Were the Yankee Sac Bunts in the 8th Inning Correct?

The answer to that question is complicated. There is no easy yes or no answer and that is not so much because there are so many variables we don’t know the answer. It has to do with game theory. Oh, in case you didn’t watch the 6th game of the ALCS or you forgot, in the 8th inning with the Yankees up 3-2, Swisher bunted with a runner on first (and no out of course) and when he reached on an ROE, Melky bunted with runners on first and second.

Many people, including those who are sabermetrically inclined, typically decry the sacrifice bunt – why give away outs? The conventional (and lazy) sabermetric wisdom used to be that sac bunt attempts were almost always incorrect – at least ever since The Hidden Game of Baseball told us so and legions of sabermetric fans and even sabermetricians looked at the RE and WE tables and noticed that the game state after an out and base runner advance was worse than before – hence the sac bunt is wrong.

The problem of course is that that is a ridiculously simplistic way to answer the question on two fronts. One, the WE or RE before and after a “successful” sac bunt, using a standard table, is based on an average batter in an average lineup against an average pitcher and defense in an average stadium on an average Spring day. At least some analysts recognized that in different contexts, those numbers would have to be revised. However, most of them also noted that the gap was so large between the “before” and “after” state (in favor of the “before” state – which assumes hitting away most of the time), that it would take an enormously bad hitter -like a pitcher – to make it correct to bunt. They would basically be right.

Now, there is a more important and pertinent reason why looking at RE and WE charts and comparing the “before” and “after” numbers do not help you in answering the question as to whether a sac bunt (by a non-pitcher) is correct in any given situation. And that is because a sac bunt attempt obviously does not lead to an out and a base runner advance 100% of the time (or even close to 100%); in fact the average result from a sac bunt attempt is not even equivalent to an out and a base runner advance. Also, the average result varies a lot with the speed and bunting skill of the batter and whether and by how much the defense is anticipating the bunt or not (among other things).

Obviously if I told you that batter A was so good at bunting and so fast, even in a sacrifice situation, and that inexplicably, the defense was not expecting a sac bunt, that he got a hit or an ROE 40-50% of the time (about the same percentage a good bunter bunts for a hit), you would realize that a sac bunt was an excellent play. Everyone would be safe 45% of the time and of the other 55% of the time, sometimes the runner would advance on an out, another decent outcome. There would even be some walks as part of that other 55%. You would easily realize that the average RE or WE after a play like that would be a lot higher than the RE or WE after an out and base runner advance and also higher than before the decision was made to bunt or not (essentially the hit-away RE or WE).

Similarly, if I told you that the batter was such a poor bunter and the defense was really expecting the bunt, such that he made an out without a base runner advance 50% of the time, you would instantly recognize that a bunt attempt couldn’t possibly be correct – the average RE or WE after a bunt attempt in a situation like that would be a lot worse than the “out and baserunner advance” that we used to look at in the RE and WE tables.

So now it should be obvious to you that we cannot answer the question of whether to attempt a bunt or not without knowing the average result of a bunt attempt – how often an out will occur with and without a base runner advance, and how often the batter will reach safely via a walk, hit, or ROE. And hopefully you realize that those things depend on the speed and bunting ability of the batter, the speed of the baserunner(s), how easy or hard it is to bunt off that particular pitcher, where the defense is playing (how much they expect a bunt), and their ability to field bunts (and throw to bases).

If you read the bunt chapter in The Book, you will see all those numbers and you will also see that it is often correct to bunt and it is often correct to not bunt – at all stages in the game. But, that is all I am going to say about that.

There is another important aspect of sac bunting which creates the difficulty in answering the question, “Was it correct for the Yankees to attempt those two sacrifice bunts in the 8th inning of game 6?” Remember that I said that the question was not easy to answer. And that aspect has to do with Game Theory.

Because how often a manager is expected to bunt or not bunt in any given situation determines where/how the defense should play in any given potential sacrifice situation, it is correct for the offensive manager to do one of three things:

One, if the defense is playing all the way back, not anticipating a bunt at all, and hitting away still yields a higher WE than attempting a sacrifice, then of course it is correct for the batter to never sacrifice (duh). That would be the case (presumably – although I am not certain) with sluggers like A-Rod and Teixeira at the plate, especially those that are poor bunters or slow runners. It could also be the case with batters who are not that good – say Jose Molina – but are so slow and/or are such poor bunters that the average result from a sac bunt attempt is still worse than the average result from hitting away (WE-wise of course) even with the defense playing all the way back not expecting a bunt at all.

Two, if the defense is playing all the way in, expecting a bunt nearly 100% of the time, and the WE from a bunt attempt, given the speed and bunting ability of the batter, and all the other variables I mentioned above, is higher than the WE from hitting away (even with the extra “holes” created by the infield expecting a bunt), then it is correct for the batter to bunt every time. This is typically the case with pitchers at the plate, at least poor-hitting ones.

Three, and here is where it starts to get dicey (and why the original question has no easy “yes or no” answer), if “none of the above” is true and the defense is (correctly – I’ll get to that in a minute) playing somewhere between all the way in and all the way back (they are not nearly 100% certain whether the offense is going to bunt or not), then the offense has to sometimes bunt and sometimes hit away, in a completely random fashion. Most of the time when there is a legitimate debate over whether a manager should have called for a bunt or not, such as those in the 8th inning of the game in question, the situation falls into this category.

Now, if it is correct to sometimes bunt and sometimes not in a certain instance (and I’ll explain why it is correct in a minute), if you observe one instance of that situation and you see a manager bunt, how can you determine whether he did the right thing or not? You can’t. What about if he doesn’t bunt in your one observation? You still can’t figure out if his decision was correct or not. That is why our initial question has no “yes or no” answer.

There are two ways you can actually answer the question – or at least the question, “Did the manager know what he was doing in this situation or on sacrifice bunts in general?” One, you can ask him what his intention was when he gave the sac bunt signal. If he says something like, “Well, in that situation sometimes I do and sometimes I don’t, and I just happened to (randomly) choose the former this time,” you know that he was right on track. You still don’t know how often he was planning on bunting and whether those percentages are correct or not, but, trust me, if a manager were to say that, he is probably a pretty smart cookie. Two, you can observe the same or at least a similar situation over many, many games and if you see that he sometimes bunts and sometimes doesn’t and you can’t really tell beforehand which way he is going to go (i.e. it appears that his decision is random), then again, he is on the right track and you have a very smart manager, at least with respect to the sac bunt. Using this method (observing many games) is better because now you can get an idea as to how often he bunts or doesn’t bunt in any given situation and compare that to the optimal percentages (if you knew what they were, which is not so easy to figure out).

Anyway, let’s get back to game theory so I can explain why it is indeed correct to randomly mix up your bunts and non-bunts when the situation does not fall into category I or II above, as well as some other interesting things about bunting and game theory.

Let’s talk about the defense, especially since they have to “go first” which is not always the case in contests that involve game theory (imagine rock, papers and scissors – the ultimate game theory illustration where both players have to act at exactly the same time so that neither player can have any more information than the other player unless one player is exhibiting “tells” or cheating). The defense has to set up first and sort of “show their hand” to the offense – which adds an important element to the strategy of the offense.

Of course, the pitcher often steps off the rubber or throws to first base (or holds the ball for a long time) in order to entice the offense to also “show their hand” and give away whether they are bunting or not. The absolute worst thing for the offense to do would be to in fact give away their strategy. A lot of managers will say or think, “Well everyone knows that I am probably bunting anyway, so I might as well give it away.” While it is true that if everyone knows that you are going to bunt anyway, it doesn’t matter if you give your intention away, the mistake is in the fact that everyone knows that you are going to bunt! In fact, that is one of the biggest mistakes that managers make. Not that they bunt in any given situation, like in Monday night’s game – but that in certain situations it is obvious that they are going to bunt nearly 100% of the time. That is almost never correct, for a position player at least. Yet you see that all the time.

Remember I said that the only time that the correct strategy is to bunt all the time is when the bunt yields a higher WE than hitting away even if the defense is expecting a bunt 100% of the time and is playing all the way in. That is not usually (in fact, rarely) the case with a non-pitcher at the plate, even in a tie game in the 9th inning with a weak batter at the plate.

I digressed a little and I hope that I didn’t lose you. This is complicated stuff and there is very little I can do to make it more palatable. Anyway, let’s get back to the defense. Since they have to play their hand openly first, what are they supposed to do? They, like the offense, have three choices.

One, if the WE for the bunt is less than for the hit with the defense playing all the way back, then of course it is correct for them to play all the way back (especially since presumably the offense is not going to ever bunt – if they are acting correctly). Even if the offense does bunt (incorrectly) with this configuration, they are making a mistake, right? You, as the defense, want them to bunt! Again, this would mostly be the case where there is a slugger or bad bunter at the plate.

Two, if the bunt with the defense playing all the way in yields a higher WE than hitting away (with the infield playing all the way up), then of course it is correct for the defense to play all the way in. If they don’t bunt because you are playing back, you gain. You want them to not bunt, even occasionally. Every time they do, they lose and you gain. This situation occurs mostly with weak hitting pitchers at the plate and occasionally with poor hitters who are good bunters and fast. It does not occur (with non-pitchers and even pitchers) as often as most managers think it does. Keep in mind that the “situation” I am talking about has nothing to do with where the defense actually plays or how often the manager bunts, but simply what the WE would be if the defense were playing all the way in and the batter bunted versus if he hit away. If the former is higher than the latter, then we have this “situation” – regardless of what the offense and defense actually do.

Three is again the tricky one. This is where if you play all the way back, the offense’s WE is higher by bunting than hitting away and if you play all the way in, the offense’s WE is higher by hitting away then by bunting. The solution for the defense is obvious. They should play somewhere in between, right? Where? Well, no one knows exactly (although my guess is that after over 100 years of playing baseball, players and managers have figured it out through trial and error), but the goal is to play in such a way that the WE from bunting and hitting away is exactly the same. There is always a spot on the field where the infielders can play such that those two WE’s are exactly equal, as long as we are in a situation that does not fall into category I or II above, which as I said is most of the time when reasonable people disagree about whether a bunt is correct or not.

That defensive alignment is the optimal one for the defense as long as the offense is playing optimally as well (which is not always the case I am afraid). Notice that once the defense sets up in this manner, it doesn’t matter what the offense does. If they bunt they have the same WE as if they don’t bunt. The defense shouldn’t care what they do. So, why does the offense have to bunt or not bunt a certain, fixed percentage of time in any given situation (that doesn’t fall into category I or II) even if the defense is playing optimally, since it won’t change the WE no matter what they do? Good question! It does matter – in the long run. Here’s why:

If the defense starts out playing optimally, such that it doesn’t matter to the WE of the game whether the offense bunts or not, what if the offense makes a mistake and starts to bunt too often? What if they are supposed to bunt 50% of the time (I’ll get to those correct percentages later), but they start bunting 60% of the time or more? Well, now the defense is not playing optimally anymore. They can actually move in a little such that the hit-away is worth slightly more than the bunt, but since the offense is bunting too often, they are losing more WE by bunting then they are gaining by hitting away. That is why it is imperative for the offense to bunt and not bunt according to a certain fixed percentage, such that it doesn’t matter what the defense does. The optimal strategy for the offense (again, assuming that the defense is playing optimally) is to bunt and not bunt in a certain ratio, given the game situation, such that wherever the defense plays, the WE is the same overall. There is nothing that the defense can do to “take advantage” of your bunting strategy (how often you bunt or don’t bunt given that exact game situation). It is the same as the optimal defensive strategy “in reverse.”

How does the offense figure out what those correct percentages are? As with the defense, it is not so easy (in fact, it is harder) and requires some combination of many years of trial and error, intuition, and analytical skills, and even then, it will always be an educated guess. “Rules of thumb” can be helpful. Practically speaking, the way to do it is this: Start with your players who you are pretty sure fall into category I – they should never bunt. Now you go from there. If you have players who are good hitters but not elite hitters and they can bunt a little and run a little, maybe someone like a Swisher, you should bunt them a small percentage of time – maybe 10-20%. Remember those percentages mean that the decision to bunt in any given situation must be random. When I say that Swisher should bunt 10% of the time in a certain situation (and I don’t know off the top of my head if that is true or not), I mean that when that situation arises, the manager flips a 10 sided mental coin (or better yet, a real coin or die in the dugout) and if it comes up one particular side, he bunts (10% of the time). If not (90% of the time), he hits away. And by the way, those percentages change as the count changes because the chances for a hit and a walk change – thus the WE for hitting away changes, regardless of where the defense is playing (and of course the defense should move as the count changes).

If you have a hitter who is an average or mediocre offensive player, but a good bunter and a reasonably fast runner, say a Melky Cabrera, you might bunt 50% of the time.

And so on. That is how you “determine” the percentages. Not very scientific, but there is no other way other than to do experiments in Spring Training or to look at the historical empirical results for hitting away and bunting for various types of batters, pitchers, etc.

One other way you can “guess” what those percentages are is to look at the defense. The problem with this method is that it assumes that the defense is playing optimally and if they aren’t, you lose the opportunity to take advantage of them. For example, if the defense is playing not quite all the way back, you would bunt 10% of the time. If they are playing not quite all the way in as they would for a weak-hitting pitcher, then you would bunt 90% of the time. If they were playing around half way between back and up, you would bunt 50% of the time. Remember that as the offensive team, you must bunt or not bunt according to the optimal ratio otherwise the defense can play up or back and take advantage of your mistake. Let’s talk a little about what to do on offense or defense if you suspect that your opponent is making a mistake (which, needless to say, occurs a lot) and then we’ll talk a little about the Cabrera bunt and wrap everything up.

As I said, and as you know if you watch baseball a lot and understand the game, the defense pretty much has to show their hand before the offense has to make their final decision as to whether and how often to bunt or not. Again, if the defense sets up optimally, there is nothing you can do on offense to take advantage of that and it doesn’t matter whether you bunt or not. On offense, if you think that the defense is playing optimally, you still must bunt or not bunt the correct amount of time or eventually the defense will play differently (a new optimal position given your mistake) to take advantage of your sub-optimal actions. In game theory this is called being “out of equilibrium.” If both the offense and the defense are playing optimally, this is called “Nash equilibrium” or just being in “equilibrium.”

Anyway, since the offense gets to see the defense set up and then they can decide whether to bunt or not, if they think that the defense is playing too far in or too far back (i.e. that a bunt and a non-bunt do not yield the same WE), they must adjust their percentages from what would be optimal if the defense were playing optimally (assuming that the offense were playing optimally). Let’s say that Swisher is up with a runner on first and no outs in the bottom of the 8th inning and the batting team is up by one run (exactly the situation in game 6). And let’s say that Swisher is supposed to bunt 20% of the time. That would imply that the defense should be playing a little in but not too much. The bunt and the non-bunt by Swisher would yield exactly the same WE.

But what if the Yankee skipper noticed that the defense was playing too far in, as if they were expecting the bunt 40% of the time or even 80% of the time (way in)? This is a common occurrence by the way. Now, we know that the WE from hitting away is greater than the WE from bunting, so there is only one thing for the Yankees to do – hit away! No question about it. So does Girardi discard his coin and simply signal Swisher to bunt? No! Why not, since hitting away is clearly the correct thing to do. He can’t do that, or at least he shouldn’t, unless this was the last game he was ever going to manage against this team at least (maybe he should hit away 100% of the time in a really important game). The reason he can’t or shouldn’t switch from bunting 20% of the time to 100% of the time, even though 100% of the time is technically correct for this one instance only, is that if he does that, eventually (and soon) his opponents will notice that when they play too far in, he never bunts. And they will stop playing too far in. In fact, they will probably go back to playing optimally and he will lose the opportunity to ever take advantage of sub-optimal defense again. What he has to do is hit away more often, but not 100%, in order to keep his opponents from fully correcting their mistake. So instead of bunting 20% of the time, he bunts maybe 10% of the time, just enough to keep the defense from moving back to the optimal position. They will probably move back a little, but not enough.

This is the kind of “jockeying” you see in poker games when expert players play against amateurs or lesser players. For example, if your opponent bluffs too much, which many poor players do, while it is correct to call a potential bluff 100% of the time against this type of player, you can’t do that or they will quickly stop bluffing too frequently against you. So you have to call their potential bluffs more than you would against an expert player, but not so much that you cause them to move too far in the optimal direction. It is the same with baseball and sacrifice bunting.

What about the defense? How can they take advantage of sub-optimal offensive strategy, which, again, needless to say, occurs all the time. The answer is the same for the defense as it is for the offense. If you know or suspect that the offense is going to bunt too much or too little, you would play more in or more back than optimal strategy (given that the offense were playing optimally) would suggest. If the offense is playing sub-optimally, you would change your defensive position such that the bunt and non-bunt would not yield the same WE, but the offense is too stupid or ignorant to take advantage of that. You are taking advantage of them bunting too little or too much. Now, as before, as soon as the offense strays from the optimal percentages even a little, while it becomes correct for you to either play all the way in or all the way back, you definitely cannot do that even if it is an important game or the last game of your career. That is because you have to show your hand first.

Let’s say that Swisher is up and he should bunt 20% of the time and you should play a little up, but not too far. In this position, Swisher bunting or not bunting yields the same WE, by definition. What if you know or suspect that Swisher is going to be bunting 25% of the time? It is correct for you to play all the way in, as if he were going to bunt 100% of the time, just as it is correct to call the bad poker player 100% of the time on a potential bluff even if he only bluffs a little too frequently. But, you can’t do that in baseball. If you were to play all the way up, the opposing manager can crush you by hitting away. So, you have to play a little more up but not too much that he changes his mind and bunts less often than you initially thought before you set your defense.

At this point, you might be thinking, “Managers can’t possibly think that deeply,” and you would be right. You might also think, “If all of this is true (and you are probably not so sure), managers must make a lot of mistakes,” and you would be right again. Let’s look at some of the common mistakes that managers make.

Let’s look at the second bunt attempt in that inning to illustrate some common mistakes by managers. After Swisher reached on the error, Melky came up with runners on first and second and no outs with the Yankees still up by one run. Many people did not like the bunt in that situation and I’m sure that plenty of people liked it (although we don’t usually hear from them), including, obviously, the Yankee skipper (and many other managers). That is more than likely a situation that falls into category II – there is a defensive alignment that would make the bunt and non-bunt yield the same WE. Therefore the absolutely correct offensive strategy is to bunt sometimes and not bunt sometimes. I don’t know the exact optimal percentages, but given that Melky is a decent but not good or great hitter, fairly fast, and presumably a good bunter, I would recommend to Girardi that he flip a real coin – bunt 50% of the time. And of course, the correct defensive alignment if that 50% is anywhere near correct, is somewhere around half way in – or wherever Scioscia thinks will yield the same WE for a bunt or a hit-away (not that he can figure that out of course). So what actually happened and who made a mistake? We’ll try and figure that out although we can’t quite be sure one way or the other.

If you remember that AB, you would have noticed that the first and third basemen were charging very aggressively. In fact, I would guess that, other than putting on the “wheel play,” that they were playing as aggressively as you can if you anticipated that the offense would bunt 100% of the time. Now, if this kind of defensive alignment yielded the same WE for a bunt and a non-bunt, which I seriously doubt, then it would be correct for the defense to do this (assuming that Girardi was going to bunt nearly 100% of the time), and it would not matter what Girardi did. If this kind of alignment (all the way in) yielded a higher WE for the bunt than for hitting away (which obviously is even more unlikely in my opinion), then it is still the correct defensive alignment but in that case Girardi must bunt 100% of the time.

But, in my opinion, this is not nearly the optimal defensive alignment if Girardi was going to bunt somewhat optimally (around 50% in my estimation). However, if Girardi made a mistake and was planning on bunting 100% of the time (or close to it) , then of course it is the correct alignment, although, as I said before, if the defense were to continue to do this (play too far in when they “knew” the offense was going to bunt all the time), eventually an astute manager would stop bunting against them, or at least a lot less often. Now, we’ll never know if Girardi would bunt 100% (or close to it) of the time if he had to play that game over again 100 or 1000 times, but if he did, then Scioscia acted correctly for that one time at least (he might lose that edge in the long run in if he continues to take advantage of opponent mistakes too aggressively).

But what about Girardi, assuming that Sciosca was making a mistake (assuming that Girardi was not making a mistake)? He gets to see the defense before he even makes his decision. What an advantage that is. In most contests involving game theory, all sides have to act at the same time or at least without knowing how the other players are going to act. Seeing your opponents’ actions before you have to act is a huge advantage if that opponent is not an expert player (if he is expert, then there is nothing you can do to take advantage of his strategy, as I already explained several times). So Girardi sees that Scioscia is playing aggressively as if he is going to bunt 100% of the time. What is the correct thing for him to do, assuming that the bunt now yields a lower WE than the hit away? Hit away of course! 100% of the time on this one instance, but less than that (but not the original 50% if Scioscia were playing optimally) in practice, because he doesn’t want to force his opponents to play optimally in the future and in the long run. Of course, in such an important game, he may want to hit away 100% of the time and “screw the future game theory implications.”

So who likely made the mistake there? If Scioscia “knew” that Girardi was going to bunt close to 100% of the time in that situation (and we’ll never know whether he did or he didn’t), then he played optimally by having his corner infielders charging aggressively, although he may have given up some future equity in doing so. If Girardi was only going to bunt 70% of the time or 50% of the time, and just happened to choose “bunt” this one time after flipping a mental coin, then Scioscia actually made a mistake even though Girardi did indeed bunt.

Girardi, on the other hand, likely made a horrible mistake by choosing to bunt when he could clearly see the defensive alignment. I say “likely” because it may be that he decided to bunt only 10% of the time (and correctly so) when he saw the defensive alignment, and we just happened to have witnessed that 10%. I highly doubt that was the case.

One more thing. Girardi compounded his error when the count went to 1-0 and then 2-0. Obviously at a 2-0 count, while the bunt WE remains relatively stable (it goes up a little because there still could be an eventual walk and the pitcher now throws a more “buntable” pitch) , the WE from hitting away (including a possible walk) is obviously much higher now. At the 2-0 count, two things should happen: One, Scioscia should clearly have his infielders playing less aggressively – while he may have been pretty sure that Girardi was bunting at the beginning of the AB (and he was probably right), I think that everyone had some inkling that he might switch to hitting away with the 2-0 count. Two, Girardi should be much less likely to bunt – in fact, even if the infield were all the way back, it might even be correct to hit away 100% of the time – category I above, where even with the infield back, the WE from hitting away is greater than the WE from bunting. At the very least, given where Scioiscia started out positioning his infield (and I didn’t see if he changed when the count went to 2-0), Girardi certainly should have switched to hitting away. I don’t think it was even close.

In general, given all the information above, the mistakes that managers make are mostly on the offensive side, as we saw in this game. On defense, I think that managers mostly do the correct thing given the likely (often mistaken) strategy of the offense. Of course if the batting team managers started to play more optimally, the defense would really be on the hot seat since they have to play their hand first. Not that that is a problem for the astute manager. He simply has to set up his defense such that the WE from the bunt and non-bunt yield the same thing and he can sit back and relax in the dugout, knowing that there is nothing the offense can do to take advantage of his strategy. If they want to bunt, fine. If not, fine too.

But most offensive managers are not very astute when it comes to bunting strategy and the defense “knows” that (they are not really aware of it, because obviously they don’t know the correct offensive strategy either), or at least they know how to respond correctly to a predictable offensive strategy and even a non-predictable one (like a LaRussa or even a Scioscia, who can be unpredictable when it comes to bunting or not). If they suspect a bunt, they play up and if they suspect a hit away, they play back, and if they are not sure, they play somewhere in between, exactly what they should be doing. On offense though, managers are way too predictable. Their mistake generally is not that they bunt too much or too little (although many managers do). It is that they don’t understand the concept that they should be mixing up their bunts and non-bunts on a random basis. This is a difficult concept for anyone to understand, much less a baseball manager. So, instead, they generally have it in their head that a bunt or non-bunt is 100% warranted in any given situation, and in most cases, the opposing manager on defense knows the same thing. As well, just like in the Cabrera example in the ALCS, managers do not adjust for the defense properly. They have it in their head that they are going to bunt whether the defense is playing all the up or not. And, as I said, in most cases, this is wrong. If the defense is going to play all the way up, anticipating the bunt nearly 100% of the time, the offense must make them pay for that by not bunting a high percentage of the time at least until the defense starts to move back – and then the “jockeying” can continue. And finally, some managers do not adjust their strategies as the count changes. Clearly if the count is in the batter’s favor, he should be less likely to bunt and the defense should move back, and if the count is in the pitcher’s favor, but not with 2 strikes, the batter should be more likely to bunt and the defense should move up. Some managers do that well and others do not. Girardi did not do that well the other night. Then again, there have been a lot of things that Girardi has not been doing right in the post-season, but that’s another story altogether and one that has been covered nicely by other writers and analysts. Happy bunting!



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Steve
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Steve
6 years 6 months ago

should the decision tree factor in win expectancies given that Mariano is pitching the 9th?

in other words, is giving up an out to maximize your chances of scoring exactly one more run (while you may be decreasing the expected number of runs overall) a good play with Mo on the mound?

does the win expectancy with Mo pitching and a 1 run lead increase to nearly 100% with a 2 run lead, close enough that the extra win expectancy of a 3 run or greater lead isn’t worth the chance that Melky hits into a DP and scores no runs?

i am only talking about Melky’s bunt, since the desired outcome was 2nd/3rd and 1 out. you were paying for the advancement of those runners with an out. does the change in win expectancy with Mo on the mound make that a smart “purchase”?

just something else to think about. good article, even if some of it went over my head.

Jeremiah
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Jeremiah
6 years 6 months ago

I have often thought that the RE tables I have seen do not have enough information for evaluating a bunt. It seems to me that you need something more like a histogram for each game state than a simple average run expectancy. It is true that the number of runs you would expect to score in a runner on second, 1 out situation is fewer than runner on first, no outs, but the chance that you score at least one run is probably greater (I don’t know for sure). In late innings where there are fewer opportunities remaining for large changes in the score, it makes sense to me that playing for one run would be optimal, especially in this situation with Rivera on the mound. In other words, taking the smaller chance that you will score a whole bunch of runs is not as good as going for a single run, because those extra runs probably won’t change the outcome of the game very much.

Steve
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Steve
6 years 6 months ago

yes, i couldn’t agree more with this statement.

Hizouse
Guest
Hizouse
6 years 6 months ago

…and that’s why MGL consistently uses WE throughout his post.

Steve
Guest
Steve
6 years 6 months ago

yes, but i didn’t think Jeremiah was talking about MGL’s post, simply musing on a similar topic.

i agreed, b/c i have often seen people use RE’s in discussing this very topic.

Rob in CT
Guest
Rob in CT
6 years 6 months ago

I’m sure Swisher’s struggles (single earlier in the game notwithstanding) played into Joe’s decision to have him bunt. Bunting with Melky is, generally, more defensible. But then there was the 2-0 count…

Also consider the hitters coming up after Melky: Jeter and Damon. Jeter is a high-BA guy and Damon is solid in that category as well. Simply getting 1 more run was probably HUGE in Girardi’s mind. I know it was in mine. They had Mariano on the mound, and he’d already dealt with the heart of the Angels order. A 1-run lead was pretty darn safe. A 2 run lead was nearly ironclad. A 3-run lead was Mt. Everest.

So, while I think Girardi is bunt happy and I’d prefer he does it less, I get it in that situation.

Mike K
Guest
Mike K
6 years 6 months ago

Yankees were below league average in sacrifices each of the last two years, despite being 3rd (2008) and 1st in OBP. And *most* of the bunts come from the guys you’d want bunting (Gardner, Molina, Cervelli, etc) and very few come from guys you wouldn’t want bunting. If Girardi is “bunt happy” it certainly isn’t compared to (most) other AL managers.

tyrone
Guest
tyrone
6 years 6 months ago

Girardi can call for fewer sacs than the league average and still be bunt-happy because he could be sacrificing much more than what his lineup calls for. As you noted, the Yankees are consistently near the top in OBP and always field a strong lineup. Given that, they should consistently be at or near the bottom in sacrificing, not merely below average.

Steve
Guest
Steve
6 years 6 months ago

unless, of course, you read the gigantic article right above this which lays out exactly why it’s ok to bunt sometimes.

and if that’s the case, why are you saying they “should” be last? that only works if bunting = bad, which maybe it isn’t.

maybe Girardi is neither bunt “happy” or bunt “sad”. he’s just bunt “blase”.

then again, that would mean we’d have nothing to feel smart about.

tyrone
Guest
tyrone
6 years 6 months ago

Huh? Where did I say that it wasn’t ok for the Yankees to bunt sometimes? Of course there are times when they should, and times when they shouldn’t. I based my comment on the idea that a team that is consistently at or near the league lead in OBP and has plenty of good hitters (i.e., lots of “Category I” guys as mentioned in the post–guys who should bunt rarely if ever), there are probably far fewer times when they should bunt compared to an average lineup. Thus, with optimal management, it’s likely that such a team would bunt far less often than an average team, and thus wind up near the bottom of the league in sacrifice rates. That’s all.

Wally
Guest
Wally
6 years 6 months ago

Steve, I think you failed to understand the part about how good your hitters are effect how often you should bunt. Given that the Yankees have had very few even average hitters, much less poor hitters, over the last two years, it seems very likely bunting at roughly the league average would be wrong. Unless, of course, the league generally bunts to little. Though I doubt that’s the case.

Over all, like the article outlines, it can be very difficult to understand when a bunt is correct. With Swisher and his .375 OBP, I have a hard time believing he should ever bunt. Obviously we’d have to do a little math to really figure that out, though the game situation did make it at least a defensible move.

Steve
Guest
Steve
6 years 6 months ago

i don’t really fail to understand how good the Yankee hitters are, but i did read where Mike K pointed out that most of the bunts the Yankees lay down are coming from guys like Melky, Gardner, and Cervelli.

did i check this claim? no. but if it is true, then i think it backs what i said about Girardi. this is especially true with Gardner, who is often bunting for a base hit.

Tyrone, i misinterpreted your comment that they “should be last in bunts” as saying they should almost never bunt. i read your comment as stronger than it was intended, sorry about that.

Rob in CT
Guest
Rob in CT
6 years 6 months ago

Girardi was not bunt happy in the regular season, I agree. I was happy about that.

I think he has gone a little bunt happy in the playoffs. It’s a close thing: I’m not ripping him, really. I just think he’s taken it a step too far.

RollingWave
Guest
RollingWave
6 years 6 months ago

Ehh, Melky Cabrera’s not exactly a low average hitter himself. and honestly from watching him play I have a hard time classifying him as either a good bunter or speedy (he seems like the perfect example of a average / mediocre player at this stage in almost every respect, he makes a lot of contact but isn’t a line drive monster, he is doesn’t walk much but isn’t a complete hacker either. he plays a average defensively position about average. and he can steal about a dozen bases a year at a rate that would neither kill you nor really help you a whole lot. and he hits a dozen HR a year so he’s neither punchless but nor is he a particular power threat)

I can’t really fault Giradi for playing for one run with Mariano on the mound in a clincher with the bottom of the order. Cabrera hit well in the ALCS but he’s true talent level is average at best. while Swisher is a above average hitter but have been scuffling . and besides, the Angel D had been questionable all series and Kazmir never had good reputation as a fielder. it’s at least not a completely indefensible gamble.

Mike K
Guest
Mike K
6 years 6 months ago

You’re mixing up Swisher’s and Melky’s at-bats. Swisher got to 2-0 and then 2-1 and still bunted. Melky however bunted the first pitch foul and then laid down the second pitch.

Steve
Guest
Steve
6 years 6 months ago

what about Swisher’s career line of .185/.241/.296 against Kazmir?

i suspect that MGL will tell me that the sample size of any batter/pitcher split is too small to be relevant. but what if it’s just one more piece of data in a complicated decision? it might tilt the scale one way or another.

i’m not claiming to know the answer, but i imagine, as MGL laid out, the decision is rarely as simple as “NEVER (or always) bunt” as either side of the debate would have you think.

Kevin S.
Member
Kevin S.
6 years 6 months ago

You’re intuition about the SSS was correct. 29 PA is too small to tilt the scales in any direction. It just doesn’t tell us anything.

B
Guest
B
6 years 6 months ago

“You’re intuition about the SSS was correct. 29 PA is too small to tilt the scales in any direction. It just doesn’t tell us anything.”

That’s simply incorrect. Steve is actually right – it is another piece of information with some value that can tell us something. Can we make any conclusions with any degree of confidence based on 29 PA’s? Of course not, anything can happen in a small sample. However, even a sample size of 1 tells us something – it does, in fact, increase the probability Swisher performs less well against Kazmir than normal…it just shifts it a very, very, very small amount. Not enough to reach any conclusions from, but if you wanted to use it as a tiebreaker, that would be a reasonable and defensible position.

Wally
Guest
Wally
6 years 6 months ago

B,

“it just shifts it a very, very, very small amount. Not enough to reach any conclusions from, but if you wanted to use it as a tiebreaker, that would be a reasonable and defensible position.”

If it is such a tiny factor, how did it take Girardi from bunt some portion of the time, to bunt always and even in a 2-0 count? Like its been outline above, we’re not talking about bunting always or bunting never. There are in-betweens. So this “tiebreaker” probably took you from bunting 10% of the time to bunting 10.001% of the time…… Kevin is right. Its far to small of a sample to tell us anything meaningful and you’re just trying to be a smart ass.

B
Guest
B
6 years 6 months ago

Being a smartass? Not the intention. I’m just looking at the topic beyond the Girardi’s decision – “do small sample splits against a pitcher tell us anything”, which is the topic Steve brought up. Yes, they do tell us something, it’s certainly more than nothing, but obviously it’s a very small amount.

“but what if it’s just one more piece of data in a complicated decision? it might tilt the scale one way or another. ”

From Steve’s original post, so that was the angle I was going for. It’s one more piece of information, albeit a very, very small piece of information, and in general if you use it to tip the scale one way or another (like in some hypothetical tiebreaker situation), there’s certainly some reason behind that.

For this specific situation (bunting with Swisher), yeah, you’re right, it’s probably meaningless in the grand scheme of what Girardi should have done. Oh well, that’s not really what I was addressing. It’s also a topic I bring up because while more people are beginning to understand the limits of small sample size, it seems to me with some people it’s gotten to the point where they realize small sample sizes are bad, so they dismiss them, but without realizing even small sample sizes do tell us something (we just dismiss them because that something is small and not enough to draw any conclusions from).

BIP
Guest
BIP
6 years 6 months ago

No, pitcher vs. batter stats really do tell us nothing because there’s another huge flaw at work here beyond the small sample size problem: selection bias.

Think about how many different batters Kazmir has faced in his career. Let’s say it’s 500. Odds are pretty good that some batters will OPS 1.000+ against him, aren’t they? And similary, some will post sub .600 OPS’s. Picking out individual batters who have done particularly well or poorly is, essentially, capitalizing on chance. One way of looking at it is that not only is there small sample size with respect to the number of plate appearances, but you’re also looking at a sample of just one batter! It’d be like if you rolled 10 dice a few times each, and then picked up the one that came up 6, 6, 5 and said, “This die is really good at rolling high!” No, you just rolled enough dice that that kind of result is unremarkable.

B
Guest
B
6 years 6 months ago

Well BIP, your example only works because you’re dealing with dice, which we know to be unbiased. With hitter-pitcher matchups, they are not all created equally. Some guys will hit certain pitchers better than others for reasons beyond just L/R matchups. The fact that a certain hitter hit a pitcher well in a small sample does raise the probability that he hits better against that pitcher than you’d expect. Should we use that information to make decisions? Of course not, we aren’t even close to being reasonably sure it’s anything more than random chance, but that doesn’t change the fact that it’s slightly more likely to not be random chance than with a sample size of 0.

And it’s not like we went through the population of hitters that have faced Kazmir and picked out one with bad numbers. We were given the situation – there’s no selection involved here. Well, if you want to argue Scoscia used Swisher’s career numbers against Kazmir as the reasoning behind creating that matchup, fine, whatever, maybe there is some bias there – but it doesn’t change the fact that small sample sizes do give us information…

Wally
Guest
Wally
6 years 6 months ago

“Well, if you want to argue Scoscia used Swisher’s career numbers against Kazmir as the reasoning behind creating that matchup, fine, whatever, maybe there is some bias there – but it doesn’t change the fact that small sample sizes do give us information…”

“Should we use that information to make decisions? Of course not”

So what’s your point here? To point out small sample sizes mean *something* just nothing we should use? So they don’t tell us anything meaningful. Like I said, you’re just trying to be a smart ass.

B
Guest
B
6 years 6 months ago

Not sure what the hostility is about. It was to point out that small samples do give us information, which is pretty contradictory to “It just doesn’t tell us anything”. As I pointed out, it’s also in response to the original point.

“Not enough to reach any conclusions from, but if you wanted to use it as a tiebreaker, that would be a reasonable and defensible position.”

That’s the point I made in my first post on the topic, which was in direct response to:

“i suspect that MGL will tell me that the sample size of any batter/pitcher split is too small to be relevant. but what if it’s just one more piece of data in a complicated decision? it might tilt the scale one way or another.”

It is one more piece of data in a complicated decision. A very small piece, yes, but another piece nonetheless. Like I said, if you want to use it as a tiebreaker (addressing “tilting the scale on way or another”), there’s a rationale for doing so.

Gilbert
Guest
Gilbert
6 years 6 months ago

This is probably more true in the reg season than postseason, that you want to build doubt of your future intentions like the poker players. But if there is only a short time left to play you would call the bluff all the time if you think that is what they are doing.
The football analogy everyone would understand is when the defense doesn’t try to hide their prevent defense up by 11 with 2 minutes to go, saying go ahead and run for a first down, like go ahead and bunt. The chances of a 60 yard TD run are similar to that of the catcher overthrowing the 1B and the runner scoring from 1st.

chuckb
Guest
chuckb
6 years 6 months ago

Really interesting post. It shows that the bunting strategy isn’t as clear cut as we like to believe. One of the things related to this that I’ve been wondering about of late is why managers (or players, for that matter) never choose to bunt w/ the bases loaded. The answer is seemingly obvious — the force at home — but aren’t there situations where this is a good strategy?

For example, Johnny Damon came to the plate against a lefty and the bases loaded and 1 out. He’s at a platoon disadvantage, is likely at least a decent bunter, and has good speed. Also, since players never bunt w/ the bases loaded, it’s likely that the first baseman was playing back for the double play. He’s not even holding the runner on first. It’s a situation where the Yankees want to get 1 run and would be happy w/ a sacrifice fly, or any out that scores a run. So why not bunt the ball past the pitcher so that the first baseman or 2nd baseman is forced to field the ball? The worst case scenario is likely an out at first w/ the run scoring b/c the defense is caught off guard. All he really has to do is make sure the pitcher doesn’t field the ball (or the catcher, of course) but if he bunts toward 1st, he’s got a pretty good chance of turning it into a hit.

As it turned out, he hit a 2 run single to left-center but the situation is still ripe for a bunt — platoon disadvantage, infield back for the DP, above average bunter and runner at the plate.

Andrew
Guest
6 years 6 months ago

How is this different fro a suicide squeeze? Or just bunting when a runner is on 3rd? It usually doesn’t work and it’s easier to get the runner in with a fly ball than by keeping it in the infield.

The Angels tried it in the 2008 ALDS and it backfired badly (though I don’t think the bases were loaded then).

Wally
Guest
Wally
6 years 6 months ago

Ramon Hernandez in the ALDS (I think) a few years back a great bunt with a runner on third and the infield playing back. The run scored, and if I remember correct he was even safe at first.

chuckb
Guest
chuckb
6 years 6 months ago

It’s different b/c it’s so unexpected. No one ever does it. The safety squeeze is used from time to time though, admittedly, not nearly as often in the AL. And Damon likely has a better likelihood of reaching via a bunt hit than a fly ball to the OF. When the infield’s playing back, it seems to me that in the right circumstances this has a better likelihood of getting 1 run in than swinging away does.

Paul Thomas
Guest
Paul Thomas
6 years 6 months ago

Hernandez’s bunt was actually with two outs and the bases loaded. It came as a complete shock to everyone (except him and maybe Ken Macha), especially given that he is in no sense a speed demon.

Wasn’t a squeeze play, though. Squeezes are rare with the bases loaded precisely because it’s so much easier to get the runner out at home on a force play. You’ve probably got an extra half-second to field the ball and still get the runner out when the bases are loaded, which is enough to change it from “extremely difficult” (very few squeeze plays end on a tag play at the plate, though many fail for other reasons like the batter missing the bunt and the runner getting caught in a rundown) to “manageable.”

Hardy
Guest
Hardy
6 years 6 months ago

Much of the post is incorrect. This seems to come mainly from a lack of one certain insight:

If a bunt and a non-bunt yield the same WE there is no single optimal bunting frequency. 0% is as good as 12.79% is as good as 50% is as good as 100%.

It is true that it might be correct to hit (bunt) sometimes if the defense plays too far in (or out) to create a similar / identical situation in the future. However, this is not a given – always hitting (bunting) might still be correct. You would have to specify (at least) how the learning works, the expectation of future similar situations and a weighting of today’s game relative to (potential) future games.

Hardy
Guest
Hardy
6 years 6 months ago

After another read, this seems to be the lack of application of this insight, because this idea is stated clearly towards the end of the post.

Sej
Guest
Sej
6 years 6 months ago

MGL is dealing with situations where the defense is not positioned optimally. I don’t think he intended for this to be read with the hypothetical perfect defense in mind. And as you say, he does mention towards the end that if the defense is positioned optimally, it doesn’t matter whether the offense buts or hits away. If I recall correctly, he deals with the various defensive positionings more deeply in other (equally long) posts about bunting.

David Brown
Guest
David Brown
6 years 6 months ago

You assume that the optimal defensive alignment is where WE_bunt = WE_hit. This assumes that there is a linear trade off between those values about that point. The optimal defensive position is the one such that

P_bunt * WE_bunt + P_hit*WE_hit is minimized.

There may be positionings where a small increase in WE_bunt cause a large decrease in WE_hit and vise versa. It gets more complicated than that because an intelligent offense would correspondingly adjust their bunt probability.

Hardy
Guest
Hardy
6 years 6 months ago

If both sides play optimally WE_bunt = WE_hit actually minimizes P_bunt * WE_bunt + P_hit*WE_hit, because the offense can react on the defensive alignment that gives you WE_bunt and WE_hit.

This leads to:

P_bunt = 1 if WE_bunt > WE_hit and
P_bunt = 0 else

Carl Robinette
Guest
Carl Robinette
6 years 6 months ago

How did you write such a long article without the phrase “I Cut you choose”. Imagine dividing a pile of sand between two people without a scale. One cuts the pile, while the other picks it. Thus its in the dividers best interest to be skilled at cutting evenly.

http://en.wikipedia.org/wiki/Divide_and_choose

Thats the game theory way of saying, if the defense plays optimally, bunting and swinging away have the same WE.

Another great Game theory principle could apply here, one taken from the world of espionage.

Q: How do you win a game of chicken with God? (cars driving into each other until one side swerves out of the way).

A: You must make God believe that you won’t swerve under any circumstances.

Lets say that Melky bunted 100% of the time in that situation throughout his career under Girardi, and there was no indication it would change. Soscia would then be correct to put on the Wheel play. Knowing this, swinging away would be correct.

Misinformation can be a powerful tool, especially this late in the season. Which makes optimal defense, and randomly generated Bunt/Hit decisions all the more important.

Thor
Guest
Thor
6 years 6 months ago

I think the “I cut you choose” game actually fits the situation better than the simultaneous-move game that MGL discusses, doesn’t it? Aren’t the defenders essentially committing to positioning before the manager chooses to bunt or not?
That is, it’s not really like the poker bluffing example.
I guess that there would still be scope for learning, but it seems like a sequential game would be easier to figure out for everyone involved.

Wally
Guest
Wally
6 years 6 months ago

Actually, its a lot like the poker and bluffing example, or just betting in general. In poker the bet is always placed before it is called, raised or folded to. And you still have varying degrees to which you can act. All-in bets might be seen as playing up, smaller bets as playing somewhere in the middle and a “check” as playing all the way back. Or something like that. Then you have the opposing players response to those bets (or non-bets) that have varying degrees. Obviously, its not exactly the same, but it isn’t a simultaneous-move game either.

B
Guest
B
6 years 6 months ago

So more important that the theoretical game theory behind the optimal move is – what is the realistic optimal way of managing? No manager is going to go through that whole thought process for every decision – you might get a smart one to incorporate some of those aspects, for sure, but between not being able to incorporate all of them and not having perfect information (I see lots of places where these decisions would be based on small sample sizes where you just don’t really know much about all the variables, along with the fact that the manager can’t know all the different variables off the top of their head), what’s the most we can expect from a manager? What are the best pieces of information a manager should remember for an optimal strategy, especially keeping in mind the other team has the same issues.

It seems to me this discussion of optimal strategy is kind of pointless and we should be focused more on what the best realistic strategy is. I’m thinking RE and WE tables for a number of different categories of hitters is probably the best and most realistic thing, while making sure the manager understands they have to vary their strategy at times just to keep the defense off balance (I don’t think it’s necessary to give them exact percentages or percentage ranges, they’ll understand this concept like they understand varying pitches even if they don’t know the optimal pitch %’s).

I also think some of the deep thinking into game theory may only give you small gains in marginal benefit, making it too cumbersome/time consuming/TMI in general to be worthwhile.

Twac00
Guest
Twac00
6 years 6 months ago

I don’t agree with bunting when there is one out unless a pitcher or someone like Bill Mazeroski is up at the plate. When there are no outs I like a bunt when there is a guy on second. I didn’t agree with Girardi’s decision to have Swisher bunt because, although, there were no outs there was also no one on second. The other reasons I didn’t like the decision is because Swisher gets on base at a very good rate, is never going to beat out a bunt unless there’s an error, and is most likely not a good bunter. I’m not sure if he’s good at bunting, but given that he’s a high OBP guy and has played in the AL all his career I’d assume he’s not. It was also a 2-0 count so the chances of getting on base have increased. I absolutely loved the decision to bunt Melky since he’s not a great OBP guy, can occasionally beat out a bunt, there were no outs with a guy on first and second, and he’s a good bunter.

waynetolleson
Guest
waynetolleson
6 years 6 months ago

You’re over-analyzing. Swisher’s not hitting well. Cabrera is not a great hitter. You’re turning the batting order over to Derek Jeter and Johnny Damon, two dangerous hitters. You’ve got Mariano Rivera in the game already, and he’s facing the lower part of the Angels’ lineup.

Just as importantly, you have a pitcher on the mound in Scott Kazmir, who was making his second-ever relief appearance. It was also his first appearance in relief since the fourth appearance of his career, also against the Yankees – on Sept. 9, 2004. Having such a player in the middle of the diamond, pitching in an unfamiliar situation in a hostile environment, represented an area of weakness, and the Yankees exploited that weakness. The Angels didn’t have the personnel to catch the lead runner, and couldn’t execute well enough to record even an out.

What I find amusing is Joe Girardi’s decisions resulted in two runs, giving his closer a virtually insurmountable three-run lead, and the Yankees won the game, clinching the AL pennant. And you’re sitting here in judgment of how Girardi isn’t really astute, and doesn’t understand game theory.

lincolndude
Guest
lincolndude
6 years 6 months ago

Ever watch the world series of poker and see someone get suckered into a hopeless all-in, only to steal the win on incredible luck on the last card draw?

I don’t think anyone sees that and says, “Yeah, he knew what he was doing. Don’t hate.”

waynetolleson
Guest
waynetolleson
6 years 6 months ago

It wasn’t incredible luck that the Yankees won that game. With Mariano Rivera in the game, playing for one run in the bottom of the eighth inning was a sound strategy. Additionally, while he posits himself as a foremost authority on game theory, with all major league managers being a bunch of neanderthals, the author fails to account for the actual game situation. Scott Kazmir is not a good-fielding pitcher to begin with, and he was pitching in an unfamiliar situation. That might not show-up in things like “Win Expectancy,” but exploiting the opposing team’s defensive weakness is actually a significant part of baseball strategy.

Girardi didn’t just roll the dice and happen to roll a seven. Girardi played the high percentage move at that point in the game. Some modern analysts here just like to think they’ve re-invented the wheel.

And who actually watches the world series of poker? I sure don’t.

lincolndude
Guest
lincolndude
6 years 6 months ago

No it wasn’t luck that they won the game, it was luck that two Angels errors made Girardi’s consecutive incorrect decisions result in two runs. Just like luck can make an incorrect decision in poker result in winning the hand.

I would guess that just as likely as an error, if not more, is a failed bunt attempt by Swish and no runs in the inning. It’s ridiculous to look at this with hindsight and say that counting on an error by a bad fielding pitcher was a “high percentage move.”

Wally
Guest
Wally
6 years 6 months ago

First, just because you don’t watch something doesn’t mean his analogy isn’t correct.

Second, poor fielding pitcher or not, I don’t any one was going to be Kazmir would air mail the baseball from 20 feet away when he damned near could have walked it over to 1st base to get an out. So, no. These plays weren’t “high percentage moves” that worked out. These were two relatively rare errors.

waynetolleson
Guest
waynetolleson
6 years 6 months ago

I simply don’t buy that because some table says the manager should do this that, that means Joe Girardi didn’t know what he was doing, or made a mistake. To do so, I believe, places too much blind faith in these Win Expectancy tables. At that point in the game, you just want one run. With Rivera in the game, you probably don’t even need that run, but if you get the run, it’s almost as good as “Game Over.”

The last thing you want to do is have your rally killed by a double play. Moving the runner up to second on the first bunt attempt achieves that objective. After Kendrick drops the ball, you really don’t want Melky to hit into a DP. You want Jeter up there with a chance to drive-in a run with an out, or two runs with a hit. You have a good bunter in Melky at the plate, and a poor-fielding pitcher making the second relief appearance of his career, and his first in over five years.

Girardi stressed the Angels’ defense, and they cracked. But if Kazmir doesn’t throw the ball away, you’ve got second and third and one out, and Jeter, Damon, and Teixeira coming to the plate.

Sometimes, when you over-analyze, you miss the forest for the trees. Girardi did make some questionable moves in the series, like his handling of the bullpen, for example. But he made the right move in bunting in the bottom of the eighth inning in game six.

Steve
Guest
Steve
6 years 6 months ago

” it was luck that two Angels errors made Girardi’s consecutive incorrect decisions result in two runs.”

wait, who said he made two consecutive incorrect decisions? where has that been proven?

i think, if nothing else, the second bunt was perfectly defensible.

Patrick
Guest
Patrick
6 years 6 months ago

Too long, did not read… I kid, I kid.

Michael, that’s a hell of a post. It’s very similar to some things I’ve read over on your book blog, about the Game Theory of bunting. (I’ll be honest, I don’t remember if it was you or Tango.)

Still, really good, well reasoned stuff.

MGL
Guest
MGL
6 years 6 months ago

In The Book, I give some practical strategies for managers. Obviously they cannot manage based on the nuances of game and probability theory. The strategies I recommend are really quite simple. They are mostly for the offense. As I said in the article, the defense can pretty much continue to do what they already do, which is to play in if they expect a bunt with a high degree of certainty, back if they expect a non-bunt with a high degree of certainty and somewhere in between if they are not sure. Now, if managers started playing more optimally on offense, which would entail being a lot more unpredictable than they presently are, then the defense would have to start playing such that WE,bunt = WE,hit away.

On offense, as I said, even without understanding and using the nuances of everything I discussed in the article, the strategy simply entails taking your obvious bunters in obvious situations (e.g. weak hitter, good and fast bunter, late in a close game) and bunting 75-80% of the time (but NOT 100%!), then taking your not-so-obvious bunters and bunting them 50% of the time, and then taking your “probably shouldn’t bunt, but are decent bunters with decent speed players” (even though they might be very good hitters), and bunt then 20% of the time.

Not only does the batter determine the percentages, but so does the pitcher and game situation of course. So, for example, early in a game, your obvious bunters might bunt 50% of the time rather than 80% of the time as they would late in a close game. Or against a very good pitcher (who is not particularly difficult to bunt against) late in a game, your 50% bunter might bunt 80% of the time. Etc.

The key is to always have a percentage when it is obvious that a 100% bunt or 100% hit away is not correct (and it is almost never correct for a 100% bunt to be in order), and to use those percentages in a random fashion.

The other thing that managers do incorrectly all the time is not use the information from the defense when the defense makes a mistake. If they think that you are going to bunt nearly 100% of the time and therefore they play all the way in, then it is rarely correct for you to bunt more than 50% of the time (or at least something less than 90% of the time, which is essentially what the defense expects), and in an important game or in the post-season, it might be correct for you to bunt nearly 100% of the time, even though you are giving up future WE equity. And of course managers do not adjust their bunting (and bunt defense) strategy for the count very well, as we saw with the Swisher bunt in game 6 (I did mix up the Melky and Swisher bunts with the 2-0 count).

What I am trying to say is that it would not be that hard for managers to come up with a useful, simple strategy for bunts/non-bunts that would incorporate the tenets of game theory and that would yield a much higher WE for the season than what they presently do. All it would require were some basic rules of thumb as I describe above. They wouldn’t need a computer or game theory expert at their side.

B
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B
6 years 6 months ago

I should try reading The Book sometime…

lincolndude
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lincolndude
6 years 6 months ago

Perhaps this is covered in The Book, but how many additional runs could one expect to earn over the course of a season by improving bunting strategy? What scale are we talking here?

Carl Robinette
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Carl Robinette
6 years 6 months ago

The most practical solution would seem to be to let the batter decide. He’s able to make the quickest decisions about the defense, if he sees the 3rd baseman creeping he can hack away. If their backpedaling he can drop it down, yada yada. Also, often the players really don’t want to bunt and show it, or just feel like bunting when they shouldn’t (Jeter). Id much rather they just put put their heart in it. People would say that these guys are just ballplayers and shouldn’t be bothered randomizing their 20/80 bunt %, but I disagree. If they get the percentages slightly wrong, its probably better than having 100% on anything. Just don’t give my Email to the 1st/3rd base coaches union.

The Typical Idiot Fan
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The Typical Idiot Fan
6 years 6 months ago

MGL,

Two things:

1). I think you just killed DMZ’s new iPhone App. =)

2). Your claim that when you make a post, it stymies further discussion is apparently wrong.

Awesome to see posts from the most prominent minds in modern baseball analysis. Keep them coming!

MGL
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MGL
6 years 6 months ago

Yes, letting the batter decide is the only real way to do it, or to give him an initial sign and he knows he can change it if the defense should change. Or the sign can be “bunt if the defense is back and hit away if it is in.” Of course, you won’t get away with that for very long. And the randomness can be throughout the PA also. On the first pitch he may bunt and on the second he may not bunt.

“Perhaps this is covered in The Book, but how many additional runs could one expect to earn over the course of a season by improving bunting strategy? What scale are we talking here?”

Good question, and I honestly have no idea. 5 runs? 2 runs? 1 run? 10 runs? Whatever it is, there are literally hundreds of decisions that a manager makes per season and if 50 of them are wrong and each one costs .3 runs, that is 1.5 wins per season which is not wood! So while any one decision is usually not worth worrying about, in sum, they all are.

Preston
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Preston
6 years 6 months ago

Going along with what Carl says, I’m not so sure that the offensive manager has quite the advantage that you suggest – it is certainly true that the defense has to show their alignment before the pitch, but they do not need to show their alignment before the sign is relayed, and just like the offense they could potentially change that alignment from pitch to pitch if they believed they were facing an enlightened manager. In this case it is best left up to the batter, but this also provides problems, as it is advantageous to the baserunner to know exactly what the batter is going to do so that he can get the best jump (this is especially true with a runner on 2nd, as it is far more common for the defense to make a play on the lead runner at 3rd than at 2nd on a sac). In the end, you are relying on the batter and runner to get a similar read – certainly possible, but another potential complication to the system.

Very interesting article, though, and the general principle certainly still stands – I’ll be applying it with the softball team I coach.

Paul Thomas
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Paul Thomas
6 years 6 months ago

Another suboptimal bit of managerial strategy I’ve noticed– they don’t change up their strategy from pitch to pitch enough. I’ve seen it happen a few times but not nearly as often as it ought to.

It’s not enough to just “flip the coin” once at the start of the at-bat and then stick to the strategy throughout the at-bat, come hell or high water. Offensive managers should be randomizing their decisions before every pitch (modified for the new count, of course).

It also might be correct to throw in some true bluffs (where you tell the hitter to show bunt but to actually TAKE THE PITCH NO MATTER WHAT) to confuse the other manager, but here I’m not 100% sure because taking a pitch involves a risk of letting a hittable strike go by. That might decrease WE enough that it makes true bluffs not worth it.

chuckb
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chuckb
6 years 6 months ago

The idea w/ regard to game theory seems to be based on the game’s leverage index. In other words, wouldn’t an astute manager, assuming he’s ahead of the curve, utilize the “incorrect” strategy during less important games (the bluff) and utilize the “correct” strategy during more important games, i.e. game 6 of the LCS? You want the opposition to believe that you might make the “wrong” play by doing it at times, but it makes sense to only do it in games that are less important. Hopefully, the other team only picks up on the fact that you’re unpredictable.

Will
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Will
6 years 6 months ago

With all due respect, stating that a decision is best made with a coin flip is pretty weak. While Win Expectancy does provide a good framework for making these decisions, the variables involved shouldn’t lead one to the conclusion that randomness is the way to go. Rather, the manager should be able to process these factors into his strategy. Such a strategy can be developed and articulated. If a manager every stated he made such a decision on a random whim, he should be fired. How you can suggest it would be a sign of intelligence is beyond me.

Ken
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Ken
6 years 6 months ago

This type of logic only works if one of the two managers is incapable of making logical choices – which may be a very reasonable assumption but is outside the scope of the basic game theory employed here.

If both managers are rational and can do this sort of analysis, it makes no sense to ever bunt when WE favors hitting away, or vice versa. If you bunt in the effort to “bring the defense in”, they won’t simply because they know that you will revert to hitting away as soon as they do.

Patrick
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Patrick
6 years 6 months ago

Will,

Think about it this way. If the manager carefully, rationally evaluates the situation based on a certain set of inputs, and then, given those inputs, makes EXACTLY THE SAME DECISION EVERY TIME… Then what?

Eventually, given a bit of time to understand the managers’ criteria, the opposition knows exactly what they’ll do in every situation. Is that good for your team?

Well, since you’re presumably making good decisions each time, it’s not awful, it’s probably better than making bad decisions… But it’ll be inferior to a strategy that forces the opponent to guess a bit and adjust accordingly.

MGL will correct me if I’m wrong, but part of what he’s saying is, in essence, that it’s important to force the opposition to guess a bit, which affects their strategy and keeps them from perfectly optimizing it to your already known action. He has some very detailed game theory arguments for this (and I think they’re correct), but I think there’s also a general understanding that it’s a good idea to keep your opponent guessing just a little bit.

Think of it that way. Does a team want to be entirely predictable in every situation? That has some huge disadvantages.

The other thing is, he’s saying that a manager should very carefully evaluate the situation, take in all the factors… And decide that this is a situation where bunting 50% of the time is the right choice. That 50% is a very detailed decision, which rests on the basic idea that not doing exactly the same thing every time in a given situation is generally a GOOD idea.

Will
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Will
6 years 6 months ago

Patrick:

If the manager carefully makes his decision to bunt, then he should be quite happy with the results of its successful execution. After all, he is making the decision to advance the runners, not surprise the opposition.

Besides, your premise isn’t really valid because part of the variable is how the defensive appears to defend the situation. So, if the defense sets their infield deep because they know that will encourage you to bunt, what exactly are they gaining? Furthermore, if a manager considers all the variables, the chances of their being a predictable pattern would be reduced. And, where one does develop, it will more likely be because the decision is almost always the better option.

Furthermore, you seem to be suggesting that the best strategy is to periodically make bad decisions so that other times you can make good decisions. If that’s the case, I think that really doesn’t make sense because now you have to differentiate between when the good and bad decisions should be made. Also, you have to assume that the other team isn’t smart enough to figure out this strategy. It’s one thing to try to conceal a good strategy and another thing to employ a bad strategy because it will be a surprise. It’s kind of like the Mariano cutter…everyone knows it is coming, but because it is so good, it usually works. I am sure Mo would shock the hell out of some batters throwing the changeup, but the few times he didn’t could be deadly.

Finally, I don’t accept that there are every 50/50 scenarios. Just like there is no such thing as a tie going to the runner (he either beats the throw or doesn’t), the balances have to tip one way or the other. If the manager doesn’t have the expertise to gleam even the slightest advantage from the available information, then that team should hire someone who can

Ken
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Ken
6 years 6 months ago

The point is that if there is an advantage to bunting, the defense should be playing further in. If there is an advantage to hitting away, the defense should be playing back further.

The interesting twist on the question of bunting is that if the manager makes the decision, he has to do so before he sees the infield position. When you think of it that way, this is really a simultaneous move game, unless the hitter makes the decision – which it usually appears is not true. How much do teams give up by not letting the players choose their strategy based on where the defense is positioned?

B
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B
6 years 6 months ago

“Furthermore, you seem to be suggesting that the best strategy is to periodically make bad decisions so that other times you can make good decisions. If that’s the case, I think that really doesn’t make sense because now you have to differentiate between when the good and bad decisions should be made.”

Theoretically, if the value of the “bad decision” is less bad than any future benefits it leads to, then yes, it makes sense to make some bad decisions. I don’t know if practically that happens in this situation, but there are at least situations it makes sense. For example, compare it to pitch selection. Not all pitches a pitcher throws are equal. The pitcher will make the decision sometimes to throw a worse pitch (which is akin to the “bad decision” you brought up). In the long run it’s a good decision, though, because his other pitches are more effective if he mixes this pitch in at times. The positive effect of making the other pitches more effective is greater than the negative effect of throwing a worse pitch. If it’s not, the pitcher will simply stop throwing the pitch altogether.

As I said, I don’t know for sure if this is the case with bunting, but just from a thoeretical standpoint I don’t see how you can dismiss mixing it up without any evidence it never makes sense…

Paul Thomas
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Paul Thomas
6 years 6 months ago

“Furthermore, you seem to be suggesting that the best strategy is to periodically make bad decisions so that other times you can make good decisions.”

Have you played poker? This is exactly what a bluff is.

Will
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Will
6 years 6 months ago

Yes, but if there is an advantage to bunting, that means there is a strong reason to trade an out for a base. It doesn’t really matter what the defense is anticipating. Also, you have to consider that by trying to maintain an element of surprise (squaring late for example), the initial strategy of the sacrifice could be compromised (by a bad bunt, the runner not getting a good jump, or the hitter being left in a poor count).

In my opinion, the bunt should only be employed when the out for base trade is obviously desired. If there is serious doubt, then throw being unpredictable out the window and let the hitter swing away.

Kered Retej
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Kered Retej
6 years 6 months ago

I think there was a Peanuts cartoon that summarized this game theory hypothetical. I think it started with Charlie Brown (in baseball uniform) declaring “The situation calls for a bunt.” Next panel, he says “Now, we know that they know the situation calls for a bunt.” And then: “But they know that we know that they know the situation calls for a bunt.” Something like that anyway.

MGL
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MGL
6 years 6 months ago

Paul, yes randomizing from pitch to pitch is better of course. In fact, it is necessary. If you only make your decision (and stick to it) before the first pitch, than after the batter squares on the first pitch or doesn’t, the defense would know exactly what you are going to do. So you HAVE to “flip the coin” after every pitch. Adjusting your strategy for the count, as you say. Some managers do this. They are usually the better ones, at least in that regard.

As I said, the big mistake that many managers make – in fact, almost all managers make at least some of the time – is that they are convinced that a bunt is correct no matter where the defense is playing. IOW, they don’t mind letting the whole world know that they are bunting. That is almost always wrong, unless a pitcher is at the plate. That should actually be obvious even to a semi-astute manager. After all, they know from experience how difficult it can be to successfully bunt when the defense knows it is coming and they can certainly envision how hitting away can be particularly productive when the first and third baseman are standing 20 feet from home plate. That is the most common mistake made by managers. There should almost never be a time when the defense knows that a bunt is coming with a position player at bat (it is possible that if the batter is weak and is very fast and a skilled bunter, like a Taveras, that a bunt attempt has a higher WE than hitting away even with the defense expecting a bunt 100% of the time – possible) that a bunt is correct.

Preston, I don’t think that a base runner particularly needs to know what is coming, although may be helpful. As soon as he sees the batter square, he knows that is coming obviously. Plus, the batter can easily signal to the runner if he is going to bunt. Batters and runners often signal to each other.

Paul, no it would never be correct to just take the pitch (and fake a bunt), unless you were going to take the pitch anyway. In any case, trying to fake an astute opponent is generally not a good idea in any game. If your opponent is not astute, that is another story. However, you can usually only get away with that one time, at least versus that opponent.

When I play poker, unlike most other players at the table, I rarely say anything about the game and I try not to have any tells at all. However, usually one time and one time only, if a player or players do not know me, I try and “fake them out” on a hand. It usually works, but it only works once.

“In other words, wouldn’t an astute manager, assuming he’s ahead of the curve, utilize the “incorrect” strategy during less important games (the bluff) and utilize the “correct” strategy during more important games, i.e. game 6 of the LCS? You want the opposition to believe that you might make the “wrong” play by doing it at times, but it makes sense to only do it in games that are less important. Hopefully, the other team only picks up on the fact that you’re unpredictable.”

Chuck. Interesting. Sure, that could work, again, if your opponent is not that astute. Nice idea. There are a lot of things you can do in baseball (and in poker and other games) that make it look like you are randomizing your actions, but you are really not. Again, gotta be careful about that against an astute opponent.

For example, in poker, most good players change their approaches from time to time. Sometimes they play aggressively and sometimes more tightly. You should “change gears” on a random basis. But, most poker professionals recommend that after you have played loosely for a while, that you change gears and tighten up, and vice versa. Gotta be careful with that advice of course. And astute opponent can pick up on that. Let’s say that you follow that strategy and you have been raising a lot before the flop (in no limit hold-em) and I finally pick up a decent, but not great hand behind you. I want to re-raise you, thinking that since you have been raising so much, you obviously are raising on a lot of weak hands. But, if I am astute and you have been playing loose and aggressive like that for a while, I might also assume that by now, you may have tightened up in order to “change gears” so I may be less likely to re-raise you without a really strong hand myself.

Kind of like this: Let’s say that a lefty pitcher like Pettitte is on the mound. The only way I can steal against him is to guess and hope that he does not throw to first. If he throws to first, I am a dead duck. If not, I am probably safe. If he throws to first 35% or the time or more, on a random basis, I can never steal (at a greater rate than 65%, which is probably not enough to justify an attempt in most situations). But what if he just threw over 5 times in a row. If he is type who does not “flip the coin” after every pitch or every pick-off attempt, I may be able to go. IOW, he may think that after 4 or 5 throw overs, he is simply going to stop throwing over. He shouldn’t do that of course. But he might. He SHOULD be just as likely to throw over (35% of the time or more) as soon as I get on base as he is after throwing over 10 times in a row (which would be unlikely of course – but could and should eventually happen).

“With all due respect, stating that a decision is best made with a coin flip is pretty weak. While Win Expectancy does provide a good framework for making these decisions, the variables involved shouldn’t lead one to the conclusion that randomness is the way to go.”

I appreciate the “due respect” but with all due respect to you, you are wrong and I am right. You do not understand the concept of game theory. I suggest you read a poker book. The principles are the same. And re-read my original article above. It might click for you. Randomly selecting pitches, pick-offs to first, bunt attempts, pitch outs, steal attempts, hit and runs, etc. are critical elements to optimal strategies for a manager. They can be pseudo-random, BTW, although technically that is not optimal against an astute opponent. By pseudo-random, I mean that as long as they appear random to your opponent, that is generally good enough. In baseball terms, that is merely being unpredictable. You will actually occasionally hear some rare wisdom from a TV commentator when a batter is at the plate, the defense expects a bunt and the batter hits away, and the commentator says something like, “That is what makes LaRussa (or whoever) such a good manager. He is unpredictable.” Now, he (Tony) may have had a “reason” for not bunting and trying to “cross-up” the opposing manager, but for all intents and purposes, it was randomly selected, from the perspective of the other team.

Ken, sorry but you are missing the point of the whole thesis. Try re-reading the article. The defense must take a position on the field (in terms of how much they expect the bunt) such that the WE from bunting and the WE from hitting away is exactly equal (or as close as you can get). At the same time, the offense must bunt or not bunt a certain proportion of time, such that it doesn’t matter where the defense plays. If either manager does not do that, then the other manager can change their strategy, but NOT all the way because it would immediately or in the future cause their opponent to act more optimally. In order for the defense to play all the way in or all the way back, when the optimal position (where the WE from bunting and hitting away are the same) is somewhere in between, the offensive manager has to be really stupid. Ditto for the offense. If the optimal bunting strategy is to sometimes bunt and sometimes not, the defense manager would have to be really stupid for the offense to always bunt or always hit away.

“The other thing is, he’s saying that a manager should very carefully evaluate the situation, take in all the factors… And decide that this is a situation where bunting 50% of the time is the right choice. That 50% is a very detailed decision, which rests on the basic idea that not doing exactly the same thing every time in a given situation is generally a GOOD idea.”

That is correct. You simply cannot bunt or not bunt 100% of the time in any given situation (given the batter. pitcher, base runner, count, score, inning, park, weather, etc., all of which effect the bunt and hit away WE) unless one of two things are true:

1) If the defense is playing all the way back, the WE from bunting is still less than the WE from hitting away – you hit away 100% of the time. This may be true for very good hitters and/or slow, poor bunters. Also depends on pitcher, defense, and game situation.

2) if the defense is playing all the way up and the WE from bunting is still greater than the WE from hitting away – you bunt 100% of the time. This may be true for fast/good bunters and weak hitters. Also depends on pitcher, defense, and game situation.

In every other instance, you must bunt and hit away some of the time. Otherwise the defense will simply play all the way in (if you bunt 00% of the time) or all the way back (if you hit away 100% of the time), making it worse for you than if you bunted some of the time and hit away some of the time.

It is not about “making bad decisions” some of the time. It is about not allowing the opposing team to play optimally against you if they know what you are going to do. You cannot let them play all the way in if they think you are going to bunt or all the way back if they think you are going to hit away. Simple as that. If you mix up your strategy, they will be forced to play half way (for some of your batters some of the time – not all of them or all of the time). And that is better for you. It increases your overall WE. It is exactly the same reason why good poker players must bluff sometimes and must play all of their hands differently in a random fashion. You cannot let your opponent have a good idea what you have by the way you play your hand.

“How much do teams give up by not letting the players choose their strategy based on where the defense is positioned?”

Depends. If the defense is playing in a position such that WE from bunt = WE from hitting away, it does not matter whether you know that before your decision is made. There is nothing you can do to exploit that – that is why it is an optimal position for the defense. However, if the defense makes a mistake and you don’t know that they will before you have to make your decision, then it is a big advantage for the offense. So the answer is that it is POTENTIALLY a big advantage to see the defense first, depending on how often and by how much the defense errs and whether you could anticipate those mistakes even without seeing them first.

Even if the offense wants to make their decision before they see the defense (they don’t want to let the batter decide or give him an option or a re-signal), that is fine. You still have to randomize your offensive strategy with some batters in some situations. You can either assume that the defense will play optimally or you can assume some mistake (if you have reason to think they will) and respond accordingly.

As I said, if the defense makes a mistake, even a little one, by playing too far in or back, your correct response for that one PA only, is technically to always bunt or not bunt, but you can’t do that. As soon as the other manager sees you doing that surely he is going to make sure he doesn’t make that same mistake again. For example, if he plays all the way back with Swisher at the plate thinking that you are not going to bunt Swisher, and you bunt him 2 or 3 times in a row (or even once), surely he is not going to play back the next time Swisher is up at bat in a similar situation, or even some other batter that he previously thought you would not bunt with.

Ken
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Ken
6 years 6 months ago

Your last point was all that I was trying to say. If the defense plays too far in – hit away, if the defense plays too far back – but. You mix your plays when the defense sets up optimally, otherwise you always have a unique best response.

There is no other logic needed unless you are seriously worried about the other manager learning the optimal strategy from the way that you play.

Will
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Will
6 years 6 months ago

You response above was nonsense, so perhaps I should rescind the “due respect”. Managers do not randomly select strategy. Many variables are taken into account, which negates the randomness of the action. If Bengie Molina is on 1st, no manager is going to have him attempt a straight unless something very drastic dictates it (i.e., the fielders are so far away he can get a 40 foot lead). The idea that a manager should flip coins is absurd and you’ve done nothing to prove otherwise.

Also, the analogy to poker is ridiculous. In poker, one player is trying to get others to sweeten the pot by betting more money. Having the better hand is not as important as winning a big pot. In baseball, there are no stakes to raise. All that is at hand is winning the game. If a team thinks it can win with a successful sacrifice, they would be absurd to abstain so that some other manager in some other game might play their infield back.

Before recommending that I read a book on game theory, I suggest that you find a good one yourself and read it carefully. Amateur analysis like this gives sabemtrics a very bad name.

chris
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chris
6 years 6 months ago

I agree with the premise that it is incorrect to either bunt or swing away 100 pct of the time.

However I can never see doing it with a hitter like swisher. Especially in the 8 spot where your next hitter is Melky Cabrera.

A guy who is gonna slug 500 and get on base 38 pct of the time is not gonna bunt… why sacrafice one of the best bats on my team?

chris
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chris
6 years 6 months ago

Mitch,

I understand that a sac bunt does not always produce an out and an advancement, however is that not the desired result?

If this is the case, why are we attempting to do something that, if sucsessful, will lower our expectancy? Unless, as already stated, we are dealing with a terrible hitter.

Matt
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Matt
5 years 11 months ago

lord have mercy that is a long article.

SOB in TO
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SOB in TO
5 years 4 months ago

Sorry for commenting late.
Sorry for merely browsing the article.

Variance in the question of to bunt or not to bunt is probably more important than the Expected Value of Runs in late situations and all you need is one run. Manager goes for the slightly surer probability of one run than the higher probability 0 runs and a slightly higher probability of four or more runs.

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