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A Statistical Defense (sort of) of the Sac Bunt

It has been well-chronicled both on this site and elsewhere that the vast majority of media and fans completely missed the point of Moneyball. Many people, if you asked them to sum up Moneyball in one sentence, would say something like "OBP iz gud!!1!". But perhaps if you gave them a second sentence, they would say "bunting is bad". Much has been made about the Moneyball-A's aversion to giving up outs, and it's been a polarizing point over the years.

Bunts have been part of the game perhaps as long as it's existed. The impetus for bunting is simple: a runner on first is more likely to score on a hit if he's at second base rather than at first. The idea behind the bunt is to give up an out to move the runner on first (or the runners on first and second) to second (or second and third) where they're more likely to score. The logic behind the sacrifice bunt is sound: give up an out to increase that runner's chances of scoring.

There's only one problem: by giving up one of your precious 3 outs, you're reducing your chances of scoring runs. Last week, we discussed run expectancy. Run expectancy calculates the average number of runs a team might be expected to score in a given inning based on the base-out state. So a team with the bases loaded and none out, on average, will score 2.27 runs that inning, while a team with the bases empty and 2 out will score an average of 0.09 runs that inning.

The run expectancy of a runner on first base with none out is approximately 0.86 runs. The expected number of runs with a runner on second base and one out is 0.68 runs. So by bunting, you've reduced your run expectancy by 0.18 runs. It's the same for bunting runners from 1st and 2nd over to 2nd and 3rd: you've reduced your run expectancy from 1.47 to 1.36, again reducing your expectancy by 0.11 runs. In other words, bunting actually slightly hurts your chances of scoring runs.

Of course, statistical analyses don't do a whole lot to sway portions of the baseball community, and the importance of sacrifice bunts remains a very polarizing subject. Full disclosure: I come down squarely on one side of the debate. In fact, just last week I tweeted the following:

But then on Saturday's game against the Rangers, the A's did their best Oprah impression: "You get a bunt! And you get a bunt!" In the first inning, Coco Crisp (who reached on a bunt single) was driven in by Jed Lowrie after a Sogard sac bunt. Sogard would later drive in another run on a safety squeeze, which would of course lead to the infamous Twitter outburst from Matt "Douchetree" Garza.

The plethora of bunts in the game made me take a closer look at bunts in general, and I think there's a lot more at play than "bunts suck!" vs. "bunts are awesome!".

Let's take a look at the classic bunt situation: runner on 1st, none out, turning into runner on 2nd and one out. The run-expectancy for a runner on first and none out is, on average, 0.86 runs in the inning. However, run-expectancy can actually give us even more exact data. It can tell us the precise chances of scoring 0, 1, 2, or more runs based on the base-out state as well.

For runner on 1st, none out, again, our run expectancy is 0.86 runs. Here's a list of the probabilities of the number of runs scored in the inning.

 Runs Probability 0 57.60% 1 18.94% 2 12.29% 3 6.09% 4+ 5.08%

Let's compare that to the situation of a runner on 2nd and one out, with a run expectancy of 0.68 runs.

 Runs Probability 0 59.39% 1 24.63% 2 9.28% 3 4.05% 4+ 2.65%

The case against bunting is apparent. You've drastically reduced your chances of scoring multiple runs in an inning. You've also increased your probability of scoring 0 runs by a slight amount (1.79%). However, you've actually increased your chances of scoring exactly one run by 5.69%. Situationally, with a weak hitter at the plate with a poor platoon split down one run in a late inning, a bunt might actually help you. Of course, bunting means you're playing for the tie at that point rather than looking to score multiple runs and take the lead, but if you have a strong bullpen it just might be a sound strategy. Still, it seems like something that would be helpful only in very specific situations. Of course, it still increases the chances of scoring 0 runs, which still hurts your chances of even tying the game. So even in that situation, I'm not sure I'm ready to defend the sac bunt with one runner on.

But what about bunting over runners on 1st and 2nd? The run expectancy for runners on 1st and 2nd and no outs is 1.47 runs, and the specific breakdown is as follows:

 Runs Probability 0 36.99% 1 22.94% 2 16.27% 3 12.23% 4+ 11.57%

For runners on 2nd and 3rd and one out, the run expectancy is 1.36 runs, and the specific breakdown is as follows:

 Runs Probability 0 33.26% 1 27.34% 2 22.28% 3 9.11% 4+ 8.01%

Now we're getting somewhere. You've still reduced your overall run expectancy. But you've decreased your chances of scoring 0 runs by 3.62%, so you've increased your likelihood of scoring at least one run. What's more, you've increased your chances of scoring exactly one run by almost 5%, and exactly two runs by 6%! Basically, the sacrifice you're making is increasing your probability of scoring 1-2 runs at the expense of scoring 3 or more. So in a close game in the later innings and runners on first and second, it (and it hurts to say this) might make sense to bunt them over.

There's one more factor that we're not considering: the defense still has to make the play on the bunt. A not insignificant percentage of bunts end up going for errors or hits. Fangraphs actually keeps a stat called BUH%, which is defined as "bunt hits/bunts". Note that this includes ALL bunts- both bunts that were meant to be attempted hits and bunts that were meant to be sacrifices. For the AL (the numbers are totally different for the NL due to pitchers bunting so often- not a single NL team is in the top 12 in BUH%), here are the top 5 teams in terms of giving up bunt hits:

 Team BUH% Yankees 41.00% Tigers 40.90% Astros 36.00% Mariners 35.60% Indians 35.10%

Think about it: batters who drop a bunt on the Yankees are batting .410 on those bunts. That's insane. I'm not saying that people should be bunting all over the place, because a huge amount of that success is clearly based on the element of surprise. But assuming that bunting hurts your offense is also assuming that the bunter will be out. If the runner gets a hit on the bunt, it obviously helps your offense significantly. For the record: Matt Garza's BUH%? 40%. This doesn't even include the times the runner reached on an error (see: Jerry Blevins last night).

In other words, a bunt with runners on 1st and 2nd in a very close game might be a net positive in and of itself, but if you've got a legitimate chance of getting on anyway, it might make a lot of sense. A sacrifice bunt still hurts your chances of having a big inning, but in a close game, it might actually have some legitimate utility. Maybe I owe that dad in the barbershop a (very small) apology.