Model

To measure trends in competitive balance, we look at the team distribution of player talent over time.

For this purpose, we offer a novel approach for measuring player talent (and team performance): The partial correlation of each player with the final goal margin. Similar to the plus-minus statistic used in hockey, this individual performance measure captures a player's impact on a match by focusing on the team's net scoring. This parsimonious measure captures the defensive and attacking quality of teams and allows us to examine the assertiveness of players to clubs over time.

For each individual player playing in a given match, we look at the difference between goals scored and goals conceded during his playing time (taking substitutions and dismissals into account). For lineup players who play a full match this corresponds to the final goal margin. We control for the position of a player to allow for differential impacts of for example offensive players or goalkeepers and allow for positional-depending life-cycle differences by including a polynomial of age of a player in a given match (measured in days). Club performance is measured by two different variables: Teams average performance as a proxy for long run institutions (and monetary endowments etc.) and the average performance of the head coach as a proxy for the medium-term performance. Furthermore, we control for the opponent, home advantage, dismissals, time and division-specific heterogeneity. We related these variables using an ordinary least square model and weight player's impact on the goal margin of a match by the fraction of minutes played.  

To measure competitive balance and its trends over time, we look at the assertiveness (the covariance) of player strength to team performance over time.

Similar approaches have been successfully applied in other fields of economics. Bertrand and Schoar (2003) for example looked at the effects of managers on firm's performance while Chetty et al. (2014) use such an approach to study long-term effects of teacher quality on students. Card et al. (2013) decompose changes in variation of individual wages in West-Germany with respect to variation of person and establishment effects.