Based on the limiting assumption that sports owners are profit maximizers the invariance proposition holds that revenue sharing has no impact on competitive balance in sports leagues. If owners are win-maximizing sportsmen instead, then revenue sharing can lead to increased competitive balance and higher payrolls. Evidence of the sportsman effect is provided by erosion of monopsonistic exploitation in the four major American sports leagues where players now share about 60% of revenues. Monopsony power erosion forces sports-league cartels to exploit statutory monopoly power in monster deals for media rights fees and public venue subsidies. New evidence on competitive balance suggests that revenue sharing leads to increased balance with or without team salary caps. Optimum competitive balance is an empirical question, and the answer lies between random competition of the NFL and deterministic dynasties of the NBA.