancy Dávila–Cárdenes + Show 1 more

Open Access

https://doi.org/10.3390/sym10060224

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Journal: Symmetry	Publication Date: Jun 15, 2018
Citations: 3	License type: CC BY 4.0

Affiliation: University of Las Palmas de Gran Canaria

Abstract

The target of this paper is to study the relevant factors affecting the victories away from home of football teams in order to fit the probability of winning an away match. The paper addressed the following research issues: (a) Is the identification of the significant variables underlying the results plausible? (b) Can information of these factors increase the probability of winning away from home and assist coaches in their decisions? Empirically, it is shown that there are more home victories and draws than away victories in the professional football leagues in Europe and this fact has to be taken into account. Thus, the classical logistic and Bayesian regression models do not seem to be adequate in this case and an asymmetric logistic regression model is therefore considered. This paper analyses 380 games played in the First Division of the Spanish Football League during the 2013–2014 season. Asymmetric logistic regression from a Bayesian point of view is chosen as the best model. This model detects new relevant factors undetected by standard logistic regressions. In view of the paper’s findings, various practical recommendations were made in order to improve decision-making in this field. The Asymmetric logit link is a helpful device that can assist coaches in their game strategies.

Highlights

In the middle of the 1990s, most of the European football leagues replaced the old point score system with a new one
To evaluate the quality of fitting, we propose three different measures: (i ) the percentage of correct fittings calculated by considering the estimates probabilities; (ii ) the Akaike information criterion (AIC) defined as AIC = 2(k − log(`(y| x, βb))); and (iii ) the deviance information criterion (DIC), given by DIC = −2 log(`(y| x, βb))
The idea is that models with smaller AIC and DIC should be preferred to models with larger

Summary

Introduction

In the middle of the 1990s, most of the European football leagues replaced the old point score system (two points for a victory and one point for a draw) with a new one (three points for a victory and one point for a draw). The consequences of the new point score system are not clear, but, at least in Spain, most teams play in order to get the victory in their home location, and in away games In this sense, in the past, teams playing a football match in an away place were satisfied with getting a draw, at least in. A classical logit model can be used to analyse the factors that determine sporting achievement, but sometimes the individual results are more clearly related to one category than to the another This is the case shown in this paper, in which there are more drawing and winning matches as a local team in the final results of the games, the asymmetric logit model can improve the estimations.

Frequentist Estimation

Bayesian Estimation

Bayesian Asymmetric Estimation

Description of Database

Empirical Results

Conclusions