## Does the DH Rule Cause Batters to be Hit? June 2, 2010

Posted by tomflesher in Baseball, Economics.
Tags: , , , , , , ,

In an earlier post, I crunched some numbers on the Designated Hitter rule and came to the conclusion that the DH adds about .3 extra trips to first base per game after accounting for trend. I’m going to play around with another stat that a lot of people seem to think should be affected indirectly by the DH rule.

The Conventional Wisdom™ is that the DH should increase hit batsman. The argument is that pitchers don’t bear the costs of hitting a batter with a pitch because they don’t bat, so they’ll be less careful to avoid hitting a batter or more likely to plunk a batter out of malice. Do the numbers bear that out?

To attack this question, I’m using the same dataset I used in the earlier post – the per-game average data for each league since 1954, with an added dummy variable for whether the DH rule was in effect that year, and with time normalized to begin with 1955 and an added quadratic term. (I pulled it from Baseball-Reference.com.) I started using the same variables as the previous post:

$\hat{HBP} = \hat{\beta}_{0} + \hat{\beta}_{1}t + \hat{\beta}_{2}t^{2} + \hat{\beta}_{3}DH$

That is, check for a trend and then after controlling for that check to see if there is a significant effect based on the DH rule. However, it occurred to me that there might be an experience effect – if more players are showing up in the league, you might get matching effects for pitchers with no control hitting batters and for batter with no experience crowding the plate because they haven’t been trained not to. I added a term for the number of batters in the league to control for that:

$\hat{HBP} = \hat{\beta}_{0} +\hat{\beta}_{1}t + \hat{\beta}_{2}t^{2} + \hat{\beta}_{3}Batters + \hat{\beta}_{4}DH$

The regression output was:

 Estimate Std. Error t value Pr(>|t|) (Intercept) 0.11060 0.02172 5.092 1.53E-06 *** t -0.00838 0.00091 -9.159 4.08E-15 *** tsq 0.00015 0.00001 10.792 < 2E-16 *** Batters 0.00044 0.00007 6.498 2.65E-09 *** DH 0.08086 0.01300 6.22 9.83E-09 ***

Residual standard error: 0.03256 on 107 degrees of freedom
Multiple R-squared: 0.8038, Adjusted R-squared: 0.7965
F-statistic: 109.6 on 4 and 107 DF, p-value: < 2.2e-16

The Batters term (and the other three terms) are all statistically significant at the 99% level. These variables explain around 80% of the variation in HBP per game, based on the R-squared statistic. The Breusch-Pagan test, with a null hypothesis of no heteroskedasticity, has a p-value of .2 – not enough to reject that null hypothesis, so ordinary least squares are appropriate here.

After controlling for time and the effect of talent pool dilution, the designated hitter rule represents about .08 hit batsmen per game, or roughly one hit batsman every 12.5 games, which translates to about 13 additional hit batsmen over the course of a team’s season. (Of course, that effect could be almost entirely explained by Kevin Youkilis stubbornly refusing to back off home plate.)