Equality of Opportunity and Equality of Outcome: Open Leagues, Closed Leagues and Competitive Balance

This paper compares conventional static measures of competitive balance with measures that take account of the mobility of teams into the upper ranks of professional leagues, which we call dynamic competitive balance. We use this measure to compare the open soccer leagues that permit entry by the process of promotion and relegation, to the closed leagues of North America where there is no automatic right of entry. We also identify the theoretical distribution on entrants to the top k ranks assuming that all teams have equal probabilities of winning. We find that the open leagues we study are less balanced, dynamically, than closed leagues, and also that open leagues lie much further away from the theoretical distribution than closed leagues.