Competition in sport takes a number of forms: competition between individuals, competition between teams in a league during the regular season and post-season, competition between nations in international contests, competition for incoming and existing talent, and others. We analyse the formation of rival leagues, one of the least studied forms of competition in sport. Most standard models of firm entry into an industry do not apply to rival league formation. In North America, sports leagues enjoy special protection from anti-trust law that allows them to operate as monopolists. At the league level, they also enjoy the advantages of scale economies, since a rival league must contain a large number of teams with adequate facilities in order to begin play; this generates large fixed costs associated with entry. We develop a game-theoretic model of entry of a rival league to an existing market. This model accounts for the strategic interaction between the incumbent and rival league, and includes fixed entry costs as well as the costs acquiring new players generates for both the incumbent and rival. We then illustrate the applicability of the model by examining rival league formation in the ‘Big Four’ professional sports leagues in North America, the NFL, NBA, NHL and MLB, over the past 110 years.