Sunday, December 2, 2007

Hawaii, and the BCS Big Conference Bias

Ever since it's inception, the BCS has been a wonderful case study of human psychology in action, as the college football wonks attempted to create a system of selecting their championship finalists that didn't depend on polls. And every year the process gave them results that differed sufficiently from the polls, they declared it flawed and altered be more like the polls.

This year a flaw in the BCS process comes to light that is more insidious, and shows once again that a good understanding of mathematics can help avoid some undesired outcomes.

The problem has actually been a part of the process many years. It was put there when the BCS succumbed to the complaints of some coaches and commentators that having computer ratings play such a large role in the process (as it did at the time) encouraged teams to run up the score against inferior opponents in order to increase their rankings. Never mind that running up the score helps one obtain superior poll numbers as well, or that no player has ever died or been psychologically scarred by giving up one-too-many touchdowns, or that what constitutes "running up the score" vs "winning convincingly" is in the eye of the beholder, or that good computer rankings (as Jeff Sagarin so patiently tried to explain) have a formula of diminishing returns on score differential. Winning by 100 does not count as 5x as much as winning by 20, but it does and should count more.

Nonetheless, the BCS required the computer rankings to ignore score. And as so often happens with good intentions, what was designed to protect the weaker teams actually hurt them far more than a 70-0 drubbing. It completely locked them out of the BCS championship game, just as surely as if they had been forbidden on paper from participating.

Here's why: with the computer rankings ignoring score, the only component that matters (aside from winnning) is quality of competition. A team from a major conference who is 10-1 is going to rate higher than a team from a weak conference that is 10-1, and that is as it should be, all things being equal. But there is the rub, for what if the major conference team has won by an average score of 21-17, whereas the minor conference team has won by an average of 52-3? Now who is superior? Hard to tell. However, it is not hard to tell who will be ranked higher by the computers - the team from the major conference. Always.

Hawaii is the victim of that this year. They are the only undefeated team in Div I (or whatever it is called now) in the nation. But they are only ranked 12th in the BCS because they play in a minor conference. They've won their games by an average score of 43-24, but it wouldn't matter if they won them 100-0, they could never reach the championship game because their weak schedule guarantees the lame #14 ranking in the computers they have now.

Now some of my more scientific-minded readers might be wondering: So what? It's only football. True, but this is not about football. This about how a lack of a good mathematical understanding in our society can lead to subtle social injustices inflicted by otherwise well-meaning people. I don't think the BCS leaders decided to exclude teams from small conferences from the championship, but they didn't understand the math, so that is exactly what they have done.


Harriet said...

Some comments: the Sagrin computer ratings does have a score component to it, and the rating with the score component is indeed a better predictor than just wins and losses.

1) we don't want teams to run up the score and
2) teams which have spread type offenses end up winning by bigger margins against overmatched teams than running teams do, even when the running team is better.
3) the human element (polls) account for winning margins (you get rated higher by humans for winning 35-0 and for winning 14-13).

As far as Hawaii goes:

Northern Colorado W 63-6 --
Sat, Sep 8 at Louisiana Tech W 45-44 --
Sat, Sep 15 at UNLV W 49-14 --
Sun, Sep 23 Charleston Southern W 66-10 --
Sat, Sep 29 at Idaho W 48-20 --
Sun, Oct 7 Utah State W 52-37 --
Fri, Oct 12 at San Jose State W 42-35 --
Sun, Oct 28 New Mexico State W 50-13 --
Sat, Nov 10 Fresno State W 37-30 --
Fri, Nov 16 at Nevada W 28-26 --
Fri, Nov 23 (17) Boise State W 39-27 --
Sat, Dec 1 Washington W 35-28

Two of their biggest wins (Northern Colorado, Charelston Southern) were against non-division I competition.

I'm sorry, but even Duke or Notre Dame would have a winning record against this type of schedule (though admittedly neither is as good as the Rainbow Warriors this year)

Ok, I am not really arguing with you; I just saw an excellent opportunity to talk football with a science type. :-)

ScienceAvenger said...

Oh I agree in large part with your analysis of Hawaii. I'm not saying they are the best team in football. My argument is that even if they were, they would not make it to the title game, and that is wrong. At a bare minimum, and legitimate competition should at least have the possiblity of any of the participants winning. As for your three points:

1) Why not? I once played on a team that lost 77-0. Did my little inflated ego good. As Sagarin put it "Winning by 100 is better than winning by 20. It's not five times better, but it's better."

2)I can see your point as far as proportions. Is the team that wins 42-21 better than the one that wins 14-7? I'd say not, and the computers might say yes. However, one could argue that 42-21 is better than 14-7 because 14-7 is only one fluke play away from a tie, whereas 42-21 is three plays away.

3) Yes, the human element of the polls does take the larger scores into account, but that is hardly an argument in your favor. Why ban it from the computers if it is a legitimate part of the human side of the equation? Whatever the beef with the computers (and #2 is legitimate one), that is paltry compared to counting a 3-0 victory the same as a 42-0 one.

Were I BCS God, here is what I would do: Call for anyone interested in having their computer ranking system used in the BCS to submit their system. I would then backtest the system using 5 or so of the previous years results, and whichever 7 systems predicted the outcomes most accurately would be used. Sure, it would be imperfect, but it would have the one most important component the current system lacks: every team would have equal opportunity to win.