Non-Transitivity in the National Hockey League: Ranking Teams, Lines, and Players using Game Theory

Abstract

The game theoretical complexity of ice hockey creates a large strategy space for teams to exploit. This suggests teams can counteract any opponent strategy; however, the clear distributions in team strength place emphasis on roster construction and collective performance. We analyze the game theoretical landscape of the National Hockey League (NHL) by modeling the transitive and non-transitive interactions between teams based on possession value of events. We utilize recent methods from artificial intelligence (AI) to rank teams, forward lines, and individual players in the NHL over three seasons. Our rankings satisfy a core social choice axiom that Elo and Bradley-Terry rankings violate in 6.8% and 3.7% of rankings respectively due to extensive non-transitivity.