Comparisons between European and North American sports leagues have occurred over the years. In this paper, we attempt to bring these comparisons down to the essential elements – what has come to be called Rottenberg’s (1956) invariance principle and theoretical insights into attempts to alter competitive balance using revenue sharing, talent drafts, and payroll caps. We also examine player reserve systems (the reserve clause in North American leagues and transfer restrictions in European leagues) and differences in objective functions (North American leagues are treated under profit maximization while European leagues are treated under utility maximization and win maximization). The focus is on model predictions compared to actual outcomes, and any differences between North America and Europe.