On the evaluation of soccer players: a comparison of a new game-theoretical approach to classic performance measures

Abstract

In this article, we analyse the relation of a new measure for evaluating the importance of soccer players, recently proposed by Hiller (2015), to classic metrics of player performance. Using state-of-the-art bootstrap correlation testing and a data set of teams for the German soccer league (Bundesliga), we find evidence that even though this new game-theoretical approach has no significant correlation to a large number of performance measures, it is significantly related to some of the most important measures typically used in academic research (e.g. the player scores published by sports magazines and the number of played matches). These results indicate that the theoretically appealing new measure can be considered an interesting variable in pay–performance regressions and should be used accordingly in future research.

Keywords:

• Shapley value
• team games
• player performance
• soccer
• bootstrap testing

JEL Classification:

• C71
• C63

Acknowledgements

The authors thank Martin Schön for giving valuable insights into the properties of traditional measures of player evaluation and specialist terms in soccer practice. Special gratitude also goes to Robert Vinzelberg for manually collecting the variables of our data set from the websites of our data providers.

Notes

¹ For an analysis of basketball, see Bodvarsson and Brastow (1998, 1999). Baseball is covered by the studies of Scully (1974), Sommers and Quinton (1982) and MacDonald and Reynolds (1994).

² Distinguishing different types of players is important because not all kinds of performance measures are equally useful for all kinds of players.

³ Our approach differs from that of Haukoos and Lewis (2005) in that we do not calculate Spearman’s rank correlation coefficient but the Bravais–Pearson correlation coefficient.

⁴ is a typical number of repetitions in bootstrap procedures (see Efron and Tibshirani, 1993; Auer and Schuster, 2011; Behr et al., 2012; Auer and Schuhmacher, 2013a).

⁵ The formal description of the four approaches closely follows Haukoos and Lewis (2005).

⁶ It does not matter whether the Shapley pay-offs are calculated from the perspective of the team or of the entire league. The nature of the Shapley value ensures numerically identical results because, in a given season, a player is only in one team. In the case of a transfer, the single Shapley pay-offs add up to a composite score.

⁷ We can take our measures either directly from the database or calculate them straightforwardly using other database variables.

⁸ A quota is defined as the ratio of the number of successful ‘actions’ (e.g. passes) to the number of total ‘actions’ (e.g. successful and unsuccessful passes). The shooting precision measures the ratio of shots on goal to the number of shots (on goal and fumbling).

⁹ Note that the goals of a player (and all other individual measures) are implicitly related to the way he can interact with his team. Thus, a comparison with the Shapley value ranking is justified.

¹⁰ As these robustness checks do not provide any additional valuable insights besides showing results similar to Tables 2 and 3, we concentrate on verbally summarizing their main implications. Detailed results can be made available upon request.