http:// http://en.m.wikipedia.org/wiki/Nonparametric_skew
I asked Shouright if there is a public database to download in order to do analyses and he didn't think there was. I think he gets pre-aggregated data from Football Outsiders and then does his own correlations.
The motivation behind using the (mean - median) / standard deviation definition of skewness is that its domain is from -1 to +1. It is thus interpretable in a similar manner to a correlation. See attached link.
I have never seen skewness used for anything. I have no idea if my hypothesis is correct. I was just "thinking outside the box" and skewness popped into my head as something potentially interesting to look at.
If Shouright had the data, he could do one of his partial correlation calculations between winning percentage and mean YPC, controlling for skewness.