Monday, January 07, 2013 :::
The NCAA division 1-A championship game (as generally recognized) is going on right now. I was cheering for Notre Dame, but I am not surprised to see that Alabama is winning decisively.
The participating teams are the top two teams as decided by a weighted average of some human poll voters (2/3rds) and some computer algorithms that are provided very little information about the teams (1/3rd). My brother and I have discussed in the past that, technically, what you would want is not the top two teams but the two teams with the best claim to be the best team. So, for example, if half of America believes that team A is better than B is better than C and the other half believes that C is better than B is better than A, we shouldn't invite the consensus second-best team, we should invite the top two teams. A practical example of when this distinction might matter is when a team is undefeated, but against a mediocre schedule and, perhaps, having squeaked by in games that shouldn't have been that hard - having beaten Pittsburgh in overtime, for example. Such a team could reasonably point out that they had yet to meet the team that could beat them, yet could also reasonably be considered outside of the top two.
I've been wondering over the last few weeks whether we don't kind of have that here. Notre Dame is undefeated against a mediocre schedule (having beaten Pittsburgh in overtime) and was a 10-point underdog in this game. It is true that the point-spread is not exactly a prediction of the outcome, and is, in fact, designed to produce the same number of gamblers on each side, so it is possible that Alabama is a 10-point favorite largely because they have a wide-spread national following and are playing a school that most college football fans across the country have barely heard of, but that is unlikely to account for the full ten-point gap -- I think it's safe to say that most people looking forward to this game thought Alabama more likely to win. While I'm going to decline to cite any evidence, I suspect a lot of people agree with me that Oregon (which had only one loss, which was in overtime to a team better than Pittsburgh) or Florida or Kansas State would have provided a stronger challenge than Notre Dame as a consequence of being a better team than Notre Dame. Nonetheless, 116 of the 119 humans involved in picking the contenders chose Notre Dame as the best team in the country, as did every algorithm (the algorithms, it should be noted, were not allowed to consider margin-of-victory).
I'm guessing that if you plied these 116 people with veritaserum or alcohol (it is a truism of computer science that algorithms don't drink), some of them would confess that they aren't entirely astonished by Alabama's (I'm jumping the gun, as the game is still in the third quarter, but I'm going ahead and calling it) victory tonight. I wonder if some of them didn't just decide that Notre Dame had earned a place here and should be defeated on the field before being denied the title. The algorithms wouldn't have thought things through in quite this manner, but by being given information on which teams beat which teams and not much else, they were rigged to give a team that -- I can't emphasize this enough -- beat Pittsburgh in overtime credit solely for having beaten Pittsburgh. If the only information available is which teams beat which teams, this presumably helps teams that beat every team they play, but that would not look as good if other considerations (like how decisively they beat those teams) were taken into evidence.
This is all, of course, theoretical, and also somewhat moot after this year or next or whenever the new playoff system takes effect. But I think it's interesting to consider that the voters may have recognized that they aren't just voting on where they think the teams should be ranked, but also more specifically on which teams should be playing for the title.
::: posted by Steven at 11:05 PM