Catching up with College Basketball's Transitive Property

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Early-season college basketball is a tough nut to evaluate. Teams are still working out the kinks, and with non-conference schedules full of big matchups and holiday tournaments, a true measure of performance and potential can be difficult to predict.

In other words, polls are useless. We know this. The only thing that really matters is what happens on the court. And with a month of games now under our collective belts, the picture is starting to get a little clearer. So what does it show?

For Kentucky, you might think that the answer is “not much.” After all, while the Wildcats are playing well, their only high-profile opponent thus far has been Duke — and that was, of course, a loss. But I think it’s fair to say that the team has progressed since that fateful night in Madison Square Garden. It’s time we found another way to judge our worth.

How’s that? I’m glad you asked.

The Transitive Property

Dissatisfied fans and bellyaching basketball writers alike have long leaned on the transitive property to justify their preexisting opinions about why one team is better than another. It’s simple math: if teams X and Y haven’t played, but X beat Z and Z beat Y, then doesn’t that mean X > Y?

It’s not the most airtight logic, but it makes sense–if you’re willing to follow a yarn to its core. And more importantly, it’s a good way to make yourself feel better about your team when they haven’t played anybody decent in a month. So let’s do that.

First, take Gonzaga. The preseason No. 1 team in the nation, the Zags looked every bit of the part this year before dropping two games in eight days to Duke and Alabama, respectively. The funny thing is, Alabama lost a game just a few weeks ago to Rick Pitino and Iona. For their part, Iona turned around and lost to Belmont the very next day. And did you know that on November 9, Belmont lost a road game to the Ohio Bobcats — the very same group that Kentucky beat, 77-59 in Rupp Arena?

There you have it. Kentucky is better than Gonzaga.

Once you realize that plain fact, the picture gets even clearer. Gonzaga beat #5 UCLA and #7 Texas earlier this year; and UCLA has beaten #4 Villanova, who beat #13 Tennessee, who beat then-#18 UNC, who just beat the living breaks off #24 Michigan. That’s seven ranked teams off the bat that are, according to math, worse than UK.

But why stop there? It’s worth noting that Alabama also beat Oakland this season, which puts us on a direct route (via Oklahoma State, UMass Lowell and Dayton) to proving that Kentucky is better than #8 Kansas. And since the Jayhawks beat #22 Michigan State in the Champions Classic, that gives the ‘Cats the edge over the Spartans, as well as #17 UConn and #21 Auburn. IT’S ALL IN THE MATH!

Still, we’re not done yet. Remember that Duke loss? Yeah, me too, unfortunately. But what if I told you your eyes deceived you that night in New York?

That’s right… bear with me here. Belmont also beat Furman, who beat Louisville, who beat Navy. Back on November 10, the Midshipmen upset #25 Virginia, who went on to defeat Providence. They beat #23 Wisconsin, who beat St. Mary’s, who beat Utah State. That would be the same Utah State team that beat Oklahoma, who just beat #14 Florida, who beat Ohio State on a wild Thanksgiving buzzer-beater. And Ohio State… well, you get it now.

It’s official: UK is better than Duke. I’m sorry, I won’t take any further questions on this point. It’s rock-solid math. That game on opening night, if indeed it really happened, must surely have been rigged in some way.

As it happens, you can trace a line of transitive superiority back from Kentucky (via Ohio or Mount St. Mary’s) to every single team in this week’s AP top 25 — with the exception of Purdue, Baylor and the other four undefeated teams in the rankings. Ergo, #9 Kentucky should be ranked No. 7 at the lowest. Checkmate, pollsters!

Please direct your fury to the crooked national media for covering up this enormous travesty. We just report the facts here.