Evidence confirming the DH "penalty"

In "The Book," Tango/Lichtman/Dolphin found that batters perform significantly worse when they play a game as DH than when they play a fielding position. Lichtman (MGL) later followed up with detailed results -- a difference of about 14 points of wOBA. That translates to about 6 runs per 500 PA.

A side effect of my new "luck" database is that I'm able to confirm MGL's result in a different way.

The way my luck algorithm works: it tries to "predict" a player's season by averaging the rest of his career -- before and after -- while adjusting for league, park, and age. Any difference between actual and predicted I ascribe to luck.

I calibrated the algorithm so the overall average luck, over thousands of player-seasons, works out to zero. For most breakdowns -- third basemen, say, or players whose first names start with "M" -- average luck stays close to zero. But, for seasons where the batter was exclusively a DH, the average luck worked out negative -- an average of -3.8 runs per 500 PA.  I'll round that to 4.

-6 R/500PA  MGL
-4 R/500PA  Phil

My results are smaller than what MGL found, but that's probably because we used different methods. I considered only players who never played in the field that year. MGL's study also included the DH games of players who did play fielding positions. 

(My method also included PH who never fielded that year. I made sure to cover the same set of seasons as MGL -- 1998 to 2012.)

MGL's study would have included players who were DHing temporarily because they were recovering from injury, and I'm guessing that's the reason for my missing 2 runs.

But, what about the 4 runs we have in common? What's going on there? Some possibilities:

1. Injury. Maybe when players spend a season DHing, they're more likely to be recovering from some longer-term problem, which also winds up impacting their hitting.

2. It's harder to bat as a DH than when playing a position. As "The Book" suggests, maybe "there is something about spending two hours sitting on the bench that hinders a player's ability to make good contact with a pitch."

3. Selective sampling. Most designated hitters played a fielding position at some time earlier in their careers. The fact that they are no longer doing so suggests that their fielding ability has declined. Whatever aspect of aging caused the fielding decline may have also affect their batting. In that case, looking at DHs might be selectively choosing players who show evidence of having aged worse than expected.

4. Something else I haven't thought of.

You could probably get a better answer by looking at the data a little closer. 

For the "harder to DH" hypothesis, you could isolate PA from the top of the first inning, when all hitters are on equal footing with the DH, since the road team hasn't been out on defense yet. And, for the "injury" hypothesis, you could maybe check batters who had DH seasons in the middle of their careers, rather than the end, and check if those came out especially unlucky. 

One test I was able to do is a breakdown of the full-season designated hitters by age:

Age     R/500PA   sample size
-----------------------------
28-32    -13.7     2,316 PA
33-37    - 6.4     4,305 PA
38-42    + 1.4     6,245 PA

(I've left out the age groups with too few PA to be meaningful.)

Young DHs underperform, and older DHs overperform. I think that's suggestive more of the injury and selective-sampling explanations than of the "it's hard to DH" hypothesis. 

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UPDATE: This 2015 post by Jeff Zimmerman finds a similar result. Jeff found that designated hitters had a larger "penalty" for the season in cases where they normally played a fielding position, or when they spent some time on the DL.