A few unexpected results have shaken up the Transitivity Rankings, while at the same time revealing some structure. All of FBS is now easily divisible into three distinct groups, which we'll get to in a moment. If you're new to the Transitivity Rankings, you'll probably want to read the introduction to our first post of the season. For the rest of you, let's see where everyone falls after eight weeks of football.
Utah, our number 1 team from the past two weeks, suffered a major tumble after losing to USC last night. The Utes dropped an eye-popping 45 spots, finding themselves suddenly in the middle third of the rankings. Yesterday's other major upset, Florida State's loss to Georgia Tech, wasn't quite as disastrous for the Seminoles, mostly owing to the fact that they weren't so highly rated to start with. Still, they now sit at number 39, an 18 spot drop from last week. Meanwhile, the victory was the first one of note for the Yellow Jackets, vaulting them 34 spots to number 59. The top of the rankings now take on a distinct feline flavor, with the Tigers of LSU, Memphis, and Clemson occupying the top three spots.
A class system for college football
If you were looking closely at the rankings, you might have noticed an interesting pattern. Every team between numbers 24 and 116 have the exact same number of transitive wins (105) and transitive losses (115). What's going on here?
Glad you asked! For the first time this season, we can now classify every team into one of three distinct groups. We'll call them the upper class (ranked 1 through 23), the middle class (24 through 116), and the lower class (117 through 128). Every team in the upper class has a transitive victory over every middle and lower-class team (and maybe a few upper-class teams as well). Every lower-class team has lost to each team in the middle and upper classes (and maybe a few of their fellow lower-classers). Teams in the middle have all beaten each other, while also beating all teams in the lower class and losing to all teams in the upper class.
Class membership may (and, in all probability, will) change as the season progresses. This happens when someone losses to a team from a lower caste, and always results in an expansion of the middle class. If an upper-class team losses to a team from the lower or middle class, they will fall into the middle class (along with any upper-class teams they have already beaten). Likewise, if a lower-class team beats someone from the middle or upper-class, they we be granted membership into the middle-class (along with any lower-class team they have already lost to). Needless, to say, this is something I'll be tracking in the coming weeks.
Interactive path finder
As always, if you would like to know who your team has beaten and what paths get you there, take a spin in our interactive path finder! Some of the paths available to you this week are especially silly. The longest path is UTSA's 28-gamer to beat Illinois (if you'll remember, the longest path available last week was only 14 games). If you're measuring the paths based on actual distances, the longest available is a near-19,000 miler between UTSA and Western Michigan. Happy hunting!