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Journal of Quantitative Analysis in Sports

An official journal of the American Statistical Association

Editor-in-Chief: Glickman, PhD, Mark / Rigdon, Steve

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CiteScore 2016: 0.44

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1559-0410
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Spain retains its title and sets a new record – generalized linear mixed models on European football championships

Andreas Groll
  • Corresponding author
  • Department of Mathematics LMU Munich
  • Email:
/ Jasmin Abedieh
  • Email:
Published Online: 2013-03-30 | DOI: https://doi.org/10.1515/jqas-2012-0046

Abstract

Nowadays many approaches that analyze and predict the results of football matches are based on bookmakers’ ratings. It is commonly accepted that the models used by the bookmakers contain a lot of expertise as the bookmakers’ profits and losses depend on the performance of their models. One objective of this article is to analyze the role of bookmakers’ odds together with many additional, potentially influental covariates with respect to a national team’s success at European football championships and especially to detect covariates, which are able to explain parts of the information covered by the odds. Therefore a pairwise Poisson model for the number of goals scored by national teams competing in European football championship matches is used. Moreover, the generalized linear mixed model (GLMM) approach, which is a widely used tool for modeling cluster data, allows to incorporate team-specific random effects. Two different approaches to the fitting of GLMMs incorporating variable selection are used, subset selection as well as a Lasso-type technique, including an L1-penalty term that enforces variable selection and shrinkage simultaneously. Based on the two preceeding European football championships a sparse model is obtained that is used to predict all matches of the current tournament resulting in a possible course of the European football championship (EURO) 2012.

Keywords: EURO 2012; football; generalized linear mixed model; Lasso; sports tournaments; variable selection

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About the article

Corresponding author: Andreas Groll, Department of Mathematics LMU Munich


Published Online: 2013-03-30


The German state betting agency ODDSET ranked Spain in third place among the favorites for the EURO 2008 with odds of 6.50 (usually, in statistics odds represent the ratio of the probability that an event will happen to the probability that it will not happen; however, European bookmakers specify the gross ratio which represents the ratio of paid amount to stake. So putting €1 on Spain as the EURO 2008 champion would have given back €6.50. Thus, European odds can be directly transformed into probabilities by taking the inverse and adjusting for the bookmakers’ margins) behind Germany (4.50) and Italy (5.50). Before the FIFA World Cup 2010 Spain was ranked in first place among the favorites with odds of 5.00 together with Brazil.

The German state betting agency ODDSET ranked Greece in 12th place among the favorites for the EURO 2004 with odds of 45.00.

Although this represents a quite small basis of data, we abstain from using earlier European championships, as one of our main objects is to analyze the explanatory power of bookmakers’ odds together with many additional, potentially influental covariates. Unfortunately, the possibility of betting on the overall cup winner before the start of the tournament is quite novel. The German state betting agency ODDSET e.g. offered the bet for the first time at the EURO 2004.

There are countless examples in history for such events, throughout all competitions. We want to mention only some of the most famous ones: Germany’s first World Cup success in Switzerland 1954, known as the “miracle from Bern”; Greece’s victory at the EURO 2004 (compare footnote 1); FC Porto’s triumph in the UEFA CL season 2003/2004.

The GDP per capita is the gross domestic product divided by midyear population. The GDP is the sum of gross values added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products.

We had to resort to different sources in order to collect data for all participating countries at the EURO 2004, 2008 and 2012. Amongst the most useful ones are http://www.wko.at, http://www.statista.com/ and http://epp.eurostat.ec.europa.eu. For some years the populations of Russia and Ukraine had to be searched individually.

Unfortunately, the archive of the webpage was established not until 4th October 2004, so the average market values of the national teams that we used for the EURO 2004 can only be seen as a rough approximation, as market values certainly changed after the EURO 2004.

Note that European national teams also gain UEFA team points. For each game played in the most recently completed full cycle (a full cycle is defined as all qualifying games and final tournament games, whereas a half cycle is defined as all games played in the latest qualifying round only) of both the latest FIFA World Cup and European championship, with addition of points for each game played at the latest completed half cycle. Similar to the FIFA points a time-dependent weight-adjustment is used, allocating to both the latest full and half cycle double the weight as to the older full cycle. Thus, the UEFA team points would reflect a lot of information about the current strength of a national team in a European-wide comparison, but as the UEFA changed the coefficient ranking system in 2008, we focused on the UEFA club ranking.

Note that this variable is not available by any soccer data provider and thus had to be counted “by hand.”

The two variables “Maximum number of teammates” and “second maximum number of teammates” are highly (negatively) correlated with the number of different clubs, where the players are under contract, and hence also include information about the structure of the teams’ squads. Therefore, we did not consider the number of different clubs as a separate variable.

This variable is available on several soccer data providers, see for example http://www.kicker.de/.

As we are in a matched-pair design, we do not exclude single observations from the training data, but single matches.

A closer look on the coefficient paths of this model shows that for sligthly smaller values of the tuning parameter than the selected one, the variables ODDSET odds and fairness would have been included. Besides, in most of the training data sets both ODDSET odds and fairness have been included at the optimal tuning parameter.

In comparison to Model 2, for glmmLasso based on LOOCV now several variables are not selected anymore, when the variable fairness (V2) is excluded. This may be due to the considerable correlations between the fairness and these variables, e.g. corV2,V10=−0.29, corV2,V11=−0.16 and corV2,V12=−0.16 (see Table 6 in Appendix A).

Three-way odds consider only the tendency of a match with the possible results winning of Team 1, draw or defeat of Team 1 and are usually fixed some days before the corresponding match takes place.

The transformed probabilities only serve as an approximation, based on the assumption that the bookmakers’ margins follow a discrete uniform distribution on the three possible match tendencies.

For convenience we suppress the index t for both teams here, which indicates the number of the game for a team, as well as the indices j and

corresponding to the match-specific random effects. As the match under consideration could have a different number in the individual match numbering of each team, one should correctly write
and
if Team k and Team l are facing each other in a certain match j, where the superscript indicates that the estimate is depends on the opponent’s covariates.

Similar to footnote 3, in the following we suppress both the indices j and

corresponding to the match-specific random effects and the index for the match numbering as well as the superscripts for both teams, in order to keep the notation simple. Note here that for the two teams of Ireland and Ukraine that did not qualify for either EURO 2004 or 2008 no random effects estimates exist and thus their random effects are set to zero. Besides, it has to be mentioned that the match-specific random effects estimates cannot be used for the prediction of new matches.


Citation Information: Journal of Quantitative Analysis in Sports, ISSN (Online) 1559-0410, ISSN (Print) 2194-6388, DOI: https://doi.org/10.1515/jqas-2012-0046.

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