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Tuesday, December 04, 2007

Regression towards meanness

So the BCS won't cotton to a play off for college football teams.

Well, that's plain mean, which is after all, the point.

Actually, the BCS methodology for determining top teams, involving polling, computer analysis, and a coin flip here and there is a much more equitable way of determining top teams than a play off. And here's why.

Consider if you would a simple roll of a die. Cast it a few times and the average result would likely be skewed from one to six. Over time and trials, the mean should always arrive at about three, and given this mediocrity principle, one can pretty reliably predict what the average value for a die roll will be.

Similarly, if you have the luxury of having a playoff series where the same two teams play a best of seven, then you are more likely to arrive at a true champion than if only one game was played. One can picture the howls decrying unfairness if the world series was merely a series of one.

The mediocrity principle is everywhere we look, as we gauge our intelligence, accomplishments, or good fortune not on one instance, but on the average of many. It's the reason that we can survive in the face of adversity, because we know the law of averages. Sports should be no different, but given time and expense, we have to settle for one playoff game whose results are no more representative of the truth than the mere role of a die.

Logically, a computer can average it all out, and come up with a nice averaged answer. A true enough result, but mediocre, and that depressing predictability is something that games are not set out to do.

Thus, the next time you are rooting for the home team, know that the if the winner is beforehand unpredictable, then it's not really a winner until it represents a predictable state of affairs. A mediocre outcome certainly, but mediocrity is after all the shade of the truth.

1 comment:

Craps said...

Hi...quick comment about the dice roll. If I am correct, a single die has a uniform distribution, and although the mean may be 3.5 over time, unlike a normal distribution where the average is more likely, the same is not true for a single die.