## Pictures and Steroids Again

I would post this in the comments to the previous post, but I don’t think I can put images in the comments. There are lots of good comments there, too. A few posters implied—or maybe I’m misinterpreting—that if the best hitters dominated the worst pitchers, shouldn’t the best pitchers dominate the worst hitters too? Well, in fact, pitchers also improved in striking out batters just as they were giving up more home runs and hitting more batters. But, the effect of dispersion has been greater on pitchers than hitters, which should lead to more great feats by hitters.

Also, Skip notes that “HR rates vs. pitchers should diverge in the 90s: the best pitchers dish out fewer, and the worst dish out more.” So, I looked at the divergence of home runs allowed across pitchers, using the coefficient of variation as the measure of dispersion.

Now some of this has to do with the increased specialization of pitchers, which might also be a function of a depleted talent pool, so I also looked at the dispersion of home run rates. The outcome is not as pronounced, and the change in dispersion since the 1993 expansion has been quadratic—decreasing then increasing. And. in a historical context, the dispersion in home runs allowed rates is low.

### 5 Responses “Pictures and Steroids Again”

1. Kenny says:

JC, Could you please clarify what the second graph shows? You have the Y-axis labeled the same in both graphs. The first graph I figure is CoV = (standard deviation)/(mean). You indicate in the text that the second graph is “dispersion.” I thought CoV was a measure of disersion? Can you explain what is different about the second graph? Any possible reasons for the difference? Thanks!

2. Kenny says:

Oh, I read it again and I think I figured it out .. is it possible that the first graph is “CoV of HRs Allowed” (looking at what pitchers gave up) and the second graph is “Cov of HRs hit” (looking at what hitters hit)? If so, would the increasing trend in the first graph and the decreasing trend in the second graph provide evidence for your hypothesis that over time the abilities of pitchers has spread out at a greater rate than the abilities of hitters?

3. JC says:

Sorry Kenny,

I fixed the label on the second graph, which measures the dispersion of the home runs allowed rate (HRA/BFP). The first graph measures the dispersion of raw home runs allowed by pitchers.

4. Kenny says:

Thanks for the clarification. I’m trying to think of the meaning we can take from the graphs. I think the first graph might not be the best one to use because of the relief pitcher issue. The second graph seems more promising, but I think it also has a flaw in that it weights equally pitchers who pitched 10 innings and those that pitched 150 innings. Would it make sense/is it possible to make yet another graph, this time weighting the HR rates by the innings pitched (without just ending up with the first graph)?

In any case, assuming we are happy with a given one of these graphs despite any drawbacks, would one interpret increasing dispersion over time to support the hypthesis that hitters are feasting on bad pitchers, and a graph with decreasing dispersion to provide evidence against it?

5. JC says:

I should also mention that the CoV estimates are for pitchers with a minimum of 100 BFP.