Bill James tackles the question, “Would Babe Ruth be a superstar today?” Although Ruth is the example, the question applies to any superstar of any era. Bill develops a model for the standard deviation of talent in leagues, something that is tough to measure. The model starts with assigning random values of talent to players, forming teams from those players, and leagues from those teams. From that he derives the standard deviation of the talent of teams:
Given a sample of 2 million “players” with an average of .500, the standard deviation of skill level was .288, actually .288573, if you need to know.
Let us assume that each fifteen players, generated at random, represent a team. What, then, is the standard deviation of skill level for teams?
It is .068.
Now that’s a really interesting figure. When I saw that figure, I realized that I would have to publish the study.
Why is that a really interesting number? Some of you already know.BillJamesOnline.com
Because that’s almost exactly what the standard deviation of winning percentage for teams actually is. Over the last five years (2014 to 2018) the standard deviation of winning percentage for teams is .070.
So the model looks pretty good, and league standard deviation comes out at .017.
In other words, the talent in the league changes little over time. If you drop a superstar from one era into a league, he’s very likely to be a superstar in that league.
Tom Tango pretty much confirms the math in the comments, using a different distribution of player talent, but getting pretty much the same results.
I wrote recently that I always think the greatest player ever is always playing today. I still think that is true, as players in general are bigger, faster, and stronger. Maybe, however, they are not as much better as I previously expected.
from baseballmusings.com http://bit.ly/2Sg0hlv
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