Maybe.

In this article, Tuffy Gosewisch, the new backup catcher for the Braves, talks catching with Fangraphs David Laurilia. He says about what you would expect from a catcher. Nothing groundbreaking or earth-shattering – nothing blatantly silly or wrong either. In fact, catchers almost always sound like baseball geniuses. They do have to be one of the smarter ones on the field. But…

Note: This is almost verbatim from my comment on that web page:

I have to wonder how much better a catcher could be if he understood what he was actually doing (*of course they do, they get paid millions, they’ve been doing it all their lives, and are presumably the best in the world at what they do. Who the hell are you, you’ve never put on the gear in your life?*).

All catchers talk about how they determine the “right” pitch. I’m waiting for a catcher to say, “There *is* no ‘right’ pitch – there can’t be! There’s a matrix of pitches and we choose one randomly. Because you see, if there were a ‘right” pitch and *that* was the one we called, the batter would know or at least have a pretty good idea of that same pitch and it would be a terrible pitch, especially if the batter were a catcher!”

If different catchers and pitchers have different “right” pitches and that’s why batters can’t guess them then there certainly isn’t a “right” pitch – it must be a (somewhat) random one.

When I say “random” I mean from a distribution of pitches, each with a pre-determined (optimal) frequency, based on the batter and the game situation. Rather than it be the catcher and pitcher’s job to come up with the “right” pitch – and I explained why that concept *cannot* be correct – it is their responsibility to come up with the “right” distribution matrix, for example, 20% FB away, 10% FB inside, 30% curve ball, 15% change up, etc. In fact, once you do that, you can tell the batter your matrix and it won’t make any difference! He can’t exploit that information and you will maximize your success as a pitcher, assuming that the batter will exploit you if you use any other strategy.

If a catcher could come up with the “right” single pitch that the batter is *not* likely to figure out, *without* randomly choosing one from a pre-determined matrix, well….that can’t be right, again, because whatever the catcher can figure, so can (and will) the batter.

We also *know* that catchers don’t hit well. If there *were* “right” pitches, catchers would be the best hitters in baseball!

Tuffy also said this:

“You also do your best to not be predictable with pitch-calling. You remember what you’ve done to guys in previous at-bats, and you try not to stay in those patterns. Certain guys — veteran guys — will look for patterns. They’ll recognize them, and will sit on pitches.”

Another piece of bad advice! Changing your patterns *is* being predictable! If you have to change your patterns to fool batters your patterns were not correct in the first place! As I said, the “pattern” you choose is the only optimal one. By “pattern” I mean a certain matrix of pitches thrown a certain percentage of time given the game situation and participants involved. Any other definition of “pattern” implies predictability so for a catcher to be talking about “patterns” at all is *not* a good thing. There should *never* be an identifiable pattern in pitching unless it is a random one which *looks* like a pattern. (As it turns out, researchers have shown that when people are shown random sequences of coin flips and ones that are chosen to *look* random but are not, people more often choose the non-random ones as being random.)

Say I throw lots of FB to a batter the first 2 times through order and he rakes (hits a HR and double) on them. If those two FB were part of the correct matrix I would be an idiot to throw him *fewer* FB in the next PA. Because if that were part of my plan, once again, he could (and would) guess that and have a huge advantage. How many times have you heard Darling, Smoltz or some other ex-pitcher announcer say something like, “After that blast last AB (on a fastball) the last thing he’ll do here is throw him another fastball in *this *AB?” Thankfully, for the pitcher, the announcer will invariably be wrong, and the pitcher will throw his normal percentage of fastballs to that batter – as he should.

What if I am mixing up my pitches randomly each PA but I change my mixture from time to time? Is that a good plan? No! The fact that I am choosing randomly from a matrix of pitches (each with a different fixed frequency *for that exact situation*) on each and every pitch means that I am “somewhat” unpredictable by definition (“somewhat” is in quotes because sometimes the correct matrix is 90% FB and 10% off-speed – is that “unpredictable?”) but the important thing is that those frequencies are optimal. If I constantly change those frequencies, even randomly, then they often will not be correct (optimal). That means that I am sometimes pitching optimally and other times not. That is *not* the overall optimal way to pitch of course.

The optimal way to pitch is to pitch optimally all the time (duh)! So my matrix should always be the same as long as the game situation is the same. In reality of course, the game situation changes all the time. So I *should* be changing my matrices all the time. But it’s *not *in order to “mix things up” and keep the batters guessing. That happens naturally (and in fact optimally) on each and every pitch as long as I am using the optimal frequencies in my matrix.

Once again, *all* of this assumes a “smart” batter. For a “dumb” batter, my strategy changes and things get complicated, but I am still using a matrix and then randomizing from it. Always. Unless I am facing the dumbest batter in the universe who is incapable of ever learning anything or perhaps if it’s the last pitch I am going to throw in my career.

There are only two correct things that a pitcher/catcher have to do – their pitch-calling jobs are actually quite easy. This is a mathematical certainty. (Again, it assumes that the batter is acting optimally – if he isn’t that requires a whole other analysis and we have to figure out how to exploit a “dumb” batter without causing him to play too much more optimally):

One, establish the game theory optimal matrix of pitches and frequencies given the game situation, personnel, and environment.

Two, choose one pitch randomly around those frequencies (for example, if the correct matrix is 90% FB and 10% off-speed, you flip a 10-side mental coin).

Finally, it may be that catchers and pitchers do nearly the right thing (i.e. they can’t be much better even if I explain to them the correct way to think about pitching – *who the hell do you think you are?*) even though they don’t realize what it is they’re doing right. However, that’s possible *only* to an extent.

Many people are successful at what they do without understanding what it is they do that makes them successful. I’ve said before that I think catchers and pitchers do randomize their pitches to a large extent. They have to. Otherwise batters would guess what they are throwing with a high degree of certainty and Ron Darling and John Smoltz wouldn’t be wrong as often as they are when they tell us what the pitcher is going to throw (or should throw).

So how is that catchers and pitchers can think their job is to figure out the “right” pitch (*no* *one* ever says they “flip a mental coin”) yet those pitches appear to be random? It is because they go through so many chaotic decision in their brain that for all intents and purposes the pitch selection often ends up being random. For example, “I threw him a fastball twice in a row so maybe I should throw him an off-speed now. But wait, he might be thinking that, so I’ll throw another fastball. But wait, he might be thinking that too, so…” Where they stop in that train of thought might be random!

Even if pitchers and catchers are essentially randomizing their pitches, two things are certain. They can’t possibly be coming up with the exact game theory optimal (GTO) matrices, and trust me there IS an optimal one (although it may be impossible for *anyone *to determine it, but I guarantee that *someone* can do a better job overall – it’s like *man versus machine*). Two, some pitchers and catchers will be better at *pseudo-randomizing* than others. In both cases there is a great deal of room for improvement on calling games and pitches.

What did you really say in this article that was not already 100% obvious?

Apparently nothing. I guess I could say the same thing about your comment.

I should have answered more truthfully and with less snark. First of all, while it might have been 100% obvious to YOU, clearly it wasn’t to other people, as you can see from the other comments. You surely know that unless you are a complete ignoramus. If my article was 100% obvious to you then you can’t be a

completeignoramus and you surely know that other people would find it valuable. In either case, your comment is arrogant and inappropriate (and 100% wrong). That should also be obvious to you unless you are a sociopath or psychopath. Why would you want to denigrate something that I wrote which is clearly valuable to other people? Even if it weren’t why would someone post such an arrogant and mean and completely incorrect comment? Had you put “obviousto me” you might have been correct, assuming that it is true, which is debatable as you have no credibility from my perspective.However, had your statement been: “What did you really say in this article that was not already 100% obvious

to me?” it would have made no sense at all and my original answer would have been correct. If I wrote a good quality article on cosmology for the public to consume and Stephen Hawking wrote me and said, “What did you really say in this article that was not already 100% obvious to me? ” I would suspect that he lost his mind. Maybe you have, I don’t know.This was a fantastic article about nash equilibrium with regards to pitch selection. It seems like GTO strategy with pitch selection is complex enough for athletes, add in GTO strategy with locating a pitch and factors like the count and optimal strategy seems incredibly difficult to figure out but a fascinating aspect of the game. A catcher that helped the pitcher take a strategy that was close to nash equilibrium would seem to add a ton of expected wins to his team.

You seem to think about this a lot, I’m wondering if you have some ideas on what pitchers seem to have good pitch selection strategies and which seem to be the more Brick Tamland types?

Thanks Daniel! Great question. Haven’t done the research yet but it is on my “to do” list. First task is to look at pitch frequencies overall to see if a NE exists and if not what the “lack of equlibrium” looks like. In order to do that I have to use a sort of “delta method” whereby I identify groups of situations, determined mostly by count, batter, score, outs and baserunners, in which the optimal “frequency matrix” is the same. In each of those groups it is expected, if pitchers and batters are acting reasonably optimally, that the value of all pitches will be the same. If not, then batters or pitchers, one or the other, are being exploited.

Doing that on an individual pitcher level is not really possible because of sample size issues, however, we could put ALL individual pitchers into 2 categories, for example, those with roughly equal pitch values in those “categories”, and those who have significant differences. We would expect that the pool of pitchers in the first group are comprised of many more “optimal pitchers” than the pool in the second group although identifying exactly which ones are pitching optimally and which ones are not with much certainty is problematic of course. If this methodology and the underlying assumptions are correct, we should see a much better overall result (like RA or FIP or wOBA against) in Group I than in Group II.

We MIGHT also be able to look at group I and look at their pitch frequencies and then assume that that those are THE optimal pitch frequencies overall. However, obviously every pitcher will have his own unique optimal overall pitch frequencies (which is just a conglomeration of many different frequencies of course, sort of like a beta distribution in statistics), depending on the “naked” quality and characteristics of each of his pitches. I use the term “naked” to mean the quality of a pitch if a batter knows it is coming or at least knows the frequency by which it is coming.

From that we might be able to separate all the pitchers in Group I by the pitch f/x parameters of their various pitches, for example, Group I consists of all RH pitchers with 90-92 mph fastballs with X horizontal and Y movement and 82-84 curve balls with a certain X and Y movement – 2 pitch pitchers. Now we can also look at those in pitchers in Group I and assume that their frequencies are near optimal as well. Now we can use that as the baseline for ALL pitches with that repertoire. Now if we go through ALL THOSE individual pitchers, rather than look at their pitch values (FB versus CB) which are too subject to random variation, we can simply compare their pitch frequencies to the optimal frequencies. I assume that pitch frequencies will have a much lower random error than pitch values.

Anyway just some thoughts for me or someone else to run with.

Thanks for the comments and question!

Interesting analysis. This has always been something I’ve found fascinating. Could the ability to “randomize” (and of course to throw multiple pitches effectively) but something that separates good pitchers from the mediocre and also be a skill that increases as you move up levels? This is a poor example, but when I played high school ball I feel like I always knew what the pitchers were going to throw. They were quite predictable. Granted, I played at a small school (and I wasn’t a good hitter anyways haha) but just a thought.

I think the second to last paragraph is a good breakdown. You’ll often hear the announcers say “He’s gotta throw his best pitch here…” Wellllll no. Even Mauricio Cabrera with his 102 mph fastball sprinkles in his changeup sometimes. When they say “best pitch” the announcers are referring to his fastball but sometimes that changeup can be his *best pitch* in a situation because of exactly what you laid out. The batter doesn’t know whether to gear up for 100+ or if he’s going to drop in 90.

Yes of course for both questions, I suspect it is.

Sure no doubt. In youth leagues many pitchers automatically throw a breaking pitch at 0-2. Now it is probably correct for pitchers to be “predictable” or “exploitable” at lower levels because they themselves are exploiting the sub-optimal batters in doing so. That is one the somewhat paradoxical keys to game theory. Game theory optimal strategies are only optimal if the opponent is also using GTO optimal play or even if he isn’t will always exploit you

if you vary from GTO play. I your opponent is not using GTO optimal play then your optimal strategy is now also not GTO, but in deviating from GTO strategies you yourself are exploitable. Most modern good poker players are very familiar with these concepts.Remember also not to confuse “predictablity” with “optimal frequencies.” Sometimes my optimal frequency is 100% one thing. That’s a “pure strategy” versus a “mixed strategy” where there is more than one choice made > 0 probability. For example, in Little League it may be correct to always throw an 0-2 curveball against certain batter at least, which simply means that even if the batter knows it’s coming, the value of that curveball is better (for the pitcher) than any other pitch even if the batter thought there was almost 0 zero chance of any other being being thrown. Same with a 3-0 count on a pitcher at the plate. In most cases the correct strategy is a pure one – FB down the middle. So while both these strategies are 100% “predictable,” they are still optimal. “Predictability” (most importantly NOT being predictable) in a pitching sense, means that once I have established the optimal frequency matrix for all my pitches prior to throwing my pitch (it will likely change on the next pitch so this is for one pitch only), I make my selection randomly – it cannot be influenced by anything such as the previous pitch or pitches, what the batter did the last pitch or the last PA. Keep in mind that the optimal frequencies themselves CAN be influenced by these things. That’s where people get confused and think I’m saying that there can be no such thing as “patterns” or the concept of set-up pitches. There can be as long as they legitimately change the game theory optimal frequencies!

For example (this is an important concept) let’s say that I have thrown a high tight fastball and the batter fouls it off in an 0-2 count so we have the same count, same situation, etc. The game theory optimal frequencies on the next pitch should be exactly the same as on the previous “brushback pitch.” So I should be exactly as likely to throw another high inside FB as I was before and exactly as likely to throw a down and away off-speed as I was before, whatever those numbers are.

Many if not most commentators, players and coaches would expect the next pitch to be a down and away pitch the so-called “set-up” pitch followed by a completely different pitch. We’ll even ignore the ridiculouslness of the concept that the next pitch WILL be (as in near 100%) orshouldbe a down and away pitch (since if that were the case the batter would know exactly what is coming which is a disaster in most cases, certainly in an 0-2 count) and just say that these players and commentators may be right that the next pitch should at least be down and away more often than the previous pitch even though nothing has changed – same count, same batter, same game situation etc. Could that be correct? Well, if can ONLY be correct in 2 circumstances: One, if the batter thought for some reason that he was more likely to get another high inside pitch just because he just got one. That is not very likely. If anything, it is the opposite of course. If he did think that then throwing the down and away pitch more often, as the commentators suggest, would be correct, but now the pitcher is veering away from GTO strategy and he is exploitable. But still it would be correct (in fact, it would be correct to throw that pitch 100% of the time but that would eventually tip off the batter and every other future batter!).The second scenario where throwing the low and away pitch more often than the previous pitch would be correct AND would still be GTO (game theory optimal) is when the high inside pitch does something to the batter (makes him back off the plate a little for example) and there is nothing he can do about it. I doubt that this is the case with most batters which is why I am a critic of the “set-up” pitch followed by an “opposite-type” pitch more often than if the set-up pitch were NOT the previous pitch.

Now, it is certainly possible that a set-up pitch like that does have some inherent affect on the batter that he can do nothing about, but still, we would need to know the quality and magnitude of that effect in order to determine how much to change our pitch frequencies on the next pitch. If on the previous pitch, the pitcher was going to throw the low and away offering 20% of the time, does that increase to 25% after the set-up pitch or 50%? 75%? Most commentators including ex-pitchers would have you believe that it’s like 80% or 90% (some of them 100%) but clearly that’s not the case and clearly they themselves did not do anything close to that when they pitched. As I said I am a set-up pitch skeptic but if there is an inherent effect, one that the batter has not control over, I suspect that it’s a small one such that the frequency of the opposite pitch would increase only slightly on the next pitch.

The interesting thing is that since the concept of the set-up pitch followed by an opposite pitch is so universally accepted by players, kit may in fact be correct to

decreasethe frequency of the “opposite pitch” andincreasethat of the same pitch! Maybe pitchers do that (and they just “talk” about set-up pitches to fool everyone), I don’t know. I doubt it.That’s right. The only time there is a “best pitch” to throw is when the correct GTO strategy is a pure one. As I explained already that occurs when that pitch thrown 100% of the time and the batter knows it is coming is still better (the value of that pitch measured in win expectancy) is higher than any other pitch where the batter does not know it is coming.

Has there been any research on the impact of ‘guessing’ correctly? I imagine it would be very difficult to do, if at all possible, but isn’t that a critical element here? If wOBA is affected minimally by ‘knowing’ what pitch is coming then randomization would not matter much. If there is a large impact then pitch selection and randomization matter a lot.

I have no idea but I am curious if there was any data available.

I’m not aware of any. We can assume that “knowing” what pitch is coming greatly affects the outcome which is exactly why randomization is so important.

Thanks. Could we use the difference in how hitters perform on different counts as a proxy for the impact on ‘guessing’ correctly? Just wondering if it is possible to quantify the impact more than our instinct that it is significant.

That’s a good suggestion about using different counts. Problem is that location is quite different and the approach of the batter is too. Might be prohibitive.

True but that could be used to set an upper bound? For example the woba difference between 1-1 and 2-0 is partially due the batter having a higher chance of “guessing” correctly and partially due to pitches more likely to be near the middle of the strike zone and less likely to be at the edges. Maybe looking at the impact of location at neutral counts could further be used to tease out an estimate? I realize there are multiple inter-dependencies and possibly not doable. In any event thanks for the responses and the thought experiment.

Yes, it might be possible along the lines that you suggest. Good insight! You think like a (good) sabermetrician!

Hey, I am currently collecting data for a GTO Optimized Pitching Metric. Let me know if you are interested and I would be happy to share my thoughts!