Today at lunch, I briefly thought about how to refine my rescaling of PER, which I call PERrate. I had noticed when doing my assessment of the Spurs yesterday that the PERrate scores tended to be clustered around the league average. This led to the understanding that I needed to create an exponential function that would convert PER onto the same scale as Wins Produced, Win Shares, and (by extension) Composite Score. My first attempt was a straight exponential function, where I divided PER squared by 15 squared, or 225. However, when I tested this using Wilt Chamberlain’s 31.84 PER season in 1963, I got the utterly ridiculous answer of .446. After that, I player around with dividing the actual PER level by a small number before dividing by 225. Even though I knew this would skew the league average downward, I find it unreasonable to believe that anyone has thought that any player is 4.5 times better than the league average, save maybe George Mikan. I started with 1.15, then 1.20, and I finished at 1.25. I decided to use 1.15 as my modifier. The final formula is: PERrate=(PER^2/1.15)/225. Chamberlain’s record-setting season has a score of .385, while the league average of 15 is .087. This is not meant to fix PER or make it more palatable; on the contrary, I believe it should be used to determine how highly is rated compared to how highly he should be rated. Of course, this is tentative, and I might try to come up with something better. Until then, I think this is a good way to measure both perception and perception relative to ability.
P.S. In the end, this would change the judgments I made about the Spurs yesterday if I wished to redo them. I will not at this time, in part because it would eliminate some of the more interesting phenomena, but I will use it in any future evaluations. It would strengthen my “Trade Tony Parker” argument considerably, though….
Revisions: (April 20, 2012) Originally, I had my modifier set to 1.2. However, after publishing this post, I was looking on the Wages of Wins Journal and seeing some old Wins Produced numbers which I only can access when reading certain articles. The fact that a .400 WP48 was not in the realm of fantasy led to adjusting my modifier downward. In the future, I may adjust the modifier depending on league size, but I am not sure if I will do this in the foreseeable future.