Four Problems with the BCS

To make a comment that is completely devoid of freshness or originality, the BCS system for determining the NCAA-sanctioned college football national champion is a complete joke. Except it’s not funny.

Kind of like this blog.

(I made a funny! I made a funny!)

Bill James had, as you would expect, a good column in Slate that outlines some of the key issues with the BCS system:

The problems with the BCS are:
1. That there is a profound lack of conceptual clarity about the goals of the method;

This is reflected in the fact that the rankings are routinely described as "computer" rankings. Computers, like automobiles and airplanes, do only what people tell them to do.

Until they become self-aware and try to destroy their creators. But at that point I doubt that we will care very much about the college football championship, so I’m willing to take this point at face value.

2. That there is no genuine interest here in using statistical analysis to figure out how the teams compare with one another. The real purpose is to create some gobbledygook math to endorse the coaches' and sportswriters' vote;

Throughout the 11 years of the BCS, whenever the "computer" rankings have diverged markedly from the polls, the consensus reaction has been, we have to do something about those computers. And they have.

I am shocked, shocked that people would disdain statistics that challenged their preconceived notion of thing. If that sort of thing really happened, websites like Fire Joe Morgan would have been wildly successful. What? Eh? Oh.

3. That the ground rules of the calculations are irrational and prevent the statisticians from making any meaningful contribution;

The prohibition against using point differentials to rank teams, of course, dates from the Nebraska-in-2001 experience, when those dirty Cornhuskers beat Troy State, Rice, Missouri, Iowa State, Baylor, and Kansas all by 28 points or more. The BCS reacted to this by requiring the computer rankings to treat a 56-7 victory the same as a 20-17 contest.

I am a rank mathematical amateur. And that’s not false modesty…I mean, I work in advertising. Outside of counting change, which I rarely use because I have a credit card, there is no reason for me to use math. (Except, of course, during baseball season, when I just look at stats in an Excel pivot table rather than watch the games because going to the games requires me to change out of my pajamas and leave my Mom’s basement. But I digress…)

The fact is that even for an amateur like me it is easy to conceive of how statistics could be used to measure the relative strength of sports teams based on competitive results among them, where not all teams play each other…just like college football where USC may not have played Texas, but they both played Ohio State.

To illustrate, imagine a small league with just four teams, in this instance, Holy Cross, Bucknell, Colgate and Lafayette. None has played before so, pre-season polls be damned, they all start with a comparative strength rating of 50 (on a scale of 1 to 100):

Holy Cross: 50
Bucknell: 50
Colgate: 50
Lafayette: 50

Holy Cross opens their season with a two-touchdown win against Bucknell. Colgate also wins by two touchdowns against Lafayette. Let’s assume, as simple math peons, that a two-touchdown win indicates a relative strength ratio of 80-20. The new ratings then become:

Holy Cross: 80
Colgate: 80
Lafayette: 20
Bucknell: 20

The next week the two losing teams play, with Lafayette running out victorious against Bucknell by a touchdown. We now have information about the relative strength of Lafayette and Bucknell. And we also have information about the relative strength of Holy Cross and Colgate, which we didn’t have before (Lafayette now being known as the more difficult opponent, Colgate’s win over them entitles them to a slightly higher ranking than the Mighty Crusaders).

From this point on, every result between any two teams must adjust, however slightly, the ratings of all other teams. The math to figure out how was beyond me. Luckily, it was not beyond Google…which took 0.00025 seconds to come back with results to my query, including the Perron-Frobenius Theorem, that may hold the answer.

I don’t claim to understand the Perron-Frobenius Theorem beyond knowing that it is different than the Infinite Sportswriter Theorem, but if a little bit of research can get me on the scent of a statistical system that could possibly determine relative strength of teams that don’t play each other, it is clear that someone who knows about these things could, too.

Except, if we used statistics to determine the best teams, what would it matter what sportswriters thought?

4. That the existence of this system has the purpose of justifying a few rich conferences in hijacking the search for a national title, avoiding a postseason tournament that would be preferred by the overwhelming majority of fans.
In the 1990s there was a strong movement, within the NCAA, to organize a national postseason football tournament. The problem was, had the NCAA in fact organized such a championship, two other events would almost certainly have followed:

1. The smaller schools, which outnumber the big football powerhouses about 5-to-1, would have voted to send a lot of the money to the smaller schools that in fact had not participated in the national championship contest in any meaningful way.
2. The big football schools would have bolted and revolted. They'd have walked out of the NCAA and formed their own organization. The two-tiered system of NCAA and NAIA schools would have been replaced by a three-tiered system with the NCAA occupying the middle tier.

It is sad that the result is neither a sixteen team playoff nor a statistical method of determining the relative strengths of teams nor even the old system that let the teams play their whole schedule and allowed coaches and journalists to vote on their relative strength based on the results of that whole schedule, but instead an arbitrary method that determines who will play for the “title game,” the winner of which MUST BE CHOSEN as the national champion.

Because that is the way these things work.

And if they don’t work, we can just adjust the computers, right?