THE BOOK--Playing The Percentages In Baseball

I’m having trouble putting the numbers to words.  What does this actually mean?

If you have extra players/events on the right hand tail… more than you’d expect from a random distribution… does that mean that the individual components of hitting HRs (strength, bat speed, hand/eye coordination, recognizing bad pitches, etc.) aren’t distributed randomly?  In other words, is someone with good bat speed more likely to be also someone who is good at recognizing bad pitches?

Reminds me of an argument I had with a friend one time.  She thought that people who were good looking were more likely to be smart, and vice-versa.  I disagreed.  In other words, if 1 out of 10 people were smart and 1 out of 10 people were good looking, I’d expect 1 out of 100 people to be both smart and good looking.  Likewise, I’d expect bat speed and batting eye to be randomly distributed… but perhaps that’s not the case.  Perhaps both are the product of hard work, and thus someone who works hard is more likely to have the many components of what makes a good HR hitter.  Is this making any sense?

This isn’t what he’s talking about.

He’s starting with a given true talent mean.  That’s his starting point.

His expectation is that this is a center of a random distribution (as explained by the binomial).  So, given that starting point, he expects sample performance to follow that normal distribution shape.

It doesn’t.

However, we shouldn’t expect it to, necessarily, since the starting mean is so low.

Gotcha… actually, I had a question that came up when I was reading the lecture notes that someone linked to the other day from that Berkeley stats class, and I think Victor does it as well.

It appears that the way to account for imperfect correlations is to regress the portion of the “r” value below 1.0.  So with .8, Victor regresses 20%.  However, I was always taught that the “r^2” describes the “percentage of variance due to chance”.  If that were the case, wouldn’t that mean that with an r=.8, that .64 of the variance was due to skill, and .36 was due to chance, and therefore you’d want to regress 36% ?

Log-normal, maybe?  Many truncated distributions are log-normal (the distribution of income, for example), so maybe it’s work with home run frequency...although home run frequency is truncated at both ends of its distribution (0 to 1).  But 1 is a lot further away from the mean than 0 is, so that probably doesn’t matter.