Baseball Musings
Baseball Musings
March 11, 2009
Shrinking Standard Deviation

Earlier I hypothesised an answer to Joe Posnanski's question as to why many more people who played in 1930 made the Hall of Fame versus the people who played in 1980. I suggested it had something to do with a shrinking standard deviation. Here's the data to back up my claim. I looked at all players with 400 AB in a season over a ten year span. From 1926 to 1935, there were 966 player seasons that qualified. From 1976 to 1985, there were 1472 such seasons. The results:

Stat19301980
Data Mean.300.274
Standard Deviation.033.027
BA, 1 SD Above Mean.333.301

Since .300 was and is our gold standard for batting average, it was a lot easier to look good in the era centered on 1930 than 1980. Basically, the voters didn't adjust for the higher offensive era very well.


Posted by David Pinto at 06:39 PM | All-Time Greats | TrackBack (0)
Comments

Well, that doesn't really back up your thesis at all. The real issue is that the mean went down by a full standard deviation. The difference betwen half of the regulars hitting .300 and less than a third of regulars hitting .300 should have been pretty easy to see and adjust for, shouldn't it? Obviously not, though.

Posted by: LarryinLA at March 11, 2009 07:16 PM

So for all the people who complain about Grady Sizemore's inability to hit .300, he would hit .300 almost every year if he played around 1930.

Also, could you explain how you calculated the SD to this non-math-savvy person?

Posted by: Rich I. at March 11, 2009 07:26 PM

I used the Microsoft Excel stdev function.

Posted by: David Pinto at March 11, 2009 07:38 PM

I understand that for hitters, but what about for pitchers? Are you going to calculate stdev on the number of wins, era? Shouldn't the theory be that as hitters had lower batting average, the era should be lower and pitchers look better in 1980 than 1930?

Posted by: Yaramah at March 12, 2009 01:08 PM

Pitchers should have lower era, but HoF credentials seem to start with wins, which don't increase in supply even if pitchers generally gain advantage over hitters. ERA also might not be that much lower if the added pitcher at-bats in 1930, which aren't going to be included when you restrict to players with more than 400 ABs, lower the overall BA enough.

Posted by: LarryinLA at March 12, 2009 01:59 PM

So, if SD for BA has not shrunk very much, does that kill your original hypothesis? Are there other metrics that have seen a dramatic reduction in SD?

And going a little bit wider: do you still think that you have decent answer to Joe's challange? Or is it, as he implies, bias against the modern players?

***********

SD can be calcuated by hand, but it a huge pain.

1) Find the average (mean).
2) Find the difference between the mean and each individual.
3) Sqauare all those differences.
4) Find the average/mean of all those squares.
5) Take the square root of that average.

But as Mr. Pinto write, the easiest way to do it is to have excel handle the math. =stdev(cellrange)

Posted by: ceolaf at March 13, 2009 01:45 PM
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