In part 3.1 I showed results for comparing a simulated true talent distribution for OBP and wOBA to the data. Here I’ll do the same for FIP-. I looked at ERA- also, but I’m not sure it adds anything over and above looking at FIP-, and I’m less sure about the statistical distribution of ERA-.
Assuming typical values for K%, BB%, and HR%, the statistical variation of FIP- has a value of about sqrt(42) per 1000 batters faced. This is something I worked out some time ago using a simulation, and the number stuck in my head. On a per PA basis, it means . Using the same techniques as for OBP and wOBA, here are the contours of FIP-, for 1969-1992, and a limit of at least 350 batters faced,
That is, the mean of FIP- true talent is 99.7 and the standard deviation, 13.3. This implies you should regress by batters faced, or innings.
Here is the comparison of distributions and the ratio of distributions,
and finally, FIP- for the 1969-1992 time frame, and the 1993-2005 time frame, with a 550 batters-faced limit,