On Game Theory, 0-2 Meatballs, and You
There was an interesting read kicking around baseball twitter this week, written by A’s fan and blogger Ken Arneson. In it, the computer scientist wonders about a great many things, the most interesting — to me — is his section on pitch selection. It’s Game Theory, I guess, but Arneson lays out four simple criteria for pitchers as they make pitch decisions:
- Choose a pitch the batter is likely to predict incorrectly
- Choose a pitch the pitcher is likely to throw with good speed, location, and movement
- Choose a pitch which will result in a suboptimal swing path, resulting either in a miss or weak contact
- Choose a pitch which, if not put in play, worsens the batter’s Prediction State for the next pitch
Makes sense, right? Easier said than done but it at least provides some food for thought. Not long after reading this, and for reasons that are entirely my own, I found myself watching highlights of old A.J. Burnett and Josh Johnson starts. Two power pitchers with filthy stuff, the videos or great starts from yesteryear showed what happens when pitchers like this have it all working.
One thing I observed made me think of the checklist above: both pitchers were able to freeze batters with 0-2 fastballs. Rather than waste pitches, these fastballs were seemingly thrown right down Main Street, middle/middle, over the heart of the plate.
Any pitch thrown in that location could be best described as “suboptimal” but, for pitches with stuff to spare on their best days, it worked as an effective pitch. They froze batters who twisted themselves into knots worrying about the hammer or an elevated fastball, the catalyst for chases.
This brought me to Baseball Savant and then it brought me here. I come bearing GIFs.
As one might expect, just about any leaderboard you can create in 2014 features Clayton Kershaw’s name right at the top. The Dodgers ace froze three batters with pitches down the middle this year, though not all lock ups were created equal. Sometimes you burn a fastball straight down broadway because the hitter has no intention of swinging.
The leaderboard features its fair share of pitchers peppered throughout the mix, but it doesn’t make these highlights any less hilarious. Kershaw’s other 0-2 highlights feature more polished hitters shaking their heads in bewilderment.
Kershaw earned three of these gift strikes this season, the same number as Nationals reliever Drew Storen. The former closer’s slider left more than its share of hitters’ mouths agape, especially when paired with his changeup, a weapon he turned to more often in 2014 than ever before.
This pitch is the result of a nice setup by Storen, throwing two straight fastballs (two seamers) on the inside half, tying Hechavarria up. It left the batter vulnerable to the front hip slider and it Storen ticks at least three of the points raised by Arneson as listed above.
Storen’s slider came after two straight changeups, one for a called strike on the outside corner and one for a swing-and-miss, over the plate but below the strike zone. The pitcher shook off a few signs, planting further doubt in the mind of batter Jace Peterson. “He feels good about his changeup, right? I’m not seeing it and here comes another one!”
Whoops.
My favorite 0-2 take this year came from a very unlikely source. Carlos Gomez ranks as one of the most aggressive hitters in baseball. Over the last two seasons, he holds the fourth-highest swing rate overall and the second-highest swing rate for pitches inside the strike zone.
On July 30th, he stepped in against David Price in what would be his final start as a member of the Rays before joining [scans notes] the Tigers??? The Rays broadcast booth set the stage with some terrific foreshadowing, for our purposes anyway.
“So we are under way, and Gomez comes out swinging as he has throughout this series.” Dewayne Staats intones as Gomez swings and misses at a first pitch changeup down and away.
“It will be interesting, this freewheeling Milwaukee Brewers offense against David Price who POUNDS the strike zone as well as anybody. This is going to be a fun battle to watch.” explains Rays analyst Brian Anderson, after Gomez fouls an 0-1 curveball down the third base line.
And then Price does this:
This is straight out of the Rays pitching backwards playbook. Gomez, who never met a fastball he didn’t like, can only walk back to the dugout after a good, long conversation with himself.
Hitting is a complicated business. Synthesizing real time information with background knowledge on a pitcher can make for overthinking and simply taking yourself out of an at bat. Some hitters are happy to see ball, hit ball.
The Rays aren’t the only team to preach pitching backwards, throwing offspeed pitches in fastball counts and vice versa, but they’ve certainly developed a reputation for doing it. It’s an appealing option but runs counter what others in the game say: a good fastball is your best pitch. The potential for making a mistake and presenting the hitter with a more hittable option remains very real, which introduces some downside to the “keep’em guessing” model of pitching.
So what’s the main point here? While these isolated examples show what it looks like when Game Theory and the physical execution of a plan come together at the same time, are they instructive when looking for an edge in the pitcher/batter match up?
How, given the “not a simulation” reality of actual baseball and the ingrained nature of pitch selection, does one weigh the value of surprise against the likelihood of poor execution? More pressing in today’s game, how can hitters compete in an interaction already stacked against them?
There are more questions listed above than answers. Because the answers are not coming easy – or cheap. Whichever team succeeds in reprogramming and rewiring their ballplayers just might benefit in the long run (one might argue the Rays already have.) The next frontier of baseball research stands before us, I suppose. Forever limited by the stubborn humanity of the players talented enough to reach the game’s highest levels as it might be.
Drew used to write about baseball and other things at theScore but now he writes here. Follow him on twitter @DrewGROF
Did he lay out 5, and you chose not to list one of them, or did he really only lay out 4?
Just four! Thanks for the nudge
It seems to me that this is missing the input of catchers calling the game, who are often as not the ones making pitch type and location decisions.
Some questions I have resulting from this:
1. Of the pitches thrown middle-middle in 0-2 counts, what were the results of the pitch compared the general case? More swings because there are two strikes? Fewer because the batter doesn’t expect the pitch?
2. Of said pitches, what is the pitch mix? More or fewer fastballs compared to other 0-2 pitches in other locations? More or fewer fastballs than pitches in that same location in other counts?
3. How often do pitchers go there in 0-2 counts compared to other counts?
4. (This will be very hard to calculate but) how often do pitchers intend to throw the ball there? Are a greater percentage 0-2 middle-middle pitches intentional compared to, say, 2-1 pitches?
from baseballsavant.com
Total pitches thrown in 2014: 704663
Total pitches thrown middle-middle: 39173
Total fastballs thrown: 435918
Total fastballs thrown middle-middle: 26576
Total 0-2 pitches thrown: 45485
Total 0-2 fastballs thrown: 24132
Total 0-2 pitches thrown middle-middle: 1301
Total 0-2 fastballs thrown middle-middle: 788
So to answer my own questions…
1. Unfortunately, as far as I can see, baseballsavant doesn’t have the result breakdown for the totals, only for individual pitchers
2. 60.6% of 0-2 middle-middle pitches are fastballs, while 53.1% of 0-2 pitches are fastballs. I’m betting this is just because there are a lot of low offspeed pitches in 0-2 counts.
Also, 67.8% of pitches thrown middle-middle overall pitches are fastballs. So, this could mean that pitchers try to throw low offspeed pitches and miss over the middle, or it can mean that with the count in their favor, pitchers feel comfortable changing speeds and trying to freeze a batter with a non-fastball.
Either, this is pretty much expected. More of 0-2 middle-middle pitchers are fastballs compared to other locations, but there are fewer fastballs there in 0-2 counts than in other counts.
3. Another unsurprising result: 5.6% of pitchers are middle-middle, but only 2.9% of 0-2 pitches are middle-middle.
If you do a simple differences of proportions test comparing middle-middle fastballs in 0-2 counts (~1.73%) versus all other counts (~3.91%) the z-stat is a stratospheric 23.6. This would give some credence to a “surprise” factor conjecture. I suspect that, as alluded, it is pitchers with over-powering fastballs that can get away with this, as their heat would be hard to adjust to.
Also, I wonder what the proportion of 0-2 pitches are fastballs (not just middle-middle) by pitch speed. It wouldn’t surprise me to find that the faster the pitcher can throw, the more likely he is to try to surprise with the heat.
Good idea, I may check to see if baseballsavant can run this query…
I think it can be done making multiple queries. I just didn’t have the time.
I wonder how often getting clever like that backfires, though. Like most things, it looks good when it works (Hunter Pence is the exception, as always). In those five instances, going middle-middle in an 0-2 count was successful, and looked smart. Presumably, there have also been instances when it was unsuccessful, and looked dumb.
It’s never dumb. I always throw the 0-2 pitch right down the middle because nobody ever expects it.
As I looked at in my too-long comment above, pitchers go to that location about half the time in 0-2 counts compared to the general case. They don’t have very many opportunities for it to backfire, and hitters would be justified in never really looking for a pitch there.
Arneson is completely wrong (among other things) about “throwing pitches that the batter does not expect.” And that is NOT game theory (well, in a sense any discussion of strategy in a contest is “game theory”).
That doesn’t even make any sense. If you can guess what the batter does not expect, then he can guess the same thing, in which case he DOES expect it. That is why you simply have several pitches that you are going to throw X percent of the time in any count/situation to a particular batter, and you choose one of them randomly.
As I have said before, the pitcher and catcher don’t THINK that they are choosing a pitch randomly, but they more or less are.
As I have also said many times before, choosing a pitch because you think it is the “right” pitch or that it will fool the batter is a dangerous way to pitch because any pitch that is NOT chosen randomly from a pitch distribution matrix can be figured out by a smart batter, one who can think like a pitcher/catcher. Evidence that pitchers and catchers do NOT act this way is this: If they did, then catchers at the plate (and other smart batters), and even pitchers, would be able to crush pitches they knew were coming with a high degree of likelihood. They don’t. We all know that catchers and pitchers are the worst hitters in baseball.
Now, be careful not to interpret “random” as every pitch is equally likely. Of course that is not true. In some cases, there might be only one pitch that is thrown 100% of the time, such as a 3-0 count to a pitcher with no one on base in a 10-0 game. Other times, say with an 0-2 count, it might be 40% curve ball, 40% change up, and 20% fastball. Or whatever.
The percentages depend on one thing and one thing only, although they are not easy to figure out. The percentages must be such that every pitch thrown has the exact same win value (run value is a decent proxy for win value). How can that be when obviously for most pitchers each pitch is not necessary as good as every other pitch? Because the value of a pitch depends not only on the intrinsic value of the pitch (including the chances that it is going to be a ball or called strike of course), but on the strengths/weaknesses of the batter AND most importantly, the expectations of the batter.
Do, for example, let’s say that a pitcher has a great curve ball and a so-so fastball and he throws that curveball 80% of the time at 0-2 counts. The batter obviously must look primarily for the curveball, but the 20% of the time when he gets the mediocre fastball, he is not expecting it and it becomes a very good pitch – in fact, exactly as good as the “great” curve ball which the batter expects (at least he expects it 80% of the time). BTW, pitch selection includes location as well as the actual pitch of course, so typically a pitcher has a half dozen or more different “pitches” to make a distribution matrix in any situation.
Here is the exact rebuttal to the claim that a pitcher tries to throw a pitch that the batter does not expect. In fact, it is the exact opposite! By definition the pitcher is more likely to throw a pitch that the batter DOES expect. It is just that the pitch most expected and most thrown is the pitcher’s best pitch (in a vacuum)!
Let’s say that at a 3-1 count a pitcher throws 80% fastballs and 20% off-speed. The batter obviously expects a fastball (80%) of the time and is going to get a fastball 80% of the time. So how is that throwing a pitch that the batter does not expect?
An an 0-2 count, again, every pitcher has a certain matrix that he uses in any given situation against any given batter. It might be, for example, off-speed 70% (many of them out of the zone) and fastball 30% (with many of those out of the zone too). Again, the batter looks 70% off-speed and that is what the pitcher throws – 70% off-speed. 30% of the time, the batter gets what he doesn’t expect and 70% of the time he gets what he expects!
By the way, those fastballs down the middle in the GIF’s were NOT trying to be thrown down the middle, as you can see from the catcher’s glove. Most of them were supposed to be inside and the pitcher simply missed his location. Although it is possible that a fastball down the middle on an 0-2 count is included in the pitch matrix (maybe thrown 5 or 10% of the time), it is unlikely. Remember that since all pitches must have the exact same value (given how often they are thrown), if a fastball down the middle has a value that is worse than the other pitches, even when it is thrown 5% of the time, then it cannot be thrown. The proper percentage would be 0.
While I think you’re right that the pitcher technically isn’t throwing a pitch the batter doesn’t expect, he is taking the batter’s expectation into account when calculating the pitch probability matrix.
So, let’s say we go back to the pitcher who throws 80/20 curve/fastball. If that pitcher happens to know at that time that the batter is sitting on the curve or guessing curve, more so than batter typically would in that situation, that will impact that matrix, maybe pushing it to 70/30. Obviously the curve is still the better pitch. Also, like you mention, if the pitcher went to the fastball 100% of the time when he thinks the batter is expecting curve, a batter could figure this out and win an advantage.
However, a pitcher certainly doesn’t treat every 0-2 count against every batter the same way. Every batter is not going to get a 80/20 split in the same situation, and the batter’s expectation is going to be one of the factors than influences that split.
Basically, I think the optimal strategy is to maintain the same split, so that the pitcher is never predictable, but that assumes the batter is applying the optimum strategy. If the batter is not doing so (let’s say he is 100% sure a curve is coming), then the optimal strategy in the general case is not the optimal strategy to use in that situation.
Just as in poker there are two ways to choose a strategy. One is game theory optimal which assumes that your opponent is using GTO strategy as well. If your opponent, in this case the batter, is, then you MUST use GTO strategy yourself or you will be “losing” the battle.
If you use GTO strategy even if your opponent is not, even though technically you can be using a better strategy, you cannot be taken advantage of.
If you don’t know what kind of strategy your opponent is using then you are typically better off using GTO strategy and NOT trying to guess what your opponent might be expecting it thinking. If you do not use GTO strategy then you open yourself up to being exploited by your opponent.
One of the interesting things about GT in this context which might surprise a lot of people is that if your opponent (the batter) is not using a GTO approach and his expectation for a particular pitch is too low then it is generally correct to throw that pitch 100% of the time in that instant. Of course you can’t do that because your strategy is not a one time thing. It has implications for future PA against other batters as well.
So for example if you know or suspect that the batter is looking fastball too often as compared to his GTO strategy then you might throw him slightly fewer FB than your GTO strategy would suggest. But, again, how long can you go on doing that until that batter realizes it and starts to look fastball less often? That is why a pitcher must use a strategy that is reasonably close to GTO.
By the way, the GTO strategy for the pitcher has nothing to do with the batters expectations. It only has to do with the value of the pitches as a function of the game situation, the batters strengths and weaknesses, etc.
The definition of a GTO strategy is that regardless of what the batter expects the values of all the pitches stays the same and are equal. So the batters expectations do not change your GTO percentages. They may, however, change your optimal strategy if the batters expectations are not GTO themselves. But, as I keep saying, a pitcher must be very careful in deviating from a GTO strategy. It can ALWAYS be exploited. It only “works” against an opponent batter who does not act optimally himself.
So, no batter actually applies optimum strategy. I’m not even clear what that means. If the optimum strategy dictates that a pitcher should throw 80/20 curve/fastball, and the batter also knows this, what does it mean for the batter? Does he guess curve 80% of the time and fastball 20%? Or does he somehow have an approach that incorporates both, so he is ready for the curve but open the chance of a fastball? It’s hard for me to conceptualize what this means.
I would think the ideal thing for a pitcher to do is to use the GTO strategy most of the time, but if certain cases, if a batter’s intention is clear, he can adjust it.
This is the kind of thing that I think might take a long time to adjust. So, sure, if you deviate from a batter’s expectations too severely you may get punished later for deviating from GTO, but I feel like a bias like this takes a long time to adjust. So, you can go on doing it for a little while because I don’t know if batters can adjust that quickly. I may wrong, but that what it seems like to me.
Here is a good analogy: Play rock/papers/scissors with someone and try and use a strategy where you put down the hand that they least expect. See how well you do. Against anyone other than an idiot, you will get killed. The proper strategy is of course choosing each hand randomly from a 1/3, 1/3, 1/3 matrix. When I say “proper strategy” I mean one in which you cannot lose (you can’t win either, of course). And of course, the “value” of your hands are exactly the same. If you play using that strategy a million times, and we add up the wins and losses for each hand, they will be exactly the same, 1/3 win, 1/3 tie and 1/3 loss, for a net value of zero. No matter what strategy your opponent uses, you will break even. If your opponent uses an optimal strategy, the same as yours, then all of your hands will have a net value of zero.
Pitching is exactly the same except that the percentages change from 1/3, 1/3, 1/3. And if the batter is acting rationally and optimally too, each of your pitches, given the same situation (batter, score, inning, count, outs, runners, etc.), will have the exact same win value. That could be positive or negative of course, unlike with RPS, where the value is always zero.
Parklife!
I think you’re right in theory, but in reality both batters and pitchers DO attempt to “outguess” each other. I think that’s because the variables that go into calculating the correct percentages are so numerous that nobody has managed to “solve” baseball. My personal belief is that it will remain unsolved, and that players who are good at outguessing other players will continue to have a noticeable advantage.
In no limit poker even heads up, no one can solve the GTO strategy either but all good players come as close as they can. Now against lesser players, good players deviate from GTO play in order to increase their advantage. In baseball, everyone is “world class” so it is not clear to me how much a pitcher or batter should deviate from GTO play based on the less than optimal approach of their opponent. As far as guessing and out guessing your opponent in baseball it is my opinion that much of that ends up being random or at least pseudo random.
“Now against lesser players, good players deviate from GTO play in order to increase their advantage.”
This sounds confusing and contradictory to me, but then I don’t really know anything about game theory, so I just want to try to make sense of this. If GTO is using the optimal strategy, then how does deviating INCREASE one’s advantage? I apologize if this is a dumb question, but I don’t want to come away from this with mistaken ideas.
“If GTO is using the optimal strategy, then how does deviating INCREASE one’s advantage?”
The “optimal” strategy gives you the best result possible on average assuming your opponent is also using their own optimal strategy. If you use the optimal strategy but your opponent deviates from it then you will gain an advantage.
If you know the opponent’s strategy has a flaw then there may be a strategy that exploits that flaw better than the optimal strategy will. The problem is that your new error-punishing strategy will itself be vulnerable to attack, if the opponent can see it.
The trick to deliberately deviating from the optimal strategy is distinguishing “my opponent is playing sub-optimally because they are not as good as I am” from “my opponent is playing sub-optimally in order to lure me into a trap”. The optimal strategy may not score as highly when the opponent is in fact bad, but will also avoid falling into the trap when the opponent is better than they look.
Pretty much what G said above. GTO optimal strategy is only “optimal” if your opponent is also using GTO strategy. If he is not, then your optimal strategy is NOT the same as GTO strategy. However, as g says above, if you deviate from GTO in order to gain a higher advantage against an opponent who is NOT using GTO strategy, then you are vulnerable to being exploited. That sounds confusing and paradoxical and it is. If you opp. is not using GTO strategy then by definition, he will not exploit you if you respond by altering your strategy from GTO to something else which is “more optimal” against him.
The key is to not alter your strategy too much so that you “tip your opponent off” that he is not acting optimally (using GTO). If you alter too much, then your opponent may do one of two things: One, alter his strategy a little such that he is not using GTO. Two, alter his strategy a lot such that he now exploits you! Of course, if he does either of those things, then you can always go back to a GTO strategy, in which case you don’t care what he does – he can never exploit you.
As you can see (maybe), unless you are pretty sure that your opponent is exploitable and you don’t think that will change, you are better off striving for a GTO strategy. Remember, even though a GTO strategy is not actually optimal against a player who is also not using a GTO strategy, it cannot be exploited, by definition. By definition, I mean that a GTO strategy is defined as that strategy such that no matter what your opponent does, the value of your strategy is always the same.
Let me give a poker example which illustrates the above concepts.
In poker, when all the cards are out, you are against only one opponent, and you have nothing, you have a choice of bluffing or not (in which case you check) when you act first or you act last and your opponent checks to you.
A GTO optimal approach dictates that depending upon how much money is in the pot and how much your bluffing bet is, there is an exact ratio to your bluffs and your value bets. A value bet, for purposes of this discussion, is defined as a bet which you make when you are certain that you have the best hand.
So you have to figure out, basically, how often to bluff with a busted hand. A GTO strategy tells you that there is an exact percentage (depending on how much money is in the pot, the size of your bet, the cards on the table, how you played the hand, etc) such that it makes no difference at all whether your opponent calls or folds. In the long run, you will win exactly the same amount of money on all your bluffs and value bets and checks (non-bluffs), whether your opponent folds or calls your bet. We are assuming that your opponent either folds or calls, but does not raise.
At the same time, your opponent, if he is playing GTO, he calls and folds when he can only beat a bluff, a certain exact percentage of the time such that it does not matter how often you bluff and how often you value bet. The average net win for your opponent will be the same regardless of what you do, if he uses a GTO approach.
How often you bluff and how often you check, with a busted hand, is exactly equivalent to how often a pitcher throws a fastball and breaking pitch in a given situation against a given batter. There is an exact percentage for each pitch such that whatever the batter is looking for, the net value of all of the pitcher’s pitches will be exactly the same and the batter cannot exploit the pitcher.
In the poker example, if you use the one and only one GTO approach which dictates an exact ratio between your value bets and bluffs given the cards and how you played your hand, your opponent cannot exploit you.
But, let’s say that your opponent is an amateur or a good player who does not know or miscalculates how often he is supposed to call or fold when he can only beat a bluff. Remember that his calling or folding decision is completely random around those fixed GTO percentages. For examples, he may be supposed to call 75% of the time and fold 25% of the time, based on the pot size, last bet size, and other factors. How does he do that? There are many ways. In Texas holdem, he may peek at one of his cards. If it is a spade, he folds. If it is anything else he calls. Some sophisticated players use the second hand on a watch. You glance at your watch and if it is in the first 5 seconds, that corresponds to an 8 or 9% random choice, etc.
Anyway, if you know that your opponent deviates from GTO even by a little (In practice it is impossible to know that your opponent deviates a little, but you can usually tell when he deviates by a lot. On the other hand, he may deviate correctly against other opponents but not against YOU!) – say he calls bluffs too often, then it is correct for you to NEVER bluff. If he is supposed to call bluffs 75% of the time in that situation, but you somehow know that he is going to call a bluff 80% of the time, then it is correct for you to NEVER bluff!
That is like I said that if a batter is looking fastball a little too much in any given situation, it is correct for you to have a 0% chance of throwing one in that situation even if GTO calls for 20% or 80%.
But in poker, what happens if you are playing against that opponent who calls potential bluffs too often and you NEVER bluff. Well, eventually, unless he is brain dead, he will stop calling potential bluffs altogether. So now you never bluff and he never calls your value hands either! That is a terrible strategy for you. You are being exploited to the max!
So, what do you do when a player incorrectly varies from GTO strategy. You try and vary your strategy subtly to take advantage of him, but not too much so that he alters his strategy in response to you such that either he exploits you or your force him to or towards a more GTO strategy.
So in the case of the player who calls potential bluffs a little too often, you still bluff (which satisfied him – he gets to pick off lots of your bluffs – of course he also pays off lots of your value bets), but you bluff slightly less often than GTO would suggest, and hopefully your opponent does not notice and alter his strategy to make it more GTO. Or you just keep using your GTO strategy, even though technically it is not optimal against this opponent, satisfied that you still have an edge because you are using GTO and he is not, you cannot be exploited by him, no matter what he does, and you don’t have to worry about accidentally forcing him into a better strategy!
My objection to this is rooted in the third of my ten points: All high-level sabermetric truths derive from lower-level truths about human biomechanics and psychology.
The rational part of the human brain (System 2 as Kahneman calls it) is far too slow to perform any of this sort of rational analysis on the fly. Once the pitch is released, the mechanism relies entirely on System 1, which is automatic and subconscious. As I stated in my article, this automatic system is subject to all sorts of irrational heuristics, including a recency bias. These biases are there, available to be exploited by the pitcher.
Rock paper scissors probably has a recency bias to it, too, when played by humans.
Remember that if you use GTO strategy and your opponent does not, even though your strategy is NOT optimal against his strategy, and his strategy is NOT optimal against yours, YOU will always have the edge! You may be able to gain a larger edge by deviating from a GTO approach, but in doing so you are risking losing some or all (or more) of your original edge!
So, essentially, what makes GTO optimal is the fact that you cannot be at a disadvantage when implementing it, regardless of the strategy your opponent uses, not the idea that it is the most optimal strategy to use in terms of giving you a better chance of winning. You can deviate from GTO against an opponent that you’re reasonably sure is NOT using GTO (such as a weaker or unskilled player), and this will give you an advantage, but you risk being exploited if your opponent was bluffing the whole time and especially if your opponent was, in fact, using GTO him-or-herself.
Your detailed explanations helped a lot. Thanks MGL and g!
So, to be really pedantic, it doesn’t mean that you cannot be at a disadvantage. You can be at a disadvantage using GTO. A fringy LOOGY will alway be at a disadvantage against Miguel Cabrera no matter what strategy he uses.
What it means, to be more precise, is that you are setting the highest possible floor for how badly you can do. You cannot be ‘exploited’ in the sense that no one can gain an advantage over and above what you can limit using GTO. That floor might not be very good for you, but the point is that it could potentially be even worse for you if you don’t use GTO, and GTO allows you to minimize the damage.
Love the poker talk in here. lol
Straight down the dick
Love your work Drew.
Just out of curiousity… who is developing a pitching ‘artificial intelligence’ that will take factors such as pitchers ability, hitters ability, recent and selective (pitcher vs. hitter or either vs. similar) history into account that managers will use to call games from the dugout. I think pitch selection is one of the greatest weapons still yet to be fully exploited in baseball.
I agree that it is an undeveloped area. I don’t think it is necessary for a manager to call every pitch optimally. There are rules of thumb that comport with a GTO strategy that pitchers and catchers can learn. It is especially important to go back into a pitcher’s history and teach and show him where he is using a clearly sub-optimal strategy, although that might be difficult given the sample size issues.
Bunting and defending against the bunt is also is very game theory oriented. I’ve written about it before.
The defense MUST play in a position for each batter, given each situation (score, inning, runners, etc.) such that the WE is exactly the same whether the batter bunts or not.
(At the extremes, that is not necessarily true. For example, if a batter is a poor bunter and/or slow and/or a great hitter, it may be correct for the defense to play all the way back and the WE from the bunt could still be less than that of swinging away. That is only because playing back also affects hitting away such that there is a limit to how far back you can play. Same with a batter who is a great bunter and poor hitter. The defense can only play so far in, so, if they do, the WE from a bunt may still be higher than swinging away, such as with a poor hitting pitcher in a sac bunt situation.)
So once, the defense established that position, it doesn’t matter what the batter does. That is the GTO strategy for the defense.
However, the batter, at the same time, must establish a bunt/non-bunt percentage such that it doesn’t matter where the defense plays. The overall average WE is exactly the same regardless of where the defense plays when the batter uses this strategy, for example, bunting 40% of the time. This is the batter’s GTO strategy.
As with the poker and pitching examples, if either party does NOT use the GTO strategy his opponent can exploit him by either bunting or hitting away all the time, or playing all the way in or all the way back. However, once again, that is not such a viable response because the opponent will immediately or soon thereafter change his strategy and YOU will not be exploited. The best you can/should do against a batter who bunts too much or too little, as compared to GTO, is to slightly alter your defensive position.
Similarly, if the defense plays too far in or too far back, the best you should do is alter your bunting/non-bunting percentage slightly.
The defense and the offense MUST be careful with bunts/non-bunts that they are not being lured into playing sub-optimally. For example, say the defense plays further back than GTO. Now the batter may bunt more often than GTO. The defense may anticipate this and charge aggressively, even more so than if they were playing GTO, thus exploiting the batter who thought he was exploiting the defense!
If the batter squares early like he is going to bunt for sure, and the defense responds by charging aggressively, the batter can pull back and hit away, thus exploiting the defense who thought they were exploiting the batter!
The remedy for all of this is to always play GTO and perhaps vary slightly if you know or suspect that your opponent is varying from GTO and will continue to do so, even if you vary in response and exploit him.
This is one area where teams/managers are terrible, especially on the offensive side. However, teams are playing horribly sub-optimally, relative to GTO, when shifting, but strangely, most batters are also playing terribly sub-optimally by not bunting enough (in most cases, not at all), which results in the defense exploiting the offense.
The equilibrium point would of course result in shifts mostly disappearing, other than against the worst bunters and/or best hitters, and batters bunting some percentage of time.
Of course, since in this case the defense must act first and show the offense their hand, it doesn’t really require the batter to bunt (he can if he wants) once the defense starts to play GTO. Until the defense does play GTO, though, the batter must bunt either using a GTO percentage of bunt every time until the defense gets to a GTO position. The batter may try and lure the defense into NOT playing optimally by bunting slightly more often than GTO would dictate and hope that the defense still plays somewhat of a shift. Of course then the batter runs the risk that the defense will play to far towards the bunt end of the spectrum and the batter will be exploited for bunting too much.
If the batter only bunts occasionally, as is the case even with batters who are shifted on and DO occasionally bunt, then the defense is correct in playing a full shift and not moving. It is like that poker player who bluffs just a little, but not enough. It is correct to NEVER call him. The batter must bunt at least as often as GTO dictates in order for the defense to want to move.
So while bunting occasionally into the shift is better than not bunting at all, the batter is STILL being exploited until such time as he reaches the GTO point.