The transitive property: If a > b and b > c, then a > c. It’s one of the most basic tenants of mathematics and an idea that every person on Earth has used at one time or another, whether they’re aware of it or not. For our purposes, let’s talk about its use in the college football rankings, or at least in how the rankings are perceived.
With over 100 FBS teams and only 12-14 games to be played, the basis of ranking college teams comes from the transitive property. If Ole Miss beats Alabama, and Alabama beats West Virginia, there should be a hierarchy in the polls of Ole Miss-Alabama-West Virginia even though Ole Miss hasn’t played West Virginia. It’s how you compare teams across divisions and conferences.
This idea is solid if we focus on a select group of teams. However, that’s not how this works because there are a lot of wires to cross. Bowling Green beat Indiana who beat Missouri, but are we going to argue Bowling Green would probably defeat Missouri? No, because specific outcomes of college football games are not definite indicators of superiority. Bowling Green played another game against Wisconsin, and it didn't go quite as well.
In any real team sport, Team A defeating Team B does not automatically mean Team A is better than Team B, it merely implies it. If we played the matchup 100 times in the same conditions, maybe Team B wins in 40 of them.
If a > b and b > c are not definitive, we cannot conclude a > c. Yet, people think a > b is definitive every time new rankings are released. The Daily Cardinal’s Big Ten poll in our Gameday issues had Wisconsin come in one spot ahead of Northwestern, the very team that took them down the previous week.
Complaining that Northwestern should be higher than Wisconsin is a total fallacy. It’s an argument that’s going to last for one week, maybe two, when people focus on Northwestern losing to Minnesota or Nebraska and Wisconsin getting back on a winning track by throwing down 400 rushing yards. Focusing on a single game or a single outcome when trying to figure out the superior team is just going to create circles because at some point, we have to use the eye test and outside knowledge.
Penn State beat Rutgers, but we ranked Rutgers higher in the Gameday poll. While their head-to-head matchup implies the Nittany Lions should be ahead, Rutgers’ wins over Washington State and Michigan and their very good offensive coordinator, Ralph Friedgen, make me more comfortable picking them. We try, to use a slightly loaded term, to be politically correct when it comes to rankings. But in the end it just leads to overly reactionary polls that will look foolish in the long run because last week's evidence is probably less usable than a whole season's evidence, even if last week is more recent.
Arizona beats Oregon last week and goes from unranked to the AP Top 10 while jumping the Ducks? Cool, but do we really think Arizona is the better team? The Wildcats went into the Oregon matchup at home knowing it was a season-defining game and played the game of their season. They were only able to beat doormats Cal and UT-San Antonio by a total of nine points. If anyone wants to bet they will stay in the Top 10 by surviving against USC and UCLA, be my guest.
In 2012, No. 1 LSU took down No. 2 Alabama at home in a game marked by suffocating defense and insane turnovers. When the two met for a rematch in the BCS national championship, Alabama pulverized LSU to the point where the Tigers didn’t cross midfield until the fourth quarter. A single, favorable home matchup gave LSU the first win. A neutral matchup with more weeks of prep gave Alabama a blowout. People insisted during that season Alabama was better despite the loss and in the end, they were fully vindicated.
It would be nice to think that we can take a single game’s result as gospel for the ability of two teams, but we can’t. College football’s context is far too broad and indefinite.