A Network-Based Approach to Ranking College Football Teams

Using win probabilities, centrality measures, Bradley-Terry rankings, and loop detection and removal, we construct an optionally weighted directed graph representing a season of college football and derive from it a ranking of the college football teams for that season. We use win probability to define “garbage time” and use this garbage time detection to produce an analogous weighted graph, which we can use for more powerful rankings. We use weekly prediction to evaluate our ten implemented ranking algorithms and compare performance with the AP Poll. We find that our modified BeatPaths algorithm outperforms all the other algorithms we tried, weighted algorithms outperform their unweighted counterparts, and our garbage time weighting scheme slightly outperforms a margin of victory weighting scheme. Notably, many of our network-based algorithms outperform the AP poll, which is traditionally considered to be the go-to metric for comparing college football teams. All our algorithms aim to be allowed for consideration by the College Football Playoff Selection Committee. 1 Problem and Context College football has enjoyed a special place in the hearts, minds, and pocketbooks of Americans since the late nineteenth century [14]. However, the sport faces a unique challenge: although many football fans would vehemently argue that their team is the best, there is no objective way to determine the national champion team. Because most games are played within conferences, each team will only directly play a fraction (on the order of 1 10 ) of the other teams. Instead of a round robin or a knockout elimination tournament between all conference champions, the College Football Playoff (CFP) Ranking Committee incorporates a sheet of statistics and the votes of expert judges to choose four teams to compete for the championship [16]. Their choice is often met with grumbling and general discontent. Thus, there remains a standing need for a more robust system for ranking college football teams. There is considerable debate over what factors such an algorithm should incorporate. According to their FAQs, the Selection Committee is allowed to consider “conference championships won, strength of schedule, head-to-head competition, comparative outcomes of common opponents (without incenting margin of victory) and other relevant factors that may have affected a team’s performance during the season or likely will affect its postseason performance,” so any ranking system we create should be in line with these guidelines so it may be used as a tool by the Selection Committee [3]. Simply observing the difference between the number of wins and losses (win-loss differential) is not enough to definitively rank teams: aside from the fact that this would lead to numerous ties, not all wins and losses are created equal. An ideal method might also factor in the magnitude of each victory and each team’s strength of schedule. Margin of victory, in addition to not being permitted, does not suffice since teams should not be encouraged to run up the score at the end of a game. Traditionally strength of schedule only accounts for opponents’ record and opponents’ opponents’ record, i.e., only two steps away on the graph of college football teams [4]. This misses a lot of information encoded in the graph (namely higher order effects) that can easily be considered by using the entire graph in the algorithm. In our paper, we leverage the latent network structure of a season of college football in order to model each team’s strength of schedule, and with this information we evaluate several ranking algorithms against the human-generated AP Poll. Our goal is to illustrate which teams have built the best season résumé and are most deserving to reach the playoffs. While many ranking systems exist, most are either completely subjective (such as the AP Poll) or are entirely statsdriven [18]. The statistics that the CFP Selection Committee uses to rank teams do not tend to correlate well with team strength or ability and do not reference margin of victory, even though margin of victory predicts winning percentage better than nearly any other statistic [8]. Most existing ranking systems do not directly consider the complete network of NCAA Football Bowl Subdivision (FBS) teams when establishing their ranking, and none manage to take score or statistics into account without encouraging a team to run up the score during “garbage time” (a facet of a ranking system that would not be allowed for discussion in the CFP Selection Committee). Our project endeavors to objectively rank college football teams (based exclusively on games from the current season) using a network-based approach. As discussed in the literature, analyzing the directed graph formed at the end of college football seasons (for example, through feedback arc removal and cycle detection) can prove to be a powerful technique in ranking sports teams [19]. By using win probability plots to determine when garbage time begins in each game, we can 1The time at which the outcome of the game is effectively determined, which often occurs well before the game ends, see section 4.2. 1