Saturday, January 31, 2015

Deflater Mess

The statistical rumble over the fumble continues. Did the first analysis use the wrong statistic (similar to miles per gallon versus the gallons per mile discussions of a few years ago), the wrong comparison distribution, or did it not account for the myriad ways and opportunities for fumbling the football? Above is the histogram of fumbles per play (the reciprocal of plays per fumble in the first analysis). The New England Patriots are still separated, now on the left, from the rest of the league, but now they do not look as extreme. The histogram looks much more like what might be obtained from a normal distribution. Now the team is 2.45 standard deviations below the mean (as compared to 3.9 standard deviations above the mean using the plays per fumble statistic). Such results would occur slightly less than 1% of the time. Certainly not the one in 16,000 chance that the plays per fumble would suggest. What we have here is a statistical "teachable moment."

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