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  1. 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.

    Comment by Steve — October 27, 2009 @ 10:22 am

  2. 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.

    Comment by Rob in CT — October 27, 2009 @ 10:25 am

  3. 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.

    Comment by Mike K — October 27, 2009 @ 10:40 am

  4. 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.

    Comment by Steve — October 27, 2009 @ 10:51 am

  5. 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.

    Comment by Mike K — October 27, 2009 @ 10:57 am

  6. 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.

    Comment by Kevin S. — October 27, 2009 @ 11:04 am

  7. 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.

    Comment by Gilbert — October 27, 2009 @ 11:08 am

  8. 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.

    Comment by tyrone — October 27, 2009 @ 11:52 am

  9. 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.

    Comment by Steve — October 27, 2009 @ 12:08 pm

  10. 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.

    Comment by Jeremiah — October 27, 2009 @ 12:37 pm

  11. 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.

    Comment by chuckb — October 27, 2009 @ 12:39 pm

  12. 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.

    Comment by Hardy — October 27, 2009 @ 12:42 pm

  13. 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.

    Comment by David Brown — October 27, 2009 @ 12:44 pm

  14. 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).

    Comment by Andrew — October 27, 2009 @ 12:52 pm

  15. 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

    Comment by Hardy — October 27, 2009 @ 12:53 pm

  16. 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.

    Comment by Carl Robinette — October 27, 2009 @ 12:58 pm

  17. “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.

    Comment by B — October 27, 2009 @ 1:05 pm

  18. 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.

    Comment by Hardy — October 27, 2009 @ 1:14 pm

  19. 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.

    Comment by tyrone — October 27, 2009 @ 1:14 pm

  20. 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.

    Comment by B — October 27, 2009 @ 1:17 pm

  21. 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.

    Comment by Wally — October 27, 2009 @ 1:20 pm

  22. 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.

    Comment by Wally — October 27, 2009 @ 1:26 pm

  23. 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.

    Comment by Steve — October 27, 2009 @ 1:30 pm

  24. 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.

    Comment by Wally — October 27, 2009 @ 1:34 pm

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

    Comment by Steve — October 27, 2009 @ 1:37 pm

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

    Comment by Hizouse — October 27, 2009 @ 1:47 pm

  27. 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.

    Comment by Steve — October 27, 2009 @ 2:00 pm

  28. 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.

    Comment by Thor — October 27, 2009 @ 2:08 pm

  29. 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.

    Comment by Wally — October 27, 2009 @ 2:20 pm

  30. 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.

    Comment by Sej — October 27, 2009 @ 2:40 pm

  31. 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.

    Comment by Rob in CT — October 27, 2009 @ 2:48 pm

  32. 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).

    Comment by B — October 27, 2009 @ 3:14 pm

  33. 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.

    Comment by Twac00 — October 27, 2009 @ 3:19 pm

  34. 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.

    Comment by waynetolleson — October 27, 2009 @ 3:27 pm

  35. 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.”

    Comment by lincolndude — October 27, 2009 @ 3:44 pm

  36. 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.

    Comment by Patrick — October 27, 2009 @ 4:04 pm

  37. 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.

    Comment by MGL — October 27, 2009 @ 4:31 pm

  38. I should try reading The Book sometime…

    Comment by B — October 27, 2009 @ 4:42 pm

  39. 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?

    Comment by lincolndude — October 27, 2009 @ 5:08 pm

  40. 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.

    Comment by waynetolleson — October 27, 2009 @ 5:18 pm

  41. 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.”

    Comment by lincolndude — October 27, 2009 @ 5:46 pm

  42. 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.

    Comment by Wally — October 27, 2009 @ 5:55 pm

  43. 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.

    Comment by waynetolleson — October 27, 2009 @ 6:12 pm

  44. 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.

    Comment by Carl Robinette — October 27, 2009 @ 6:28 pm

  45. 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!

    Comment by The Typical Idiot Fan — October 27, 2009 @ 7:35 pm

  46. 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.

    Comment by chuckb — October 27, 2009 @ 9:15 pm

  47. 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.

    Comment by MGL — October 27, 2009 @ 9:48 pm

  48. 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.

    Comment by Preston — October 28, 2009 @ 1:01 am

  49. 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.

    Comment by BIP — October 28, 2009 @ 1:50 am

  50. 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.”

    Comment by Paul Thomas — October 28, 2009 @ 3:00 am

  51. 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.

    Comment by Paul Thomas — October 28, 2009 @ 3:11 am

  52. 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.

    Comment by RollingWave — October 28, 2009 @ 4:21 am

  53. 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.

    Comment by chuckb — October 28, 2009 @ 7:57 am

  54. 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.

    Comment by Will — October 28, 2009 @ 8:05 am

  55. 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.

    Comment by Ken — October 28, 2009 @ 9:38 am

  56. 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…

    Comment by B — October 28, 2009 @ 10:08 am

  57. 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.

    Comment by Patrick — October 28, 2009 @ 10:09 am

  58. ” 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.

    Comment by Steve — October 28, 2009 @ 10:20 am

  59. 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

    Comment by Will — October 28, 2009 @ 11:26 am

  60. 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?

    Comment by Ken — October 28, 2009 @ 12:59 pm

  61. 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.

    Comment by Will — October 28, 2009 @ 1:36 pm

  62. “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.

    Comment by Wally — October 28, 2009 @ 2:07 pm

  63. 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.

    Comment by B — October 28, 2009 @ 2:52 pm

  64. “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…

    Comment by B — October 28, 2009 @ 3:01 pm

  65. 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.

    Comment by Kered Retej — October 28, 2009 @ 3:03 pm

  66. “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.

    Comment by Paul Thomas — October 28, 2009 @ 4:44 pm

  67. 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.

    Comment by MGL — October 29, 2009 @ 2:25 am

  68. 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.

    Comment by Ken — October 30, 2009 @ 9:12 am

  69. 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.

    Comment by Will — November 19, 2009 @ 2:35 pm

  70. 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?

    Comment by chris — November 20, 2009 @ 4:02 pm

  71. 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.

    Comment by chris — November 20, 2009 @ 4:18 pm

  72. lord have mercy that is a long article.

    Comment by Matt — June 3, 2010 @ 7:10 pm

  73. 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.

    Comment by SOB in TO — January 12, 2011 @ 8:00 pm

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