Note: this article is the distillation of the final project for a Society & Networks class and, as such, explores college football as a network of teams. I’ve done my best to simplify the language and explain what unfamiliar terms mean. I absolutely could not have done so much analysis without the help of my dear friend (and roommate) Michael Lynch.
In the coming years, conference realignment will dramatically change the college football landscape, with all five major conferences in line for changes. The Southeastern Conference (SEC), Big Ten, Big 12, and Pac-12 have all made waves since July 2022 by announcing the arrival and departure of some of college football’s biggest teams. Each of these moves will change the way schedules are built, most importantly by reducing the number of out-of-conference games played as these “super conferences” are formed.
While speculating on the impact of a USC move to the Big Ten is fun, the underlying impact that moves like USC’s will have on the broader college football network may not be entirely noticeable on first glance. Questions about playoff implications, recruiting, and when Notre Dame will join a conference have flooded ESPN talk shows. Here, I look at the dynamics of the current college football network, hoping to answer 1) how those dynamics might change as teams shift away from out-of-conference games and 2) how those changes might impact significant outcomes (bowl game implications, playoff seeding, etc.).
The Data
Before getting any further, let me briefly talk data. This analysis uses data from the 2000 college football season, consisting of 115 colleges (AKA nodes, the dots on the above network graph) who played a total of 613 games (AKA edges, the connections between dots). A typical rule of thumb might be to not use data that precedes you. Today, we’ll ignore that rule.
Conference alignment has been relatively stable from 2000 to now, and as such the scheduling from the 2000 season is similar enough to modern day for us to draw accurate comparisons. As importantly, Mike and I couldn’t find more recent data in the right format, and this project had an ever-approaching due date.
For a quick refresher on the 2000 season… the majority of teams played 11 games, with a maximum of 12 and a minimum of 7 (UConn, who played fewer total games and multiple non-FBS opponents who were excluded from our analysis). The Oklahoma Sooners defeated the defeating champion Florida State Seminoles in the national championship game. Notre Dame went 9-2 in the regular season before losing to Oregon State in the Fiesta Bowl.
Which teams are the great connectors of the network?
Each year, the College Football Playoff Selection Committee determines the best teams in the nation. With only 9.4% of all possible games being played, head-to-head matchups often don’t exist between top teams, and teams in different conferences can play entirely different schedules. The committee is thus tasked with the difficult task of comparing teams without much comparable data— how does a 10-win SEC team stack up against a 12-win Pac-12 team? Frequently, the committee will look at common opponents — if Notre Dame loses to Georgia by 40 and beats USC by 20, it’s reasonable to assume Georgia is better than USC. Notre Dame often finds its way into these debates because of its consistent team quality and cross-conference schedule, serving as a valuable connector across the wide college football network. As teams become more insulated within their conferences, teams like Notre Dame will only become more important to the dialogue surrounding college football. A deeper dive into our network confirms this view.
First, a quick intro to some network-related terms… A few different measures exist for determining the importance of a team as a connector between two other teams. Closeness measures the inverse distance of a team to all other teams in the network. Betweenness measures the number of shortest paths a team lies on. Simply put, both of these measures indicate how many links you’d have to follow to connect two teams. Teams with high closeness and betweenness are teams that serve as connectors between other teams, while teams with low closeness and betweenness would be those on the outskirts of the network, harder to connect to the rest of college football.
In 2000, Louisiana Tech was the best connector team, scoring first among our 115 colleges in closeness and second in betweenness. Louisiana Tech was a conference-less independent team at the time, and faced opponents from 5 different conferences as a result. The ties created from playing such an atypical schedule meant Louisiana Tech was closely connected to other parts of the network. In theory, this would make them the most impactful game for other teams, serving as the easiest direct comparison across conferences. In practice (where perhaps the 2000 Louisiana Tech team spent too little time), a 3-9 Louisiana Tech team would be a bad loss but a relatively meaningless win in terms of comparison. Wins matter, and that is why Notre Dame finds itself in the national spotlight year after year with its wide-reaching independent schedule.
Independence is the biggest shared trait among teams with a high closeness/betweenness, and a similar pattern can be seen on the other end of the spectrum. Oregon State had the lowest measure of betweenness (Notre Dame was #1 in betweenness, with a score eleven times higher than Oregon State’s). Playing a Pac-12 schedule with strictly west coast non-conference games limited Oregon State’s geographic reach and thus its level of connection to the rest of the network.
For teams like Ohio State and Georgia, adding Notre Dame to their non-conference schedule can be the boost needed to compare them to and differentiate them from top teams in other conferences. A team like Oregon State, on the other hand, may find difficulty developing a national case for a high ranking because of the limited scope of their schedule, even if they are a true top team.
What is the impact of conferences on the network now?
Transitivity, also called the clustering coefficient, represents the likelihood of the network to have adjacent nodes interconnected. Higher transitivity indicates the presence of tightly connected communities. The visual existence of clusters (pictured above; each color represents a cluster) and the conference schedule requirements are signs that clustering is fairly robust in the network, and transitivity would thus be quite high. Both global transitivity (transitivity across the whole network) and local transitivity (individual values for each team, from which maximum and minimum values can be isolated) can help understand how prevalent clusters are in the network. Global transitivity was relatively high at 0.41. Bringing down this network-wide score was independent teams, whose wide variation of opponents meant their opponents were unlikely to play each other. As we saw with closeness, Louisiana Tech’s independence made it the biggest outlier, with a network-low transitivity of 0.11. Wake Forest led the way with the highest transitivity at 0.67. A schedule composed of almost entirely ACC teams who played each other helped insulate Wake Forest from the rest of the network. Transitivity shows the impact of conferences is extensive, limiting the unique games teams can play and, thus, reducing how interconnected the network can be by creating significant clusters.
Given the role conferences play in college football, we knew there would be a high likelihood of finding communities within our network. What does an algorithm think the “conferences” in college football are given the games that are played?
Overall, our community detection methods proved very successful due to the conferences of college football — clusters already exist in the network. This resulted in ten communities, ranging in size from nine to fourteen teams. Overall, these clusters are fairly robust. Since teams within a conference tend to play the same geographically-similar out-of-conference teams, clusters may include non-conference opponents, and thus overlap more than might be expected.
To further understand the network, we ran multiple Exponential Random Graph Models (ERGMs) to determine the probability of a node forming a tie with another node at random. We again anticipated the requirement of 8 conference games to significantly impact this figure, and it did. Our model found that a team had just a 4.9% chance of playing another team at random. This is significantly lower than the 9.4% of possible games that were played and shows just how impactful conferences are in limiting the randomness (and connectedness) of the college football network.
So what’s changing with all this conference re-alignment?
Now that we understand the “base” college football network, we can simulate how the network and corresponding measures might change as conferences expand and reduce out-of-conference games.
To keep this exercise somewhat simple, we looked at how an SEC super-conference might play out, removing its connections to other conferences through three different isolation scenarios — removing a random 50% of the SEC out-of-conference games, a random 75%, and finally 100% of these games from our original network. The resulting schedules were beefed up by adding inter-conference SEC games for those teams which randomly lost out-of-conference games. The new networks allow us to compare centralization, clustering, and distance metrics across scenarios.
So what happened? As we removed more out-of-conference games from SEC teams’ schedules, influence became more centralized in the SEC. We saw an increase in all of our measures of centrality, a decrease in the number of communities and their size, and an increase in the average distance between nodes.
In terms of centrality, we also see a significant increase in closeness when the SEC removes out-of-conference games entirely. This is because the average shortest path from each team to every other team (the calculation for closeness) decreases once the SEC became unreachable. If the SEC were to only remove 50-75% of its out-of-conference games, closeness would still increase as the deepened connections within the SEC bring the entire network closer together. This, of course, would only further solidify the SEC as the most powerful conference.
Our community detection found fewer clusters — 9 instead of 10 — and higher modularity across all scenarios, meaning clusters were easier to find. This can be explained by the SEC’s cluster becoming more defined as it further distanced itself from the rest of college football. Essentially, this measure shows that conferences were more clearly defined that before.
Finally, the average distance between teams increased slightly as we reduced SEC out-of-conference games by 50-75% before increasing significantly when the SEC removed these games entirely. This means that teams become harder to connect (and compare) to one another as the SEC breaks away from the rest of the network, and much harder once the SEC isolates itself entirely.
When paired with the SEC’s strength relative to the rest of college football, these measures show that influence becomes more centralized in the SEC after the creation of its super-conference. Teams become harder to connect without SEC teams serving as connectors and college football thus becomes more fragmented.
Ultimately, this analysis supports the SEC’s attempts to create a super-conference and also signals a need for a larger college football playoff. In a more conference-driven scheduling landscape, comparisons between teams in different conferences will be blurrier. The old saying “you won’t know who will win the game until they play” will ring far truer. The only way to make clear comparisons will be by playing the game.