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What I would add is that mean values are given far too much value. Sure a gain of 82 points of OPS is average, but what is the variance? Is the distribution symmetric? My guess is the variance is greater than the mean. In other words, there is a high likelihood it drops 20 points or rises 200. The problem with 'predictive' baseball tools is that the variance is so large the mean values are not useful.
You identify this intuitively. Somehow I have to reduce the variance so that the mean is more significant -- only look at catchers, for instance, as you suggest. Maybe a GM down selects based on personality, work ethic, and shoulder MRIs, information she has that the general public lacks. Future performance is strongly correlated with health, if I could take out the health variability, I would expect the variance to narrow.
One of the ironies of fangraphs style analysis is that because of an obsession with, and misunderstanding of, sample size they mix in oranges with the red apples and wonder why the expected color distribution of red apples has an asymmetry to the orange part of the color wheel. If we just had a larger distribution of red apples and oranges the asymmetry would go away!?! It's like saying UZR takes three years to stabilize, when we are know for a fact player performance can have extremely large variance over a three year period. What does it mean to stabilize a measure of an intrinsically unstable property. Averaged over all human history, people look effectively dead. Averaged over their lifetimes, Adrian Gonzalez has produced more than twice the WAR per year as Gil Hodges, he must be twice the player!?!