Fuzzy Math: Why the BCS Doesn't Work

Jan 8, 2009 at 2:24 pm
So I was in my automobile last night, driving along as I often do, and I heard something really interesting. So interesting, in fact, that I very nearly drove right off the road into some nice person's front yard. Luckily, my reflexes were good enough to save both myself and someone rhododendrons. 

What I was listening to was that new ESPN affiliate on the FM side of the dial. The number is 101.1; I don't remember what the call letters are (Ed. Note: WXOS). Anyhow, Doug Gottlieb was on, and he said one of the smartest things I think I've ever heard on sports talk radio. Granted, that isn't generally that hard to do, but it really was remarkably smart, and it certainly made an impression on me.

What Mr. Gottlieb was talking about was the men's basketball team from Boston College. See, Boston College just a little while back scored the biggest upset of the college basketball season by beating the undefeated, Tyler Hansbrough-led, Number 1 ranked, North Carolina Tar Heels. Then, just a couple of days later, Boston College played Harvard, and lost. 
Gottlieb brought up something I never expected to hear on a sports talk radio show: the Transitive Property. And what's more, he used it in a completely correct manner. 

Now, for those of you who don't remember ninth-grade algebra, the Transitive Property is basically this: if a=b and b=c, then it holds that a=c. It's pretty basic algebra, really; a simple rule regarding the relationship between groups of things. 

Now, why did this come up on an ESPN radio show? Because Mr. Gottlieb was using it in talking about the whole UNC/Boston College/Harvard triangle. See, if the Transitive Property were to be applied directly to this situation, one would conclude that, since Boston College beat North Carolina, and Harvard beat Boston College, then Harvard can, and should, beat North Carolina. 

Well, of course, we all know that that doesn't really hold in the sporting world. Just because Team A beats Team C and Team B beats Team C, we can't make any assumptions about Team A in relation to Team C. It simply doesn't work that way. And that's exactly the point that Mr. Gottlieb was making. It was a remarkably well constructed argument, and, as I said, nearly sent me in to someone's flower bed. 

But wait, he said! There's more. 

In the very next segment, Mr. Gottlieb had on Mel Kiper, Jr., and they were arguing about the whole BCS system. Turns out that Mr. Gottlieb is a big fan of the BCS system as it stands now, for a variety of reasons. Mr. Kiper was screaming and ranting and raving about how awful the system is, but Doug just kept right on talking about why it was good. 

And that's when it hit me. Mr. Gottlieb had already ruined his argument for the BCS with his previous segment. He just didn't realize it. 

See, the BCS system is based almost entirely on the Transitive Property. It's essentially a giant mathematical equation that takes all the opposing squads a team beats, figures up how strong the defeated teams were, and then assigns a value to that victory. What you end up with, in the end, is something along the lines of this: since Oklahoma beat Texas Tech, and Texas Tech beat Texas, then Oklahoma can beat Texas. Follow me so far? 

The problem with that, of course, is the Oklahoma did not, in fact, beat Texas. Texas beat Oklahoma, and rather handily at that. What's worse is that these same principles are applied across conference lines, with teams that never even come close to playing each other. Hell, some of the teams that will end up ranked right next to each other in the final standings.

So when those final rankings come out, after the dust has settled following tonight's BCS Title Game, look at them and then ask yourself whether or not you really believe those teams should actually go in that order. Ask yourself whether you believe that Team A has any business being ranked above Team C, based on their relationship to Team B. Or, honestly, in most cases, their relationship to yet another team who happened to play a team who then, at some point, played Team B. 

As long as the BCS stands as it is, and there isn't even the most basic of playoff systems, we're essentially going to be ranking college football teams by the Transitive Property. And, as Mr. Gottlieb was so nice as to point out, in sports, that's just not the way that things really work.