Drilling Down into a Bunt Situation

Mitch Moreland led off the bottom of the sixth inning Monday night with a single and stood at first with the score knotted at zero. Elvis Andrus was at the plate with Michael Young and Josh Hamilton due next. Given the pitching duel seen so far and expectation for the remainder of the game, an Andrus bunt would not have shocked many people.

Followers of win expectancy rightfully agree with that call not being made. Sacrifice bunts rarely increase a team’s chances to win. It is, however, a bit more complicated to apply the tenets of win probability to an exact situation than it is to speak in broad concepts.

For one, win expectancy is blind to the specific players involved which can play an important part in skewing the numbers. But there are more subtle assumptions present as well that are worth delving into. A pertinent one in this case is that the markov chains inside win expectancy are calibrated around a run environment. Typically, we use the average run environment for the park in play, but on an individual game basis the environment can vary quite wildly due to the two pitchers in the game.

Examining whether a bunt call might have been proper involves figuring out the expected run environment of the game going forward. Based on the pitch counts of Cliff Lee and Tim Lincecum, the strength of the bullpens behind them and the venue, the number I roughly calculated pegged it at 3.4 runs per team per nine innings. Ignoring the chances of a failed attempt and a fielding error and making the simplistic assumption that a sac bunt would move Moreland to second 100% of the time, that presents a bunt play as being worth -1.4% of a win to the Rangers.

So even with the lower run environment, the call is still overall a bad one, but how low would the run environment need to be before a bunt would result in a positive change in win expectancy?

Change in WE per run environment

The break even point is around 1.1 runs per team per nine innings, which should give you an idea of how far off the bunt was from being profitable due to the run environment. One point one runs is not a realistic assumption under almost any condition.

How about the timing though? If the same situation presented itself later in the game, with fewer innings left to play, would that make it profitable? It certainly increases the benefit of the bunt play, but it turns out that it still never gets it past the 0% barrier.

Change in WE per inning of bunt

There are times that sacrifice bunts are called for probabilistically. Nearly all of those,however, have to do with moving a runner from second to third. To justify moving a runner from first to second, a manager would need it to be late in the game and the run environment to be abnormally low.

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Matthew Carruth is a software engineer who has been fascinated with baseball statistics since age five. When not dissecting baseball, he is watching hockey or playing soccer.

28 Responses to “Drilling Down into a Bunt Situation”

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  1. B N says:

    “Ignoring the chances of a failed attempt and a fielding error”

    Does this basically mean ignoring the possibility of an unproductive out and a hit (by any means)? Or does it just mean eliminating the possibility of an unproductive out and 2 men on due to a fielder’s error? I assume it’s the first, but it’s not quite made clear.

    Because if it’s the second option, I have a hard time believing it has a negative win contribution- unless Andrus is just a horrible bunter. Thinking about it logically, if Andrus is a good bunter (a maybe), I would think he would have a decent chance at legging out a good bunt. In that respect, bunting would be very much like him just trying to get a slap hit.

    In fact, without that possibility, I’d have trouble imagining why any team would put down a sacrifice bunt unless they had the most incompetent hitter at the plate (see: pitcher). For example, see:


    A rather unsurprising trend emerges: guys that have a lot of sac bunts are very fast, as a group. While the outcome may be classified as a sac bunt, they probably had a fairly typical BABIP chance of getting on base. In that light, it’s hard to see why a bunt by Andrus would have such an impossibly negative win expectancy- unless we’re basically distoring the situation just to prove (for the 100th time) that pure sacrifice bunts kind of suck.

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    • B N says:

      In fact, judging from this:


      “great “bunt for hitters” are generally in the 40s as far as reaching first when they get a bunt down. Cabrera (50), Bourn (47) and Ellsbury (47) are the best of the guys on the leaderboard.” (2009)

      One could make the argument that players are attempting too few bunts. A BABIP of 40% is pretty solid. As long as you can make contact reliably so you can send the runner at first, a bunt is as good as any other type of batted ball. (Also interesting that guys like Pena and Ortiz don’t bunt more. Guys bunting against the shift have had very good odds, > 50% in many cases. You’d think they’d bunt until defenses had to be more honest)

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      • Bhaakon says:

        There’s some huge selection bias in there. Not only are those guys all speedy and exceptional bunters, they’re almost certainly waiting for spots when the defense is not defending the bunt. If they started laying down a bunt every 10 or 15 at bats at bats, defenses would adjust and that BABIP would plummet..

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      • tarlinian says:

        Seems like a rather obvious case of professionals failing to play minimax. I’m almost 100% sure that wOBA on non sacrifice bunts for most player is higher than for all other plate appearances. You would think that bunt rates would increase. I have a hard time believing that increasing bunt rates even slightly would drastically reduce the effectiveness of an attempted drag bunt.

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      • B N says:


        However, right now they’re showing a better BABIP with one type of hit than another. This would seem to indicate that they’d be better off taking more chances at bunts, until either:

        A. Their BABIP for bunts and regular hits are closer together.

        B. The defenses adjust, allowing them an advantage in hitting the ball over the defense when it’s pulled in.

        Getting the defense to move in is an advantage itself for hitting. See the same issue about bunting into the shift. If you can get on base bunting, the defense can’t shift as much. To me, this indicates that people aren’t bunting enough.

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    • It means that when comparing the delta WE in this case, 100% of the time it was assumed that the “bunt” would result in a runner on 2nd and 1 out.

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  2. Hank says:

    Interesting article as it tackles some of the limitations of the run/win expectancy models that people ignore.

    The analysis on the overall run expectancy for the game (and obviously the inning) is something that people seem to ignore and it was good to see that impact graphically.

    Two questions
    1) How significant is the possibility of a bunt hit, especially with a faster type runner (not merely just a fielding error). Are bunt singles in the case of attempting a sacrifice fairly negligible such that it can be ignored (I have no clue)
    2) Is the breakeven point analysis looking at the overall game run expectancy simply a function of the absolute # of runs or also the expected delta between the teams? In other words if the teams run expectancy is closely matched does that make the impact more important than if they are mismatched? (intuitively this would seem to be a significant factor) To use an example if the run expectancy in the game was a score of 2.2-2.1 vs 2.6-1.7 vs 2.2-1.0, wouldn’t that make the impact of the bunt different in those secnarios?

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    • Hank says:

      One additional question on your analysis of a calculated run expectancy of 3.4runs per team per 9 innings….

      – Since it was the 6th inning were your doing the calculation based on a 0-0 score and only 4 innings of potential scoring? (in other words the run expectancy at that point was no longer 3.4 runs, but 4/9* 3.4 runs)… meaning it was only expected that the Rangers would put up 1.5 runs with that many outs left (I’m assuming 0 outs at the time, I forget if it was 0 out or 1 out at the time)

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      • It was 0 outs and yes, I was accounting for the current inning in estimating the future run environment.

        The previous two questions I don’t really have good answers for.

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  3. Padman Jones says:

    Couple of considerations to increase the profitability of a bunt:

    1) Pitcher at the bat. Terrible hitter gets his expected out and advances a runner instead of, say, striking out? Well, considering the increased likelihood of not advancing a runner (or GIDPing) with a pitcher at the bat, it’s not such a bad outcome. Team (relatively) profits.

    2) Managers keep getting paid to abide by conventional wisdom. As long as they’re not the manager of a team that anyone here is a fan of, we all profit. BAM.

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    • Eric M. Van says:

      Tom Tippett looked at bunting by pitchers and presented the results at SABR in (IIRC) 2002; not sure if he’s published them.

      He did the same thing CC is doing, just looking at the delta WE in an average run environment, and he found that the WE still goes down after a successful sac, with good and even average hitting pitchers.

      Basically, MLB managers, even the ones who understand that WE almost always goes down with a successful sacrifice and are employing it as part of a minimax strategy, overestimate the impact of both the run environment and batter-weakness effects.

      They also fail to take the bunt off when the hitter gets ahead 1-0, 2-0, but that’s a different (and rather more puzzling) thing.

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  4. kardo says:

    I’d love a 3D plot giving the WE per Run Enviroment per Inning!

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  5. MGL says:

    Ignoring the chances of a hit/ROE/walk, etc. and a non-successful bunt (no runner advance, K, occasional DP, etc.) renders ANY analysis useless. Period. So does ignoring the game theory aspect of a bunt attempt X percentage of the time (if the WE from a bunt attempt and a non-bunt attempt are somewhat close to one another, the offense must bunt some percentage and NOT bunt some percentage of the time in order to keep the defense from playing all the way in or all the way back, thus increasing the WE for either alternative).

    I wish these analyses of a “bunt” without understanding and addressing the importance of how often the bunter reaches base safely and how often the bunt is not successful at all, and without understanding the game theory aspect of the bunt attempt, would cease.

    We ALL know by now that simply assuming a runner advance and an out rarely if ever increases the standard WE for almost any run environment. But, as I said above, that is NOT ever the question so what is the point of that kind of incomplete analysis? If the answer to that question (whether a runner advance and an out increases or decreases a standard WE) is that it decreases WE, that sheds NO light on whether a bunt ATTEMPT increases or decreases WE. If the answer to that question is that it increases WE, that also sheds NO light on whether a bunt ATTEMPT increases or decreases WE.

    The “answer” is that in almost any inning and any run environment, the best and fastest bunters must bunt sometimes and the worst and slowest bunters must never bunt. I would think that the Andrus situation falls into the former category.

    If you want a detailed analysis of the sacrifice bunt attempt, ad nasuem, read The Book.

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    • Luke in MN says:

      Yeah, this. There is definitely a range of other possibilities on both sides of a successful sacrifice that have to be accounted for before you can tell me for sure it’s a good or bad idea. Having watched the Twins this year, the failure side of the coin looms largest in my brain. Lots of popped up bunts and a ton of just running the count to 0-2 before giving up the endeavor.

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    • B N says:

      My thoughts also, though I’m far less angry about it. ;)

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    • I considered all those points MGL, but I’m somewhat limited by space and I had no interest in writing a 3,000 word treatise on the sacrifice bunt. It’s been written before and I doubt it would make any converts.

      Not everything needs a comprehensive scope. I thought taking one precise situation and evaluating it in one precise way, looking at only a couple variables, would provide some insight into how sacrifice bunts fit into the overall scheme of options. That necessitates simplifying certain things.

      I heartily reject your notion that everyone who watches baseball knows that advancing a runner at the expense of an out decreases the standard WE for any run environment. You know this, but I wasn’t writing this for you.

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  6. William says:

    Matthew –

    Just wanted to say that you made a really interesting insight when you raised the issue of specific pitchers as a factor in actual WE… thanks for that.

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  7. Mr Punch says:

    Depends on the batter (Huff more than Andrus) but the DP risk does seem to weigh with managers. Otherwise, I suspect, you’d never see a sac bunt advancing runner to second by a decent hitter.

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  8. Luke in MN says:

    Can someone who understands it better tell me: Is Win Expectancy robust enough that it can handle a situation where the value between 1 run and multiple runs is minimal? For instance, in some situations (late in close games), a higher run expectancy is not the same as a higher win expectancy, since a single run is all you need and you’d rather have a better chance at 1 run with little-to-no chance at multiple runs than a lesser chance at 1 run with a greater chance at multiple runs, even if the second situation would result in an an overall greater run expectancy. Practical application: Don’t you have a better chance of getting at least one run with one out and a guy at second than with zero out and a guy at first, even if the no-out situation has a higher overall run expectancy?

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    • B N says:

      Two things:

      1. Firstly, I’m pretty sure it takes that into account. Since it’s a Markov Chain analysis, I assume it’s looking at the probabilities of state transitions that lead to a win (your score higher than other team’s score after 9, for example). So at the end game, all the winning states go into the objective function.

      2. Secondly, while it may seem that way- this article has just stated that in most cases the answer is no. One out is worth quite a bit and a runner on first with no outs is a pretty good position. You have a 35% chance generally of getting the guy at the plate on base with no outs, which may be an extra base hit. Plus, even in a hit attempt, you could still move the runner over. Besides, even if you get the runner to 2B you still need a solid knock to get him in. By giving up an out, you give up the chance that:
      A. Batter hits a double, triple, or HR and scores the guy at first.
      B. Batter gets a hit and now you have two on with no outs.

      While it may seem non-intuitive, this analysis is one of many that shows that trading an out for a base is in general a stupid idea.

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    • DrEasy says:

      Going by http://www.tangotiger.net/RE9902score.html

      Runner on second, zero outs: 36.8% of the time no runs are scored
      Runner on third, one out: 33.8% of the time no runs are scored

      So, a successful sacrifice would indeed improve your situation in the case where you only need one run to win. However, the odds of a successful sacrifice aren’t 100% either, so that would have to be taken into account.

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  9. Bigmouth says:

    I’d like to see a similar analysis of the decision to have Huff bunt for the first time in his career during game 5 of the World Series. Bochy is getting tons of accolades for his managing. But my impression is that he got lucky in the sense that several moves like that bunt could have backfired badly but didn’t.

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  10. MGL says:

    “looking at only a couple variables, would provide some insight into how sacrifice bunts fit into the overall scheme of options.”

    As I said, it provides NO insight for the reasons I explained. How does something provide insight when if the WE increases with a “successful bunt” it doesn’t tell you whether a bunt attempt might be correct and if the WE decreases it doesn’t tell you whether a bunt attempt might be correct?

    You clearly suggested that because the WE decreased after an out and a runner advance, that a bunt attempt by Andrus probably was not a good idea even in a low run environment. And that conclusion is clearly wrong because you simplified the situation to the point where it is useless in an analysis.

    Sometimes simplifying a model provides insight into a particular question and sometimes it doesn’t. In this case it doesn’t, I am afraid. Nothing personal. And just because you don’t have the time or space for a long treatise, that is not a justification for writing a short, but poor analysis. If I wrote something about how batting average can be used to evaluate offensive value because I don’t have time to explain how OPS, wOBA or lwts is a much better way to do the same, would that be acceptable to you (on this site)?

    This is 2010. We (analysts/sabermetricians) do NOT analyze sac bunts by assuming an out and a runner advance. Period. Sorry. As I said, nothing personal.

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    • Well, I don’t really get the point you’re trying to make. I feel like you’re assuming far too much intent on the post. I was trying to provide a specific and easily relatable example and *some* of the machinations behind analyzing it. Not all of them and I don’t believe that I gave off the impression that I was attempting to.

      It was mainly an exercise to introduce how run environments can affect changes in WE of certain plays. I intentionally avoided ironclad statements like “never bunt” for these exact reasons.

      If you wrote something about how batting average can be used to evaluate offensive value in a way that I felt would help people better understand some of the processes involved in measuring offensive value, then absolutely that would be acceptable to me.

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  11. MGL says:

    Matthew, no problem. There is value in looking at how WE and RE can change in various run environments, which is essentially what you were doing, without concluding one way or another whether a bunt in that situation was definitely warranted or not. As you know, it is a complex issue which is better handled in other venues. I just wanted to make sure that the readers realized that one can never determine whether a bunt attempt is appropriated without looking at the complete distribution of possible results (from an attempted bunt), as well as consider the game theory aspects. Carry on!

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