My daughter completely schooled me this week. In the 2013 Baseball Prospectus Annual, I talked about how she, at the tender age of three, was a better sabermetrician than I, because she’s much more experimental about life than I am. She turned four a few months ago, so she’s not really young for her level any more, but she’s still better at this than I am. Last week, my wife and I were in the kitchen and my daughter was busily drawing a picture of… something. My wife mentioned that one of her friends had made a bunting (the kind that a baby wears) for her infant daughter. My daughter asked what a bunting was and my wife explained. As an afterthought, I tacked on, “and it’s a bad strategic play in baseball.” My daughter stopped drawing, looked over at me, and asked her favorite question, “Why?”

Now, I briefly entertained the thought of explaining a run expectancy matrix to her, but had to settle for “Daddy’s just being silly.” That’ll do for now, but some day, when she gets older, she too will be tempted to call for a sacrifice bunt at a key moment in an important game. What will I say to her then? I need to be ready.

It’s a question that I haven’t really asked in a while. It’s something of an article of faith among sabermetricians that sacrifice bunts are a bad idea, and I assumed that when I had a little time to play around with some numbers, I would confirm what I already knew, that bunting is mostly a bad strategy because it costs a team runs.

In fairness, we already know that there are situations where bunting is actually a good idea. In The Book, author Mitchel Lichtman makes the case that completely abandoning the bunt won’t work, because there’s a game theory aspect to it. Dropping one down once in a while keeps the defense honest. If they know that a bunt isn’t coming, they can play back with impunity. In 2004, James Click suggested that a bunt makes sense for really bad hitters (read: pitchers), or in very specific situations, such as a tie game, when a team needs one run and can forgo a multi-run inning (his work is summarized in a chapter of Baseball Between the Numbers).

The standard argument against bunting has been that according to the run expectancy matrix, having a runner on first with no outs actually leads to more runs, on average, than does a runner on second with one out. And getting the runner to second with one out is supposed to be the point. In 2013, a team with a runner on first and no outs could expect 0.826 runs in the rest of the inning, while a runner on second with one out had an expected value of 0.637 runs. Advancing the runner is a good thing, but the out is clearly more valuable. Why intentionally waste one?

Both Lichtman and Click point out that one nice thing about a bunt is that sometimes it produces more than just the standard “batter out, runner to second.” Sometimes the batter gets a hit. Sometimes the fielding team throws the ball into right field. There are lots of things that can happen once the third base coach puts his right arm in and then takes his right arm out and then shakes it all about. I think that was the bunt sign. But of course, both Lichtman’s and Click’s works are approaching their 10th birthday. Maybe it’s time for a fresh look at the subject.

In April, Sports Illustrated’s Tom Verducci wrote an article-slash-lament about hitters becoming more “passive” at the plate. I dug into the numbers there and found that what he was pointing to was that the game was evolving, and that a tenet of sabermetric wisdom (take lots of pitches!) was losing its effectiveness because teams had made a counter-adjustment. I think we’re seeing the game evolve in another way that makes “Bad manager! You bunted! You shall now be summarily fired!” obsolete. It’s more complicated than that. It always is.

Warning! Gory Mathematical Details Ahead!
Here, I’m specifically looking at bunting by non-pitchers. I found all instances from 1993 to 2012 in which there was a runner on first base with no outs and the guy at the plate was not a pitcher. I also dismissed situations in which that runner advanced (or was eliminated) by an independent baserunning event (like a stolen base or pickoff) or made it to second on a wild pitch/passed ball or a balk.

One thing we do know is that the bunt has fallen out of favor over the past 20 years. In 1993, managers pressed the “bunt” button 9.4 percent of the time in these situations. By 2012, that number had shrunk to 6.3 percent. Look at this lovely graph!

Well, if bunting rates are down, are success rates down? Let’s first talk about what we mean by “success.” Usually, “success” is defined as the batter being out and the runner advancing to second. That’s still the most common outcome (rates of things ending that way have fluctuated between the high 60 and low 70 percent range over the last 20 years, with somewhat of a downward trend.) And we know from the run expectancy table that this is a net loss. There are other outcomes that are more positive (“extra value”), while others are much more negative (“problematic outcomes”). Rates of both the good and bad “non-standard” bunt attempts have gone up a bit over the years. Here’s another graph!

We need to take those alternate outcomes into account as well. We often critique managers for their use of the bunt, but all they do is make the call. Let’s look at the historical run expectancy for the situation “runner on first, none out” split between whether there was a bunt attempted or not before we know the outcome of the bunt.

In 2012, situations in which the bunt was employed actually netted out a higher number of runs (on average) than did situations in which the batter swung away. Now, 2012 looks like it was something of an aberration (something similar happened in 2001, although for a different reason), but let’s look at the net advantage in run expectancy for swinging away compared to bunting in this next graph. This is the run expectancy of swinging away minus the run expectancy of the bunt.

There’s a lot of noise in there, probably owing to the fact that there really aren’t a lot of sac bunts laid down by non-pitchers in this situation (there were 599 in 2012), and spikes in happy outcomes (or valleys in overly sad outcomes like double plays) can play havoc with our run expectancy. Plus, there’s been a general downward trend in run scoring more generally over the past five years, while bunts have maintained a greater portion of their value. However, there is something of a downward tilt in that graph. Innings where the bunt is invoked still produce fewer runs than those where the batter swings away, but there’s some suggestion that the gap is closing. The bunt isn’t as big of a rally killer as we thought, at least not lately.

Beyond that, we still have a problem with using run expectancy to evaluate whether or not bunts work. The run expectancy matrix is an aggregate of all situations in which a team found itself in the situation of “runner on first, no outs” (or whatever situation you prefer). It doesn’t distinguish whether the batter in this situation is Miguel Cabrera or Colin Wyers. But managers are very aware of who’s at the plate when they make that distinction. In fact, if there’s something that I hope to eventually leave as my sabermetric epitaph, it’s that baseball analysis is really mostly about adjusting for the fact that managers exist only to screw up the nice little randomized controlled study that I was hoping to run. I still have a petition in with MLB to kindly assign playing time (and everything else) in a random fashion. It would make my job a lot easier.

We start by recognizing that the players who are asked to bunt are generally weaker hitters. In 2012, the weighted on-base percentage of players who were asked to bunt in this quintessential bunting situation was .300, while those who didn’t get the bunt sign had a weighted on-base percentage of .319. We have to take into account the fact that if the hitters who were asked to bunt had swung away, we would have expected below-average outcomes from them. When I looked at “runner on first, no outs” situations in which hitters did not bunt, and entered the batter’s OBP as a predictor into a regression to predict the number of runs that would be scored in the inning, that 19-point gap in OBP was worth about .04 runs. (I tried other, more complex models and got basically the same answer.) Yes, when players bunt, we see fewer runs, but the mere fact that they were asked to bunt means that they were the kind of players from whom we shouldn’t have expected as many runs from anyway. If we look at the preceding graphs and adjust it downward by .04 runs, it still doesn’t bring bunting completely into line with swinging away, but the net loss is much less than is generally believed.

Managers also bunt in front of better hitters than average. In 2012, the on-deck hitter when a bunt was called for had a weighted on-base percentage of .322, while in the swing-away condition it was .314. That difference has an effect of .03 runs or so. Again, managers seem to be on to something. The fact that the manager deemed this a bunting situation is a marker for the fact that run expectancy is actually greater than normal. Managers generally pick bunting situations—whether consciously or not—when there’s already a greater chance that the bunt will “work” because there’s someone hitting behind the bunter who can drive in the runner.

Evolution within the Revolution
What’s fascinating about all of this is that it leads to a couple of rather surprising corollaries. It is commonly accepted that a “successful” bunt is one that advances the runner on first to second with the batter being put out. The batter usually gets a gentle clap from the fans for this. Even after all of the adjustments that we might make, if a bunt actually ends in this outcome, it is counter-productive, and roughly 70 percent of bunts end this way. This has still not changed.

It is also commonly accepted that bunting is a conservative strategy and that the manager is playing small ball either for tactical reasons (we need only one run) or for psychological reasons (we want to score first, even if it is only one run). The only thing that makes bunting worthwhile is the roughly 1-in-8 chance that a fortuitous event happens, like the bunter beating out the throw for a hit. The manager (consciously or not) is actually betting on the bunt forcing the defense to “make a play” and then benefiting when the challenge goes un-met. Bunting turns out to be a very high-risk strategy, when looked at properly. It’s playoff time, and there will be plenty of bunting going on. I wonder if managers know what a huge risk they are taking when they call for a little tap.

Bunting is also something that actually should experience a small Renaissance, assuming that the era of lower scoring sticks around for a while. Rates of run scoring when batters swing away aren’t that great. Bunting has a certain value for hitters who aren’t all that gifted, and while it isn’t much, with offense down there isn’t that far to climb until it’s worth it.

Managers, for all the grief that we sabermetricians give them, do show some skill at picking their spots. It’s not that everyone should bunt all the time, it’s that managers, as a collective, show some smarts in knowing when it’s a good time to bunt and when it’s not. On average, they still do get it slightly wrong, but the net loss is only a few hundredths of a run each time they do it. And there are probably cases where calling for a bunt is perfectly defensible. It’s still somewhat fashionable to rage against bunts (#killthebunt?) but the game has evolved to a point where the sin is not worth the outrage. Sabermetricians are fond of saying that they want to revolutionize the game. In fact, the game has evolved. We need to evolve as well.

Yes, constructing the lineup to insert a poor hitter in the two-hole so that he can bunt is still silly. Having your .300/.400/.500 hitter drop one down is silly. A bunt is not the solution to all sentences starting with “there’s no one out and a runner on first.” But it is one tool in the belt that can be used in certain situations as part of a larger strategy to score runs. And yet it is woefully misunderstood.

So yes, I got schooled by my four-year-old. She stopped to ask a question that I assumed that I knew the answer to. And it turns out that the answer has changed a little bit.