THE BOOK--Playing The Percentages In Baseball

My vote for part 2:

(Worthy of note, though a subject for a different time, is how the umpire positions himself differently for the two batters.)

Take a look at the picture that this refers to, as well as the ump’s eyeline relative to the plate.  Fascinating… I have to assume the ump calls pitches differently in these two scenarios, because must see the ball at a different angle in each situation.

Also, Mike: why is the ump positioned, in both shots, well to one side of the plate?  Shouldn’t he be positioned directly behind the plate to get the best view of the ball as it crosses?  Have you ever looked to see if umps who position themselves closer to the middle of the plate are any better/worse at identifying strikes (according to gameday)?

Tango, interesting question.  There will probably be some significant noise no matter how you try to determine which HBP were intentional, but I can think of several possible criteria:
1. As you suggested, first pitch after a home run
2. First pitch to a batter after he hit a home run in a previous inning
3. Any HBP on a 0-0 count
4. Any HBP on a 1-0 count that followed an inside pitch on 0-0
5. Any HBP that resulted in an ejection
6. Any HBP on the first pitch of an inning
7. Any HBP on the first pitch thrown by a new pitcher
8. Any HBP to the first batter after a HBP in the previous inning

Depending on what was discovered from analyzing those criteria, one might be able to refine and combine them to get a more focused set of likely intentional HBP occurrences.

Mike/1, the umpire usually positions himself in line with the inside edge of the plate, in the “slot” between the batter and catcher.  As far as I know that is true for all major-league umpires.

I do believe that the position of the batter and catcher affect the position of the zone that umpires call, though, other than umpires calling relative to the catcher target, I haven’t been able to isolate the physical cause(s) for this.

For your #8, do you mean previous half-inning (i.e., retaliation)?

And, it’s not too important to try to get all intentional HBP.  What we care about is the following: get a sample such that there’s a disproportionate share of intentional HBP.

So, if we look at #1, perhaps 2% of first pitches following a HR result in a HBP.  But, given that we have a HBP, 95% of those were intentional.

For #8 (retaliation CONDITIONS): perhaps 3% of leadoff batters in half-inning following a HBP results in a HBP.  But, given that we have a HBP, 70% of those were intentional.

Therefore, as long as we get a disproportionate share of intentionals, in whatever subsample we have, then we’re happy.

Ideally, we get the sample large enough, but the risk there is that the “disproportionateness” starts to shrink.

Hopefully, all that made sense (to somebody who can say it with more clarity).

Basically, create sub-sample conditions, such that the level of noise in that sub-sample is minimized.

So, first pitch following any at bat: not good enough conditions.

First pitch following a HR: pretty good conditions.

(All numbers noted above for illustration purposes only.)

For your #8, do you mean previous half-inning (i.e., retaliation)?

Yes, that’s what I meant to type.

And, it’s not too important to try to get all intentional HBP.  What we care about is the following: get a sample such that there’s a disproportionate share of intentional HBP.

Agreed.  My idea with listing some other potential criteria is that I was afraid that the list for post-HR HBP in the PITCHf/x era would be too small for any meaningful analysis.  But I don’t know that for sure.

I don’t think there’s any way to ever perfectly separate intentional and unintentional populations.  I agree that’s not necessary for most analysis.  In addition to trying to figure out how to get a population that was heavily intentional, I was trying to think how to get a population that was heavily unintentional.

I don’t at this point even have a good feel for what the ratio of intentional to unintentional HBP would be.  That’s also a question that could be interesting to try to answer.

Basically, create sub-sample conditions, such that the level of noise in that sub-sample is minimized.

So, first pitch following any at bat: not good enough conditions.

I was thinking that if one excluded all 0-0 and 1-0 pitches (or even just all 0-0 pitches and all 1-0 pitches following an 0-0 pitch inside off the plate), that one would have good confidence that the sample included a very heavily weighted population of unintentional HBP.  So, though I did not state it explicity in my original post, I was thinking about how to achieve a sample with the opposite weighting from what you suggested.

Would you want to excluded HBP above some certain LI that didn’t result in an ejection?  I’m guessing pitchers will wait to hit someone until it matters less (e.g. tomorrow’s game) to retaliate rather than plunk a guy in the 8th inning of a run one game.

I’d also would guess more intentional HBP come with two outs than first batters of the inning.

I have zero basis for any of these assumptions.

I don’t have results of previous at-bat in the data I have available to me at the moment, but I did look at games with multiple HBP as compared to games with a single HBP.  There is very little difference in pitch types between those two populations. 

Multi-HBP are 66% fastballs as compared to 65% fastballs in the single-HBP sample.  The increase comes at the expense of sliders, and other pitch type percentages are virtually unchanged.

I also looked at my criteria #7 (any HBP on the first pitch thrown by a new pitcher), but I think it is too biased by its dominance by relievers to useful for comparison without adjusting for that.

Perhaps the two most restrictive criteria would be the most useful: post-HR HBP, and HBP leading to ejection.  I’m guessing those will each provide samples in the range of 100 to 200 occurrences.

Maybe obvious, but in addition to all those mentioned, another filter criteria for intentional HBP would be pitch type - fastballs only.

Greg/10, I did that filter and the results are in the article.  I don’t see that it’s terribly illuminating on the intentional/unintentional split.

I see what you are saying, that presumably all the intentional HBP would be fastballs, so that if I were looking for only unintentional HBP in my sample, I could simply remove all the fastballs.  But then what?  What question would we be looking to answer?  I don’t think you can answer any interesting questions with the remaining data.

Mike, this is just great stuff. Well done!

In answer to Tango’s question, we have data for 30 HBP on the first pitch following a home run.  Of those, 23 occurred on fastballs, and 24 were on the torso.  Those rates are somewhat above the normal expectation, which would be for 19-20 fastballs and 22 on the torso.  I have no idea to what extent this sample is biased the identity of pitcher and batter or other factors.

Mike: excellent, thanks.

I have to say therefore that I am quite surprised.  Of the 7 that were not fastballs, what were they?  Could they be “slow” fastballs that were clustered into something else?  Other than maybe a changeup, I don’t know why a pitcher would throw anything else (I’d expect no sliders, nor curveballs, if the HBP was intentional).

Thanks again for everything…

You might want to do this as an article anyway.  With only 30 pitches, you can probably get some good graphs that we can follow.  The horizontal/vertical, the spin deflection / speed charts would be two great ones.  And if you have those 7 outliers, then we can see how they link up in the two charts.

Just a thought for you…

Tango/14, the implication to me is that a sizable fraction of these are not intentional.  Perhaps HBP following a HR is not a good criterion to select on after all.  I don’t know how to tell for sure.

Of the 7 non-fastball pitches, 3 were curveballs, 1 was a changeup, 1 was a slider, and 2 were cutters.  All 7 appeared to be properly classified at first glance.  One of the cutters was from Jesse Litsch, who uses a cutter as his main pitch.  So you can up the fastball count by one for that if you want, but then the baseline expectation for fastballs would also need to be increased accordingly.

One thing that I thought was interesting was that the HBP rate is suppressed on the first pitch after a HR.  I had expected the opposite.  (I’m not sure exactly how much it’s suppressed until I go back and calculate the normal HBP rate on 0-0 pitches, but the post-HR rate is roughly half the normal rate for all counts.)

Okay, the HBP rate is about normal after a HR, given that it is an 0-0 pitch.  I need to do more careful calculations to figure out exactly how it changes by count, but it’s in the right ballpark.

Fascinating.  So, the rate of HBP on the first pitch after a HR is the same rate as on the first pitch after an average event?  I would not have believed that.

But I guess with only 30 HBP (on, what, 10,000-15,000 first pitches?), then 1 SD is about 5 HBP.  So, even if you were expecting 30, we’d expect to see 20-40 95% of the time just by random variation.  Similarly, if the true rate was actually 40, we’d still see 30-50 95% of the time by random variation.  And so, we end up observing less, even if we expected more.

The other thing is that following a HR, maybe most pitchers intentionally try to AVOID hitting the batter on the first pitch, while a small group intentionally tries to hit them, such that overall, you still get the expected 30 HBP that you’d get from random.  So, you have two competing groups of pitchers that cancel out their efforts, so that it looks random, even though we know it can’t possibly be random.

The final thing is that the payback may not necessarily be on the first pitch, but later on in the at bat.

Anyway, fascinating stuff!

Rather than looking at pitchers that intentionally hit batters I think the more interesting situation to try and isolate and study are batters that intentionally let themselves be hit.

Peter, I find both of them very difficult to study in large samples, i.e., by defining criteria for a database query as opposed to watching video.

But I agree that the batter angle is very interesting.