THE BOOK--Playing The Percentages In Baseball

Interesting point. Puts a completely different perspective on something I saw way back when, that is during Javier Vasquez last season with the Expos. There was that at-bat where he had a guy on a similar count (can’t remember who it was, but it was some speediy left-hitting infielder; Furcal?) and once he got to 1-2, he just kept throwing curveballs. Frank Robinson was the manager and Schneider was the catcher. Anyway, Vasquez threw something like 4 or 5 curves to said speedy LHB, all down inside, and SLHB kept fouling them off, until he finally ripped one for a double. Everybody (I mean, 4 or 5 guys among the dozen or so who still wached em by then) was up in arms about it, but today, I have to wonder. Do we have access to more detailed PBP data from those years other than retrosheet?

I think it’s this game, 4th inning.

BIS and STATS record that data.  Now that you mention it, we don’t need pitch f/x data to research those kinds of things.  If a pitcher is truly randomizing his pitches (again, “adjusted” for the batter, the count, and the game situation), we should see long strings of the same pitch being thrown, like you mention above, occasionally.  If we don’t see that from a pitcher occasionally, he is probably falling into that trap of, “I’ve thrown him enough of pitch X, I better throw something else.  That can’t be correct, especially if batters tend to think the same thing, which I think they do.

Now, good pitchers and catchers not only randomize their pitches and adjust them to the batter’s overall strengths and weaknesses (and the count and game situation), but they also adjust them to what is going on with the batter during that AB.  For example, if I throw 2 straight curve balls to a young batter and he looks foolish on them, I might throw another curve ball a high percentage of the time.  Might not do that with a veteran though.  Same thing with any other pitch - if a batter looks foolish once or twice in an AB on a particular pitch, I might throw that pitch again more often than I normally would, even to a batter with the same overall tendencies as the batter at the plate.  Or if I throw a bunch of fastballs and the batter is late on all of them, I might be reluctant to throw an off-speed pitch, even if the batter is known to be a fastball hitter.  Personally, I think that an intuitive pitcher and catcher can adjust his pitch selection a lot by what the batter does or does not do in that AB.  I do it all the time mentally when I am watching a game on TV…

This, by the way, is an area of research that is sorely lacking in the pitch f/x work so far. Hear that guys?

I have been of the opinion that a study like this was too difficult given the limitations of the data we have.  I’m open to being convinced otherwise, but given the challenges I’ve encountered on simpler projects, I’m not eager to tackle the much thornier game theory stuff.

If the question is simply for a given Pitcher X, say Johan Santana, or whoever, what’s his optimal mix and does he randomize properly, I think the sample sizes are much too small to tell.  The random error will dwarf any real signal in the data.

If the question is for a larger group of pitchers or the league as a whole, then you run into the problem that we don’t have accurate pitch classifications.  The more you are willing to be fuzzy with the pitch classifications, the less accurate your conclusions can be.  It’s one thing to be fuzzy when you’re looking at things like average run values or BABIP across the strike zone, but when you are looking at pitch sequencing, the pitch classification IS the basis for your investigation.

MGL, what’s a simple experiment that you would propose for a particular pitcher (you can pick the pitcher)?  I’m willing to listen.

I’m actually very interested in this stuff, wondering for example, about the stuff you hear so often about a pitcher setting up a batter in their first matchup or two in the game for something he wants to do later in the game.  This being said about guys like Greg Maddux who are supposed to be crafty pitchers.  But I never could figure out how to test that accurately because there are so many variables: ball-strike count, pitch type, pitch location, baserunner/game state, previous pitches in the at bat, pitches in previous at bats to the same batter, pitches to previous batters in the same inning, weather conditions (wind blowing in or out), size of the umpire’s strike zone…

It might be easiest to start with a reliever who only throws two pitches which are easy to tell apart, e.g. Jose Valverde with his fastball and splitter, or one of the other many relievers who is a fastball-slider pitcher.

This was in the “Peanuts” comic strip once. Charlie Brown is on the mound talking to himself.

Frame 1: “This guy will never be expecting a fastball...”

Frame 2: “With the bases loaded he’ll be expecting a curve. But he also knows I know what he’s expecting...”

Frame 3: “So if he’s expecting me to pitch what I know he knows I know he knows he’s expecting...”

Frame 4: “Where was I?”

First of all, the two basic pitches are fastball and off-speed. For this type of study, at least for a first pass, you don’t need any more than that.  And pitchers should be thinking along those lines anyway.  A batter basically has to gear up for one or the other.  If a batter is anticipating an off-speed pitch, it doesn’t matter that much whether it is a change-up or slider.  Same for a fastball. If he is geared up for a fastball, he is going to have some level of success, as opposed to being geared up for an off-speed pitch or being agnostic, whether it is a cutter, a 2-seamer or a 4-seamer.

Anyway, one of the first things I would do is to look at every count and every base/out situation and see the percentages of each type of pitch thrown, again, using the fastball/off-speed dichotomy only.  I would do that for all pitchers combined and for individual pitchers.  Since there are too many buckets, I would probably combine similar buckets, at least for starters.  I might make a few categories for bases/outs and a few categories for the count.

Then another thing I would do is to look at the frequency of each category of pitch thrown (fastball or off speed) given the bucket, but this time, given the last pitch thrown, the last two pitches thrown, etc.  I think someone did something like that already.

Basically what we want to know is if pitchers are NOT randomizing their pitches enough.  The only way a pitch becomes non-randomized is when the frequency of a pitch is influenced by what was thrown prior to that.  Again, I would do that for all pitchers combined and for individual pitchers. I’d also do it for “good” and for “bad” pitchers.  I’d also want to know which ones are more successful - the ones that appear to be random or the ones whose frequency appears to be a function of prior choices.

You might even isolate some examples.  You might use exactly what we were talking about in this thread.  Look at all 0-1 and 1-2 counts where the pitcher just threw 2 consecutive pitches of the same type, and see how often he triples up versus how often he doesn’t and compare that to the frequencies when he has not just thrown the same pitch 2 times in a row. And then see which pitch was more effective by looking at the lwts value.

One of the problems (of many) you will run into is that pitchers tend to throw pitches according to the overall strengths and weaknesses of the batters they face.  So if a pitcher throws a couple of curveballs he might be more likely to throw another curveball simply because the batter’s weakness is a curveball.

But, thankfully, that would actually be the opposite of what I expect. I expect that after 2 curveballs, a pitcher is more likely to throw another pitch for the reasons I have already discussed (he is reluctant to keep throwing the same pitch).

You also want to look at the outcome of prior pitches to see how pitchers respond to that.  For example, my guess is that if a pitcher throws a curveball and a batter swings and misses, he is more likely to see another curveball, as compared to if the batter hit it hard but fair or laid off of one outside the strike zone.  Whether that is correct or not, I have no idea, but I certainly would like to find out.

So yes, this stuff is very tricky and I’d have to really sit down and think about what I would like to see done, although I am not prepared to do that right now.

But definitely something that is sorely lacking.  We REALLY need to know what makes pitchers good and bad, especially in the pitch selection and game theory department.  The reason we really need to know that is because that is the one area that we can teach pitchers to be better at relatively easily if we understand it (which we don’t).  You can’t teach a pitcher to add 3 mph on his fastball and it takes years to develop a good curve ball if at all. But presumably anyone can learn to pitch more effectively by optimal pitch selection and game theory application.

There are basically several things that make for the quality of a pitcher:

1) The velocity and movement on his pitches, which can be called the “physical quality of the pitch.”

2) The command he has of those pitches.  Basically the pitcher’s ability to locate a pitch where he wants to throw it.

3) The deception that a pitcher’s motion provides, whether it is intentional or not.

4) The selection of his pitches and the application of game theory and randomization (which is critical to proper game theory strategy).

I want to know all about all 4 things. I want to know which are more important, although it might be impossible to quantify the relative importance.

I want to know how each pitchers rates on each of these things.

Once I know these things, I might be able to really evaluate a pitcher without too much data.  No one does that now.

For example, while scouting a pitcher in a few real games or even in the bullpen, or perhaps by giving him some “tests,” I want to rate his “stuff” (including the deception), his command, and his ability to mix up his pitches at the various counts and randomize them as well.  Of course all of these things are related.  If, for example, my command is poor, I am not going to be able to mix up my pitches very well.  I will be forced to throw fastballs in fastball counts.  Which is why command is perhaps the most important part of the equation (and why catcher glove position is so important to the data).  It has a double-whammy effect.  If my command is poor, of course I will accidentally throw many hittable pitches AND I will not be able to throw off-speed pitches (which are inherently hard to command) in hitter’s counts or I will walk too many batters.

That is all I have for now.  You guys (Fast, et al.) are really good at designing and implementing pitch f/x studies.  Eventually you will have to start to unravel the pitch selection/game theory mystery…

MGL - I’m afraid that 2 and 3 are going to be very nearly impossible for most pitchers.  I’ll start with #2. 

Command is almost impossible to quantify, because we do not know where the catcher sets up.  In some instances, like Dave Allen did with Mariano Rivera, a pitchers command is so extreme that it’s easy to tell, but I would suspect that with the majority of pitchers, it is almost impossible to take a look at command using Pitch f/x. 

I suppose, and this would tie in with game theory a little bit, you could take a situation where you know where the pitcher is trying to throw it.  For example, if you found that 80% of sliders on an 0-2 or 1-2 count were thrown down in away, you could measure each individual pitchers percentages in that situation.  However, as you game theory teaches us, a pitcher SHOULDN’T throw all sliders down and away so as not to be predictable.  He may be throwing it inside or even high intentionally, and we wouldn’t be able to tell. That’s the measurement error part, and of course their is a lot of sampling error as well, as some pitchers clearly have the ability to control certain pitches better than others.

Another possible way to measure command would be to take a look at the pitchers distribution of pitches in the strike zone.  You could separate the zone into 9 or 12 or 16 bins, and figure out the percentage of pitches thrown in each bin.  However, that still doesn’t show intent which is a HUGE key.  Do you have any other suggestions as to how to measure command? 

As for #3, that seems impossible.  The only thing that Pitch f/x picks up in that regards is release point, but that would probably miss a huge peice of the possible.  Also, how would you possible measure the impact of deception?  I suppose you could take the sum of all of the other pitcher attributes, and subtract it from overall performance and that would leave you with “deception index” or something.  But that would have HUGE measurement and sampling errors to it. 

And yes, I definitely agree with game theory.  I think that combined with information about the pitchers stuff, and limited info about his command and deception, would give us a pretty decent picture of a pitchers true ability.

Sorry for all of the typo’s and grammar mistakes on post 8… just woke up.

You would think that the announcer being “shocked” to see the same pitch a third time would convince him that it could be a good idea.  After all, if the announcer is shocked, the batter might be shocked; and if the batter is shocked, he’s less likely to be able to make contact; and if he’s less likely to make contact, then it was a good pitch.

It’s been a couple months since I read it, but I think this paper talks about some of these issues.

http://www.bepress.com/jqas/vol5/iss2/7/

Josh Kalk looked into pitch sequencing.  (Click my name for the link.)

Nick, my list wasn’t something that could be looked into or solved with pitch f/x data.  It was just a list of all the attributes that make up pitching quality. I agree with most of what you said.  Yes, you can infer command to some extent from the pitch f/x data.  I have also said that we REALLY need target location in the data.  Some people disagree.

And yes, the way to infer “deception” is simply to subtract the value of a pitch from the value of a generic pitch in the same game situation of the same speed and movement.  You can aggregate counts and situations.  For example, let’s say that pitcher A throws a fastball 73% of the time and that fastball is 91 mph with X and Y horizontal and vertical movement.  You look at all pitchers (starters or relievers only) who throw a similar fastball around 70-75% of the time. The difference in value between pitcher A’s fastball and the whole group combined is his “deception value.” Of course there will be sample size and other issues.

MGL, the thing is that both you & the announcer/player are making unproven assumptions regarding the optimization of pitch selection.

The hypothesis that you seem to be stating is that pitchers should be truly random in their pitch selection, ie that the dominant purpose of pitch selection is to surprise the batter with the type and location of the next pitch.

The announcer’s viewpoint is that a truly random pitch selection would be a bad thing, because of the notion that giving a batter practice against a particular pitch gives the batter an advantage (even in the case where they’re surprised to see that pitch for the 4th consecutive time).

I don’t think you can say with any certainty that either of these viewpoints are true, but I will say that the traditional baseball wisdom is not outlandish.  Cognitive science research (not to mention your ordinary life experiences) provides all kinds of examples in which “priming” one part of the brain dramatically alters effectiveness or speed of performing a particular task.  For example if you flash a word on a computer screen for about 1/20th of a second (ie, subliminally) and then later show a 2nd word, MRIs show that the brain is much faster at recognizing the next word when the two words are the same.

Or if that’s too technical, grab a handful of kibble and toss it to your dog… and let me know if the dog is equally good at catching pieces thrown repeatedly to the same spot as it is at catching pieces thrown with random arcs to random locations.

Basically, I think that there is a cognitive bias towards repetition and that an optimal pitch selection should exploit that.

Guido, you are confusing the word and concept of random with some other word or concept.  OF COURSE all pitches need to be thrown randomly otherwise the batter will either know what is coming or have a better idea what is coming than the pitcher intends.  You seem to think that the word “random” means “each pitch is to be thrown with equal likelihood.” The pitcher can use whatever he wants to determine the likelihood that he throws each of his pitches, including all the things that you mention and more.  Then when he determines those percentages he needs to execute them in a random fashion!  That is a given.  If after 3 straight fastballs, he thinks that the batter has learned enough that he should reduce the likelihood of the fastball coming on the next pitch, as compared to the previous pitch or the one before it, then so be it.  But it is unlikely that that is what the announcer means when he says that he would be shocked if he throws another fastball in that location (or just another fastball).  He probably means that you “can’t just keep throwing the same pitch over and over again,” which is senseless and misguided thinking.  Especially if the batter is thinking the same thing!

Certainly the pitcher should not throw an off-speed pitch 95% or 100% of the time just because the batter may have gotten used to the fastball or learned something about the fastball.  If the batter is almost certain that a breaking pitch is coming, it is probably not such a good pitch to throw.  In order to keep the batter from thinking that the pitcher is going to throw an off-speed pitch (or whatever) 95% of the time, he needs to throw it far less than that.

I will reiterate my main point.  Every pitch that the pitcher throws must be thrown in a random fashion.  By that, I mean that he determines in each situation how often he is going to throw each type of pitch and then he flips a mental x-sided coin.  It might be 99/1, as with a 3-0 count to the opposing pitcher to lead off an inning, or it might be 50/50 or 25/25/25/25 is he has 4 pitches.

The tricky part is that it is very difficult for human beings to randomize things, so they usually have to do things that are NOT random but look random to an observer.  If you think that randomizing things in your head are easy, try playing rock/paper/scissors with an “expert.” He’ll kill you, even though all you have to do to be unbeatable is to randomize your throws (with no tells and no cheating on his part of course).

If that’s your main point, then no offense but you’re not making a strong statement of anything at all.  Of course the pitcher cannot be a deterministic machine that chooses every pitch using some non-random process.  And of course that’s not what the announcer was suggesting. 

What he was saying, implicitly, is that when a pitcher throws two of the same pitch in a row, he should adjust the distribution from which he chooses the next pitch to include a “shockingly” low probability of choosing that same pitch again—because of his belief that the negative value of “batter gets 2 practice swings” overwhelms the positive value of “force the batter to consider all pitch options”. 

In other words, he feels that the random variable should be conditioned on recent pitch history (in addition to the count & game situation)—and your initial post seemed say that you find this outlandish, but I don’t see that it is.  And I certainly don’t see any evidence that proves that two consecutive pitches (with the same count & game situation) are truly independent events.

I don’t disagree with the fact that after two straight similar fastballs, there might be a familiarity or learning effect such that the pitcher might throw that same fastball less often on the next pitch than he would given the same count and game situation but NOT two consecutive previous fastballs.  I don’t disagree at all.

I don’t think that is what the announcer had in mind though, although I might be wrong.  I’ll say this one more time (I said it 2 times already), but I think there is a prevailing and incorrect notion that a pitcher should NOT keep throwing the same pitch over and over gain, but NOT for the (legitimate) reasons you mentioned.

My evidence that that is not what the announcer meant is:  One, he could have elaborated but he didn’t.  He used the words, “I’d be shocked,” which implies that he thinks that the correct percentage of the same pitch is something like less than 10% (or you can substitute whatever number you think would constitute being “shocked” him - personally when something happens 10% of the time, I am not shocked - shocked for me usually takes something like 1 or 2% - for example, if a I flip a coin 4 times and it comes up heads all 4 times, I am not “shocked” even though I am aware the the chances are 15-1 or around 7% that that would happen).

Well, given that the game situation and count (1-2) were exactly the same on the 3rd pitch as the 4th one, I would be shocked if the correct percentage for the high fastball (the same pitch) was now less than 10%.

So I have a question for you?  Say that a pitcher throws two pitches:  A fastball and a curveball.  And say that on a 1-2 count he typically throws 50/50 fastball/curveball, which I don’t think is unreasonable.  Now say that he just threw two fastballs in a row and the count is 1-2.  So typically (without any consideration to what he just threw in the prior pitches) he throws a fastball 50% of the time on the next pitch.  What do you think the percentage for the fastball should be given that he just threw two in a row and why?  And if he just threw one fastball in a row (the one before than was a curveball), what do you think the percentage should be?  How about one curve ball in a row, and then two curve balls in a row?  So 4 answers and why.

I have been thinking about game theory and pitching.  I think a smart thing for a catcher to do is have a sign for the pitcher to shake off the sign.  For certain batters that may tend to try and guess what the pitcher is trying to throw it might be useful to get him thinking that the pitcher is going to his 2nd or third option in a critical situation.

Peter, pitchers do that all the time.  They shake signs off and then wait for the pitcher to go back to that sign.  It is for the reason you say, although if the pitcher and catcher are truly randomizing his pitches, it is not necessary and could be dangerous. For example, let’s say that the count is 3-0.  If the pitcher takes the first sign that the catcher puts down, the batter may assume that it is a fastball.  The pitcher may try and shake off a few signs to get the batter to think that he is not throwing the fastball.  Of course, the danger in that is if the batter is smarter than the pitcher, he may be able to figure out what is going on and know more about what is coming than he should.  In all games involving game theory, you have to be careful about trying to trick your opponent.  If he is smarter than you, you may be doing worse than doing nothing at all.  For example, in poker, when an inferior player tries to disguise whether he is bluffing or not, he is usually at a disadvantage against better players.  Most good professionals don’t do that (try and trick other players by their mannerisms) at least against other good professionals.

MGL - I realize that some pitchers occasionly do this on their own.  I don’t think that is a particularly good idea. The catcher has to run through too many signs to get back to the original sign.  That is why I suggested what I did.  Much better to have the catcher pick the time and particular batter for deception. Catchers are much smarter than pitchers.