RANKING TEAMS IN AMERICAN FOOTBALL THROUGH TOTAL ENUMERATION

The American National Football League (NFL) stands as a significant sporting event withprofound economic and social implications. Due to the physically demanding nature of the sportand the associated risks to player health, a full round-robin play format is not feasible withinthe league. Therefore, achieving fair and merit-based rankings of teams is imperative. Thispaper proposes a total enumeration approach as a precise solution to the ranking formulationput forth by Cassady et al., despite the NP-hard nature of the quadratic assignment probleminherent in the mathematical model. Total enumeration not only furnishes an exact solution forleagues with a small number of teams but also serves as a benchmark for evaluating the efficacyof heuristic methods for larger-scale problems. The implementation of the total enumerationalgorithm in VBA facilitates performance analysis, with its efficiency assessed for a leaguecomprising nine teams through statistical modeling using the JMP software package. Futureresearch avenues include the incorporation of pruning strategies inspired by the quadraticassignment problem literature and the exploration of heuristic methods for practical leagueapplications. Additionally, the development of a hypothetical, probabilistic game offers anexperimental framework to assess team rankings, enhancing our understanding of competitivedynamics within the NFL.