Competitive balance and assortative matching in the German Bundesliga

In this paper we consider trends in the distribution of player talent across association football clubs over time. Player talent is the most important prerequisite for team success in professional sports leagues and changes in players' assortativeness in regard to the clubs they play for may arguably be an important factor for changes in competitive balance. We offer a new approach for measuring player talent and its distribution - the partial correlation of each player with the goal margin. We use this measure to analyze the degree of competitive balance over time. This approach enables us to examine how player mobility drives competitive balance over time. Empirical results are based on 19 seasons of the first two divisions of the German Bundesliga as well as domestic cup games. Our results show a decrease in competitive balance over time; better teams tend to attract increasingly better players. We show that this is driven by an increasingly unequal inter-divisional distribution of teams, coaches and players, as well as increasing assortativeness in the 1st Bundesliga. We further demonstrate that player transfers between Bundesliga teams results in assortative matching between players and teams. These domestic transfers do not, however, explain the reduction in competitive balance over time. Furthermore, we show that UEFA Champions League payments may have contributed to the reduction in competitive balance over the last two decades.