Sporting contests with games on the field

Masaki Fujimoto


This article studies professional sports leagues where each team consists of offensive and defensive units and plays games on the field during the league’s regular season. It is shown that (i) if each team independently determines the offensive and defensive talent levels demanded so as to maximize the expected win percentage (Pythagorean expectation) subject to the budget constraint, then the teams in the leagues are divided into rich offensive-minded winners and poor defensive-minded losers, and that (ii) if the payroll of each team is the same, then the unique equilibrium talent allocation is Pareto efficient. Otherwise, it is Pareto inefficient.


sports league; games on the field; win maximization; Pythagorean expectation; team payroll; Pareto efficiency

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