# A>B, B>C; A>C?

One of things I hammer on sometimes is that there is no such thing as a transitive property in football. We’re hearing a lot of this while the Bowls wind down. And it’s garbage.

The argument goes like this: Team A beat Team B; Team B beat Team C; therefore Team A is better than Team C. To put a face on it, I heard Mike Tirrico arguing that since Mizzou whomped Arkansas and Arkansas beat LSU, that must mean the SEC sucks and Mizzou should be a title contender (this was obviously before the Big 12 champ got dismantled by West Virginia). Another example was someone who claimed USC belongs in the championship because they beat Illinois and Illinois beat Ohio State.

The problem with this is that:

• Using the transitive property ends up with silly results. Based on the transitive property, I know have to assume that Pittsburgh, lowly 5-7 Pittsburgh, would dominate the Big 12. After all, they beat West Virginia in a must-win game. And West Virginia crushed Big 12 Champ Oklahoma. All hail Pittsburgh, the best team in the country!
• You often wind up going in circles. Tennessee beat Kentucky. Kentucky beat LSU. LSU beat … Tennessee. So who is the best of those three teams? The only way out is to not get hung up on a single game and consider the entire body of work.
• And that brings me to my most important point. A team’s performance can vary dramatically from game to game. A few years ago, I looked at Sagarin’s system, which assigns each team a numeric value and claims to predict margin of victory based on the difference between the numbers. So if LSU is 95 and Georgia is 87, LSU should beat Georgia on a neutral field by 8 points.

I found that team performance varied by an average of 7 points from the numerical values. In other words, it wouldn’t be a huge surprise if Oklahoma (Sagarin’s current #1) lost to UConn. Sagarin’s system can give you a probability (if he chose to run it that way). But a certainty? No sir. Not with the way football works in the real world.

The point is this: it is foolish to base your opinion of a team on a single game. On College Gameday, they were going on about how USC can’t be the best team in the country because they lost to Stanford. But flukes happen. If USC plays Standford ten times, they beat them nine times. But the game only happens once in reality. And sometimes, reality lies. Sometimes, a team has a bad day. Sometimes, a team is really motivated (think Michigan two days ago). Sometimes a field goal drifts wide or a fumble bounces into the wrong guy’s arms or the pass is dropped. Shit happens. It’s why football is so fun to watch.

• Even if you could assign each team some objective measure of quality, it still wouldn’t be precise enough to evaluate how two teams match up. Football is all about matchups. A lousy team can beat a better team because they are able to exploit their weakness. Let’s pretend that a lowly 3-8 team sucked at everything but passing while a high-flying 8-3 team excelled at everything but pass defense. Put them on the field and the 3-8 team has a good chance at an upset. Not because they are better but because the matchup favors the underdog.

Concrete Example: Weeks ago, Aaron Schatz of Football Outsiders predicted that the Giants would be the toughest test for the Patriots down the stretch. Not because they were a great team but because their strength — pass rush and defensive line play — was a problem for New England.

Mizzou found that Arkansas’ power rush defense was terrible and exploited it for a record-setting game. that proves Mizzou can beat Arkansas. They still lost to Oklahoma. Twice.

• When it comes to picking a national champ, you want a team that can do everything. A team that’s good on both sides of the ball, has speed, brawn and brains. Can stop anything. Can score in any fashion. There’s probably no team like that in college football right now. There rarely is. So what do you do when you can’t pick out two teams that can do it all, that clearly stand out from the pack?

Well, a playoff might be a good idea.