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A Zidane Clustering Theorem - Why top players tend to play in one team and how the competitive balance can be restored

24.09.2013 | HWWI Research Paper | von Henning Vöpel

This is a revised and enhanced English version of HWWI Research Paper No.1-3. Empirical evidence suggests that top players often play together in one team. Based on the "O-ring theory" (Kremer 1993) a Zidane clustering theorem is derived. It is argued that the best midfielder is most efficiently allocated when combined with an ace striker, and vice versa. This implies that better teams can payer higher wages, because players are more valuable for better teams than for weaker teams. In equilibrium all teams are of homogenous quality, otherwise a reallocation would occur on the players market. Obviously, such a clustering effect negatively affects the competitive balance. It is shown that the clustering effect must be compensated by decreasing marginal revenue for sporting success in order to restore the competitive balance. This is certainly not the case in the UEFA Champions League where the prize money is exponentially increasing thus contributing significantly to the inherent monopolization in professional sports leagues


Prof. Dr. Henning Vöpel