I am taking all pro athletes to be in the same skill class purely as my own approximation. I haven't supplied any evidence because I don't have any and I didn't claim that I did. I only have the loose statistics that my friend showed me in a few charts for the presentation he is making. I thought it was obvious from my post that I was speculating a plausible explanation given what appears to be evidence that the physical parameters of games have evolved to produce certain statistical regularities in performance.

When you move away from professional caliber athletes, these statistical regularities go away (i.e. pro baseball has a total on-base percentage of about 0.5 but high school baseball is much less). My personal experience playing high school and college sports leads me to believe that as the skill level increases, the variance among the participants goes down rapidly. I felt it was reasonable to extrapolate from this for the sake of an anecdotal comment on a discussion post.

But by all means, if you need every statement I made to be qualified with direct evidence, you should seek better sources than my off the cuff remarks. I never claimed otherwise.