Keeper, it's a mathematical formula, as far as I know.
I'm starting to see the errors in this. This is what I was hoping for.
First of all, kudos to Dipre for the little primer on UZR, it was informative. There seem to be some fundamental errors in it. 1B seems way too low, CF seems way too high. The range is much greater than I would believe.
However...what seems to be the biggest problem is the lack of a "cap", or maybe better explained as a logarithmic jump rather than a linear one.
It seems to me that to get a true value of someone's defensive ability, it should be bell-curved. Let me elaborate further. I'm not sure what the major league baseball average, and the exact number is truly unimportant. Let's say the average batting average is .270. The farther you get away from .270, in either direction, the harder it is to maintain. The norm will drive you to that average. This is the reason that .400 is very tough to do, but .350 is done ever year for the most part. Even the worst pitchers don't bat .000. Opposite end of the spectrum.
Batting average for major league players falls into this curve..as will most stats that we derive offensively or defensively.
Realize I'm more or less thinking out loud here.
What happens is that there should be a range. Using Dipre's values that he quoted for UZR, there should be a "cap" or logarithmic jump. Say we look at a CFer. He is average, so he gets rated a 4. However to go to 5, to make him equal to an average 3B, he's got to be a good CF. To get to 7, an average 2B, he's got to be Wille Mays. It should be next to impossible to get him to equal an average shortstop. The values should be averaged, and put on a bell curve scale in logarithmic fashion. As of now, in linear format, it's next to useless IMO.