from Amazon
Wednesday, April 09, 2008
HR distribution
Victor looks at the distribution of HR. I wrote this at BallHype:
Good job, Victor. The shape you show is pretty much what I expected. After all, the mean HR rate is around .03 HR per PA. At 500 PA, 1 SD = .0076. So, if a guy gets zero HR, then he’s at -4 SD. You can’t get any lower (at 500 PA). Because your mean is starting so low, the downside is very limited, compared to the upside.
I would guess that if you were to compare the HR distribution, not to the normal distribution, but to a random distribution whose mean is .03, you’ll get something very very close to what you are showing.
I would imagine that OBP, BABIP, and XBH/H would show something much closer to a normal distribution. Probably even K/PA. (As a bonus, K/PA is not really frought with the selective sampling issues that Victor noted.)