THE BOOK--Playing The Percentages In Baseball

I wrote to Stephen Dubner to ask him to give Colin’s article airplay, in light of him giving this piece a platform:
http://freakonomics.blogs.nytimes.com/2009/02/19/when-a-batter-is-hit-by-a-pitch-whats-the-next-batter-thinking-a-guest-post/

I mean, nine years for all players of data, against one guy, one season?

Does Colin have a day job?  Impressive productivity.....

It does look like a small edge to the pitcher against the plunked batter.  On the other hand, I can see a selection bias in that the starter is still in the game 9 batters later despite hitting (at least) one batter.  While you didn’t find (in the Book) a big predictive power for a starters’ performance in the early innings, I think I remember that after 4 or 5 successful innings a starter does perform somewhat better than usual over his remaining innings (i.e. starters do have ‘good days’ and ‘bad days,’ to an extent).  So Colin may just be picking up some of that effect.  It would be interesting to see if pitcher had an edge when looking only at hitters’ 2nd and 3rd PA…

That was written by Pizza Cutter.

OK, does Pizza Cutter have a day job?  :>)

Yeah, that was PC, not me. I do have a job, although it doesn’t take place during the day.

Ouch, sorry Pizza.  Don’t know why I thought it was Colin.

because we’re all nerds over there

Two things come to mind (before reading the article):  One, to avoid potential selection bias, such as that which Guy mentions, it is sometimes nice to do “controlled” or “matched” studies rather than just comparing actual performance to “expected” performance.  In this case, to avoid the kind of selection bias that Guy mentioned (a pitcher still being in the game some 6 or 7 innings later), one can do the exact same thing for similar batters (or all batters) who were not hit.

Another thing, although it won’t really change the conclusion (that a batter who is hit will perform less than expected in subsequent PA against the same pitcher or perhaps any pitcher), is it not entirely possible that a certain small percentage of hit batters sustain a pretty serious injury but keep playing anyway such that overall, the batters will see a pretty big drop in production (IOW, a small percentage of batters who were hit perform horribly and the vast majority are not affected at all)?

I’d also like to see not only how they perform against the same pitcher, but against any other pitcher later in the game.  IOW, if there is an adverse affect on the batter, is it fear of that pitcher, or is it injury or transient fear no matter who is pitching?

I’m going to go through the article and write some thoughts and questions down as I do:  Let me say that despite my critique, this is really good work.

At the beginning (and throughout) Pizza (not Colin - the “psychological” discussion should have been the tip-off, Tango!) talks about whether the HBP was or is “worth it” for the pitcher.  A couple of things about that.  I don’t think that teams/pitchers do or should concern themselves with how much a HBP is “worth” in terms of making the other batters or the same batter in a subsequent AB worse hitters.  No matter how you pitch, you will occasionally hit a batter no matter what.  If you are generally wild, obviously you will tend to hit batters more frequently than average.  If you choose to pitch inside intentionally, then sure, you are “gambling” that whatever you gain makes up for the increased frequency of hitting a batter.  You also think that gain from pitching inside is mostly (not completely) due to the fact that you are changing the location of your pitches more often than a pitcher who only pitches middle and away, as well as the fact that you can probably pitch outside more effectively when you pitch inside more than average.  Of course, the less control a pitcher has, the less he should try and pitch inside (he’ll hit too many batters) and the harder you throw, the more you should pitch inside, all other things being equal (because inside hard pitches are much harder to hit than inside easy ones).  In other words, there are many reasons to pitch inside, but I think one of the least important ones is instilling fear in the batter or batters.  It is mostly about pitch sequencing and game theory.  I do realize that Pizza is trying to be “dramatic” in his article though.

One more thing (after I read the conclusion):  When a pitcher intentionally hits a batter, I don’t think that he (or the manager or coaches) ever seriously thinks that it is “worth it.” You intentionally hit a batter because you are an idiot.  If you are not much of an idiot, you do it in a blowout or in an otherwise low leverage situation, like 2 outs, no one on base and a poor batter coming up.

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.

I don’t understand the last clause in that sentence (after the parenths), but that may just be me, and it is not important.

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.

Kind of an odd paragraph on many different levels.  One, I am not sure I would say anything about .334 versus .333.  Is that even remotely significant?  I don’t know, but if not, end of story - no noticeable effect.  If it is a statistically significant difference (say, even at 1 or 1.5 SD), Pizza just gets done telling us that it probably has something to do with him being a little wild in that inning.  I definitely agree with that!  It is also likely that the lighting is bad in those innings and it is windy, etc.  So we EXPECT the subsequent batters in that inning against that pitcher to be better than just using an odds ratio with each pitcher and batter’s yearly numbers.  In fact, given that, .334 to .333 might actually be the batters doing WORSE not better, given the fact that we expect the pitcher to be having control problems, the lighting and weather to be bad, etc.  In fact, if we look at any inning where there is a walk, hit, HR, etc. (an offensive positive event), we would expect there to be a higher than expected offense in the other parts of the same inning, for the same reasons (selection bias).

So, why would he say this:

Apparently the effect of being fired up is an extra walk/base hit every thousand plate appearances.

Again, I would think that that is absolutely untrue.  That there is no “fired up” effect.  That any effect, if a one point sample difference is even “real,” would be due to the pitcher being unusually wild for whatever reason (injury, bad day, etc.), bad lighting, windy conditions, etc.

Finally (for that paragraph), why does he write:

And he’s easier to hit.

Why would he be easier to hit in an inning where he hits a batter?  Maybe I am missing something there.

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.

OK, here he implies that the previous 1 point difference was significant (at what level?) and that the one batter effect is not.  Same issues with the one batter though.  Is there a cause/effect or do we have selection bias (any bad - or good- event for the pitcher in one inning suggests a higher than average rate of bad - or good - events for the rest of the inning and probably rest of the game).

One general question:  Why do we use regression - logit or otherwise - for this type of inquiry?  Can’t we just look at expected versus actual results for the entire pool of players combined?  Isn’t that going to give us exactly the same results and yet be more transparent to the reader and easier to “follow?” I mean, the only reason to use regressions rather than just aggregate results in studies like this is to guard against a small minority of of the data skewing the results such that in aggregate there is a difference but that there really is no relationship when you do a regression.  With this kind of research though, that is not an issue. If your expected OBP is .333 and all of your players combined are an aggregate .350, that is all you need to know.  You don’t need to do a regression.  It is not likely that a few matchups are going to make your actual results be so different from your expected results.  Impossible in fact.  I am not opposed to regressions, but I don’t think you should do them unless you are specifically looking for “relationships” not just aggregate results.

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.

OK, I don’t really understand the data.  He is looking at the hit batter’s subsequent PA.  It could be against the same pitcher and it could be against a new one.  Chances are it is maybe 60/40 I would guess.  So are you (Pizza) comparing the batter’s overall (from that entire year) OBP with the overall (that entire year) OBP of the “new” pitcher?  If you are, then that is fine.  But if you are only using the overall OBP of the original pitcher for the “expected”, then there is a big problem.  If 40% of the time, it is a new pitcher, the OBP of relievers are going to be quite a bit less than the original starter, no?  Not to mention the fact that a starter who is selected for allowing an HBP is going to be a below average pitcher in the first place.

Now, if you do use the overall OBP of the new pitcher to compute the “expected” OBP, then why would you say, “there would be a bias?” There would be no bias.  So I don’t understand what you are saying here.

OK, I guess he scrapped that idea anyway and looked at the batter’s next PA against the same pitcher.

The effect was not significant, but favored the pitcher, and dropped the batter to a .326 expected OBP.

Again, when he says “not significant” I’d like to know how “not significant.” In my mind, there is a big difference between .5 SD and 1.9 SD (assuming that he is using 2 SD as the arbitrary and magical cut-off point of “significance").

As Tango and Guy say, we have two important issues:  One, Pizza really should be using a “times through the order” adjustment for figuring his expected OBP.  As Tango says, the effect may be a lot more significant in favor of the pitcher than it appears, after taking into consideration “times through the order.” Then again, as Tango says, there might be something to the notion that a pitcher allowed to still be in the game might be pitching better than his overall average performance (or it might be favorable conditions at the park).  Although Tango’s “time through the order” adjustments should already account for the amount of time a pitcher remains in a game, so I am not sure that Guy’s issue is a legitimate one.

In either case, I think there should be a control group in this type of study so that all other conditions, biases, etc. can be controlled for.

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.

I am afraid I don’t understand this paragraph, although, again, it might just be my declining (with age) cognitive abilities.  Is Pizza talking about Tango’s “times through the order” effect?  What “could be a coincidence?”

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.

That is interesting, but…

How far back are you looking?  Are you looking at all PA of a batter/pitcher when that batter was hit by that pitcher at some point in the past, even 7 years earlier?  If yes, I question that result.  If not, can you at lest tell us the limit of how long in the past the HBP occurred?  Again, I might be missing something here. OK, you say “or 3 years later” so apparently you mean ANY time in the past.  Again, I am skeptical of those results.  There must be something else going on. I mean what percentage of all batter/pitcher PA had a prior HBP for that same batter/pitcher combo?  5%? 10% 60%? 

How about if we look at all batters who have been hit by a pitcher, period (all subsequent PA against any pitchers)?  Do we see a decrease in that batter’s expected performance, perhaps due to injury?  The problem with that approach would be that that would probably include all PA, no?  OK, forget that…

Anyway, good work…

One more thing:

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…

I agree that adjusting for time-thru-lineup would pick up any “good day” impact.  But that won’t be a linear +.008 wOBA per appearance if you include all PA, because hitters do not gain anything on the 4th+ PA (IIRC, there’s even a slight drop), presumably the result of the Good Day bias.

Oh sure, I do all the work and Colin gets the credit.  And yes, I have a day job.

Many of the issues that were brought up here are good points, and many of them crossed my mind, but took up more time than I had (cf. aforementioned day job.)

MGL, a few answers.  On the inside pitches that are not HBPs.  Those are the pitches that “just missed” the batter’s head.  They’re probably pretty traumatic, but in the scorebook, they’re just balls.

When I say significant, I mean statistically significant (p < .05… usually using the 2 SD cutoff).  Statistically sig doesn’t mean big.  It just means “not zero.”

I made something of a clumsy attempt at “times through order.” It’s one of those things that I would need more time to really churn out properly and this was meant to be something of a first pass.  As a psychologist, I was interested to see whether there are psychological sequelae of different events.  I actually have a few more ideas in this general framework for future studies.

And thanks to Colin for writing such a great article.

Pizza:  Just for the record, the “day job” comment was a compliment, re: your impressive research output, not a dig.  Ditto for your co-author Colin.

Colin and I both work nights, Eric, I don’t know, he justs seems to write for everyone.

Unfortunately, I found out I can’t get on FanGraphs wp-admin from work, so I can only post new articles from home (I’m on the road 3-4 days a week)