Sunday, October 24, 2010

Bayesian Approach

The NFL blew a call today because they don't appreciate the Bayesian philosophy in statistics.

Here's the situation. A player for the Steelers was running to the end zone. He lost the ball before he scored a touchdown, but the referee didn't see and ruled it a touchdown. The Dolphins challenged the the officials ruled that it was indeed a fumble but that they couldn't give the ball to the Dolphins because the Steelers always get preference (see Super Bowls XL and XLIII), er . . . . because it wasn't clear who recovered the ball.

Let's suppose that the league wasn't just favoring the Steelers and that they believe that when there is a loose ball and the refs can't determine who recovered, the ball should go the offense. Under that rule the ball will go the right team approximately 50% of the time, since the offense will recover a loose ball about half the time. Under a rule that gives the ball to the team that appears to have recovered the ball--the team that is most likely to have recovered the ball--the ball will go to the team that recovered the ball > 50%.

The later rule is based on the Bayesian philosophy, which is the dominant point of view in statistics today. Other approaches have fallen in disfavored because they give an (often) arbitrary preference to some hypothesis--in this case that the Steelers recovered.

The moral of the story is that everyone should study statistics, or just use common sense. But a lot of people lack the later . . .

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