## Sunday, July 30, 2006

### Are pitchers from the South too politically correct to hit black batters?

Are pitchers from the South too genteel to plunk black batters? Maybe.

study posted at the Retrosheet research page (and filled with psychological jargon about “social identity,” “hostile attributional bias,” and such), author Thomas A. Timmerman studies a few decades worth of Retrosheet HBP data and finds some anomalies among Southern-born pitchers.

Timmerman used a logistic regression to predict the probability of a hit batsman from a whole bunch of factors, including pitcher wildness, batter quality, etc. He specifically considered three retaliation situations: (a) whether the previous batter hit a home run; (b) whether this particular batter hit a home run his last AB against this pitcher; and (c) whether one of the pitcher’s own teammates had previously been hit by the opposing pitcher.

He also considered race of the batter, and only studied HBPs by white pitchers.

The basic results were pretty much as you’d expect. Batter quality (OPS) was the most significant factor, twenty standard deviations above the mean. The year, score, and wildness of the pitcher were also highly significant.

The most important retaliation factor was whether the pitcher’s teammate was hit – if he was, that increased the logit of the HBP probability by 0.321, which translates to about a 38% increase in the chances of a HBP.

(Mathematical explanation which you can skip: If I remember my logistic regression, the 0.321 is the log of the number you need to multiply the odds by. Specifically: the antilog of 0.321 is about 1.38. In the entire study, the odds of a HBP were 20,357 to 3,973,869. To get the odds after the teammate is hit, you multiply by 1.38, and the new odds are now 28,093 to 3,973,869. This is equivalent to a probability increase from .00512 to .00707, which is a 38 percent increase. So hitting a batter increases the change of your own team getting hit by 38%.

The results in the author’s tables are presented only as logit coefficients. That’s kind of annoying, and you have to read the text to get the percentages out – or figure them yourself by studying all the interactions. It took two of my fourth-year statistics courses for me to be able to figure out the table. I hope I got it right.)

Second most important was if the previous batter hit a home run – that would increase the odds by 19%. Third, if the same batter had hit a homer last at-bat, that would increase the odds by 11% (which wasn't enough to be significant at the 5% level). And, finally, there was no significant difference between black batters and white batters.

So far, nothing unusual. But now, Timmerman considered the birthplace of the pitcher. This is where the shock starts:

For case (a), when the previous batter hit a home run, normally there would be a 19% increase in HBP. But when the previous batter hit a home run and the pitcher was from the south, the increase was 22%, suggesting that southern pitchers are 16% more vindictive than average.

But look at the breakdown by race. If there were no discrimination on the part of the pitchers, you’d expect equal results: a 22% increase against white batters, and a 22% increase against black batters. But instead, there was a 55% increase among white batters, and a 4% decrease among black batters!

For case (b), when a black player hit a home run off the southern pitcher his previous time up, he was 10% more likely to be hit than average. But when a white player hit a home run off the southern pitcher his last time up, he was 50% more likely to be hit.

Finally, for case (c), southern pitchers did still exact revenge on black batters – 12% more HBPs than normal. But for white batters, it was 55% more. (Also notable is that southerners were no more likely than Northerners to hit a batter just because their own teammate was hit. That is, they were more eager to avenge themselves, but no more eager to avenge a teammate.)

So black batters are treated very, very nicely by Southern pitchers. Timmerman suggests the southerners are motivated by a stronger desire not to appear racist. Or, he says, perhaps it’s that pitchers from the South are afraid of blacks, and worry that they’ll charge the mound if hit. Personally, I think the first explanation is more likely.

Either way, the results are still freak me out. I never would have expected this.

----
(late note: found a calculation error in para beginning "For case (a)". Correct number is 22%. Now fixed.)

At Monday, July 31, 2006 12:14:00 PM,  Beamer said...

Another nice post. Good summary -- I tried to read the actual study and got (a) bored and (b) frustrated with the presentation of the analysis because as you point out the author doesn't present the exp(b) coefficients so you have to work it out yourself ...

At Tuesday, August 01, 2006 10:15:00 AM,  Tom Timmerman said...

I've finally reached the pinnacle of academic success! I've taken something interesting and made it completely unreadable! But thanks for the review. I really like your blog. One point that was missing from your summary that startled me. It's easier to see this in the figures, but pitchers not from the south appear to be much more likely to target blacks in these "high-risk" situations. Since there are many more non-southerners than southerners, it appears as if hitting blacks is "normal" in these situations and southerners (for whatever reason) are more likely to refrain from this. I'm working on an update that includes the most recently released retrodata.

At Tuesday, August 01, 2006 10:37:00 AM,  Phil Birnbaum said...

Hi, Tom,

Thanks for the comments! I just posted a follow-up, which you've probably seen by now. My comments on the BTF thread talk about how I'm not fully convinced that the non-south pitchers are unfairly targeting blacks -- to me, the data only show a difference between the two groups of pitchers, but are insufficiently persuasive to show where the 'right' level of HBPs is.

At Friday, April 03, 2009 10:09:00 AM,  Anonymous said...