[packs]

Originally Posted by darwinbulldog

Good stuff, but in a normal distribution over 4% (not just 1%) of outcomes deviate from the mean by more than two standard deviations. What I would focus on though are the standard errors of the means, which become tiny with all of the data in a 20-25 year career.

Naturally there's going to be some regression toward the mean, as you allude to in your footnote, but that doesn't have any impact on the rank ordering of where you expect the players' careers to end up if you replayed them under slightly different circumstances. Sure, it's possible that Don Mattingly would end up having the best career in MLB history, but it's more likely that Griffey would, more likely still that it would be Mantle, and even more likely that it's Mays.

I would say it's equally possible that Griffey never becomes Griffey because he sustains an injury earlier in his career.