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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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.


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.


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


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


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.