Did I scare you?

Traditionalist baseball fans like whining about three things.  The DH, the lack of “hard-nosed” players nowadays, and the decline of the brushback pitch.  Come to think of it, they usually whine about all three together.  Players have become pansies wearing all that body armor, pitchers don’t have to bat any more (and face the same 95 mph fastball that they might aim at someone’s head), and the league has clamped down on the time-honored tradition of throwing the ball at someone’s head because he dared to hit a homerun off you.  How rude!  Why if Nolan Ryan were here

People are generally afraid of hard objects hurtling toward them at a high speed and the pitcher, who just happens to hold a hard object in his hand and has an arm that can accelerate it to a high speed, knows that.  In theory, the idea behind plunking a batter is that the fear induced in him, and perhaps in his teammates, is actually worth more than the disadvantage of giving up first base on a freebie.  Perhaps he and his eight friends will back off the plate a little bit allowing the pitcher to work the outside corner a little bit better.  Maybe they’ll be a little more hesistant to swing.  It’s always been taken on faith that this one is true.  I’m not sure that anyone’s ever checked to see if the data actually support it.

Being hit by a pitch is a traumatic event, no doubt.  I remember getting plunked in 3rd grade rec league softball, and it still kinda gives me the willies.  It’s easy to picture how batters might be a little leery their next time up or how the guy on deck might get a sick feeling in his stomach at his next plate appearances.  However, not everything that makes sense is true, and not everything that is true makes sense.

Research on people who experience much greater traumatic events (think six months in a war zone or being witness to a murder) show that about 33% of them develop a disorder called PTSD (post-traumatic stress disorder), which affects all areas of a person’s life for an extended period of time.  It’s mostly an anxiety reaction.  Another percentage has a smaller reaction that either doesn’t last as long or is less severe or both.  But then there are some people who don’t see any effect on their life or mental health at all.  Are these the types that play baseball?

Does knocking a guy over cause him to be nervous?  What about watching one of your teammates get knocked over?  Is it worth it for the pitcher?  In order for it to be “worth it”, there should be some evidence that hitting a batter produces some sort decrease in batting skills, and this decrease should outweigh the fact that the price of hitting a batter it to put him on first for free.  If it doesn’t, then teams are putting themselves in a hole and the only benefit that they get is stupid male posturing.

I took all plate appearances from 2000-2008 (something like 1.6 million of them) and calculated the yearly on-base percentage for the pitcher and the hitter in the matchup.  I then calculated the expected on-base percentage for the at-bat, using the odds ratio method, and then took the log of the odds ratio (I’m putting this into a binary logit regression as a control.  If you don’t know what I’m talking about, don’t worry.  Just nod and smile.) 

I then looked for all HBP’s.  Now, we don’t know whether those were “message pitches” or fastballs that just got away (*wink wink*).  We also don’t know if they were full on plunks in the head or if they just grazed the jersey or whether the batter took one high and tight and got out of the way (for a called ball) that wouldn’t have been coded as HBP.  But, we’ll make do with what we have.

First, I looked to see whether the subsequent batters in an inning after a HBP showed any sign of being scared.  I entered the expected OBP for each matchup in the equation and then a dummy (i.e., dichotomous, i.e., yes or no) variable coding whether any of the batter’s teammates had yet been hit in the inning (not whether any would eventually be hit… it was a smart dummy variable… kinda like a jumbo shrimp… and knew whether the HBP had happened yet).  The dummy variable predicted that there was an effect on batter performance.  Batters get better after one of their teammates has been plunked, at least for the rest of the inning.  Of course, it probably has something to do with the fact that the pitcher is probably on the shaky side of control in this inning.  And he’s easier to hit. Given my methodology, it’s hard to say that the batter is X points of OBP better without knowing what batter/pitcher we’re talking about, but assume a league average batter faces a league average pitcher (using 2008 numbers, an OBP of .333).  If a batter has been hit previously in the inning, the expected OBP for that plate appearance is .334.  Not a huge effect.  Apparently the effect of being fired up is an extra walk/base hit every thousand plate appearances.

What about if we kept it only to the batter who immediately followed a hit by pitch?  The effect is no longer significant, but what effect there was again favored the batter.

But what of the hit batsman himself?  After all, he’s the one who has to endure the trauma and the bruise of being hit.  What happens the next time he comes to the plate?  The answer is that he is a less effective hitter in his next plate appearance.  Again, assuming he’s league average and facing a league average pitcher, he falls to an expected OBP of .321 in that next plate appearance.  Here, I’m not controlling for whether he’s facing a new (fresher, better?) pitcher, which could be a bias.

So, I kept it to those situations in which the batter was facing the same pitcher within the same game.  It must be pointed out that the pitcher has now faced 8 more batters (and thrown 30ish more pitches) so it’s biased in the other direction.  Psychologically, it makes sense that the batter would be more likely to be scared if he were facing the same pitcher, rather than a new one, and the memory will be freshest on the same day.  The effect was not significant, but favored the pitcher, and dropped the batter to a .326 expected OBP.

Interestingly enough, the effect of 30 pitches on the pitcher’s arm is about 4 points (.004) worth of expeted OBP in favor of the batter.  It looks like the overall effect, psychologically of getting plunked and then facing the same pitcher later is 10 points in favor of the pitcher.  The effect of facing a pitcher after he’s plunked you in the same game is about 7 points (it was actually 6 and some change).  Could just be a coincidence that those seem to match up rather well.

Perhaps there is even a carry-over effect, even if the batter doesn’t face the pitcher the same day.  I looked to see whether the batter showed some carry over effect whether his next meeting with the pitcher who hit him came 30 minutes or 3 years later.  There was.  Having previously been hit by a pitch by the same pitcher took an average batter vs. an average pitcher to an expected OBP of .323, no matter when it happened.  Some things you just never forget.

So, let’s call the effect of being hit by a pitch 10 points worth of OBP in the next at bat.  I checked to see whether there was an effect two plate appearances out, this time, an even stronger effect of 13 points.  The third appearance?  The effect is gone.  Being hit by a pitch seems to have an effect for two plate appearances, and then no more.  After that, players seem to have conquered their fear.

Now, is it worth it to intentionally hit a batter?  Not really.  You’re exchanging one at-bat in which you make a player a 1.000 OBP hitter (raising the average hitter’s chances by 67%) for two plate appearances where you drop his chances by about a percentage point.  Plus, you make his friends really angry.  But with that said, there’s a real effect, even if it is small, of being hit by a pitch.  Turns that out that hitters are only human and are a little shy the next few times that they come up.


8 Responses to Did I scare you?

  1. Millsy says:

    Man, you guys have some fun. This is kind of neat, though, as you said, it’s tough to pull too much from it, given the multiple biases. Either way, I would agree that actually hitting a guy at the major league level doesn’t have a whole lot of effect.
    I’ve been trying to convince my girlfriend that reading baseball articles is part of my study. Wink wink. She does research on fear extinction and PTSD. Maybe I should refer her to this article and suggest a joint study? Extinction period of 2 at bats. Good to know.

  2. Pizza Cutter says:

    It makes sense. Consider that the treatment for trauma and anxiety most often involves exposure therapy. After being plunked, the best exposure is to get back into the batter’s box. After a couple times, he has a couple of examples that show that not every at-bat ends in him getting buzzed.

  3. Brian Cartwright says:

    Try it by not assuming that all pitchers are equal. The batter’s fear may be based on the expectation that it may occur again. If the pitcher has a reputation as a head-hunter (someone who has a HBP% above a certain threshold) I would expect more of an effect than if the pitcher has a low pct, where the batter might view the plunk as a random event unlikely to occur anytime soon.
    Also, in recent years there has been an increasing number of hitters who do not avoid HBPs, seeing it as a way to pad their OBP. These guys presumably have no fear, or they wouldn’t be getting hit 20 or 30 times a year.

  4. Dan Novick says:

    In the article, you say this: “I entered the expected OBP for each matchup in the equation and then a dummy (i.e., dichotomous, i.e., yes or no) variable coding whether any of the batter’s teammates had yet been hit in the inning (not whether any would eventually be hit…”
    And then this: “Of course, it probably has something to do with the fact that the pitcher is probably on the shaky side of control in this inning. And he’s easier to hit.”
    To check that bias, couldn’t you just compare the data that you did run to the data on ALL innings where there was a HBP? This way, you eliminate the fact that worse pitchers are on the mound when HBP’s occur. Maybe eliminate is the wrong word… but you can see if that bias does exist, and how prevalent it is.

  5. Dan Novick says:

    Reading my comment again I’m not sure if I’m making myself clear. I’m suggesting you look at every inning where there was a HBP, regardless of when it happened in the inning, and compare that to the data that you used in this article.

  6. jw says:

    Nice work! Now all we need is functional MRIs of players with visual cues of pitches coming at them before and after they’ve recently been plunked, as well as before and after seeing a teammate getting plunked. Don’t worry, I know a guy*.
    * – I actually do**.
    ** – He’s pretty busy, though, and functional MRIs require a lot of time in the MRI machine, which is expensive.

  7. Pizza Cutter says:

    I actually know some people too. I ought to pull out the trauma/fMRI literature and take a look. Or I could just give the Trauma Symptoms Checklist to the guy in the on-deck circle.

  8. MGL says:

    Yes, as Dan above says, it would be nice to see the same data in the inning BEFORE the HBP occurred. That will give us great insight into the potential selection bias of the pitcher, game conditions, etc. In fact, the more that I think about it, that is a necessary control…

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