Well, home runs per game is a completely weird statistic that is far from the normal distribution that the media would require to support any conclusions about changes and causes. It has 5 modes and is far from normal.

It just takes a bit of thought to see why it is a bogus statistic. If you think for a moment about the constraints of a ball game, it becomes obvious that home runs per game cannot be a well-behaved statistic that can be used to make sharp comparisons.

The number of home runs in a game is an integer, not a continuous variable. The number of league games is an integer too. Dividing these numbers will give rational numbers, but they will not be distributed normally. Since games are almost fixed, the distribution of home runs per game will have modes where the integer-valued home runs are most likely to occur. The result is a very odd distribution that is very far from normal. This picture Home Runs per Game Distribution shows this kinky distribution with the normal overlaid. Not even close.

A bit of reasoning reveals that the progression of a game sets constraints on home runs. If one home run is hit, the odds that two will be hit go up. And if two are hit, the odds that three will be hit go up. And so on. But, as more home runs are hit in a game, the odds that greater numbers will be hit decline because innings and at bats run out.

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Posted by: Flower Online at September 12, 2006 3:30 AM

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