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 it...to 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.