A network-based ranking system for US college football

Abstract

American college football faces a conflict created by the desire to stage national championship games between the best teams of a season when there is no conventional play-off system for deciding which those teams are. Instead, ranking of teams is based on their records of wins and losses during the season, but each team plays only a small fraction of eligible opponents, making the system underdetermined or contradictory or both. It is an interesting challenge to create a ranking system that at once is mathematically well founded, gives results in general accord with received wisdom concerning the relative strengths of the teams, and is based upon intuitive principles, allowing it to be accepted readily by fans and experts alike. Here we introduce a one-parameter ranking method that satisfies all of these requirements and is based on a network representation of college football schedules.