Once a staple of a Major League Baseball team's arsenal, the sacrifice bunt has continued to see less and less use by season. Take a look at this graph from the Northwestern Sports Analytics Group (https://sites.northwestern.edu/nusportsanalytics/2021/04/02/is-the-bunt-dying/):
Why is this so? To many, a bunt seems like the only "correct" play when there is a runner on 1st or 2nd base with no outs. A runner on 2nd or 3rd base with only 1 out appears to almost guarantee a run. To fans, seeing an At-Bat (AB) end with the hitter striking out and not moving the runner over can be very frustrating. "WHY DIDN'T HE BUNT!" has almost become a common sentiment over the past few seasons where the sacrifice bunt has sharply declined.
Is the sacrifice bunt the "correct" play? To answer this question, we will first need to analyze the probability of the different outcomes of a plate appearance. For sake of simplicity, we will look at 6 possible events, and using 2021 MLB team hitting data from Baseball Reference, we can find their corresponding probability.
Out: 69.6%
Single: 13.8%
Double: 4.3%
Triple: 0.4%
Home Run: 3.3%
Walk: 8.7%
Now, we can use these outcomes to run a simulation of an inning of a MLB game. To keep things simple, we will make some assumptions.
There are no productive outs. i.e) Runners cannot move up a base if the hitter has recorded an out.
A base hit moves runners up based on the corresponding hit. i.e) Runners move up one base for a single, two bases for a double, and three bases for a triple.
Each sacrifice bunt is 100% successful.
Now, lets define two teams; Team Bunts always performs a sacrifice bunt whenever the opportunity presents itself, and Team No Bunts never bunts at all. Our first situation will be an inning with no outs and a runner on first base.
Let's see how Team No Bunts will perform in this situation. We will use the aforementioned outcomes and assumptions to simulate the inning 10,000 times in R and find the average runs scored per inning to see how many runs Team No Bunts is expected to score.
As expected, we have a distribution of runs that is highly skewed to the right. Due to the fact that an out is the most common outcome (69.6%), it will be very common to finish an inning with no runs. However, the indefinite nature of baseball implies that there will be instances where an abnormally large amount of runs are scored. In our simulation of 10,000 innings, the max inning score was 10.
More importantly, our expected runs per inning is 0.6187. Now, this is not the exact answer since we performed a simulation and did not calculate the theoretically correct answer. However, due to the 10,000 innings or trials, we can be fairly confident that this estimate is around the exact answer. Furthermore, 26.95% of innings in out simulation resulted in at least one run being scored.
Now, let's perform the same simulation with Team Bunts.
The expected runs per inning when bunting is 0.4504. That's roughly 0.15 runs LESS than the expected runs per inning when not bunting. Thus, using data from the average MLB team in the 2021 season, our simple simulation tells us that sacrifice bunting can actually hurt a baseball team. In addition, 25.61% of innings when bunting resulted in at least 1 run being scored. This is very close to the percentage when not bunting. However, there is no significant data to prove that sacrifice bunting can provide a competitive edge.
Our next situation will be an inning with no outs and a runner on second base. This is the controversial "ghost runner" extra inning rule that was implemented for the 2021 season and will continue in 2022. We will begin with Team No Bunts, and the same assumptions as in the first situation.
As expected, the expected runs per inning increases in this situation to 0.7145. This is roughly a 15% increase from not bunting in our first situation (0.6187). Furthermore, 36.53% of the 10,000 innings in our simulation resulted in at least one run scoring.
Let's see how Team Bunts does.
When bunting, our expected runs per inning is 0.6207 which is roughly a 38% increase from always sacrifice bunting in the first situation (0.4504). This increase is much larger than Team No Bunts' because our simulations assume that a single can only score a runner from third base. The single is the 2nd most common At-Bat outcome at 13.8%, and practically, we know that runners often score from 2nd base when a single is hit. However, for sake of simplicity, our simulations do not assume this which slightly devalues 2nd base.
That being said, the expected runs is still less when sacrifice bunting as opposed to not bunting. However, the main difference in the two situations is the percentage of innings that result in at least 1 run scored. When sacrifice bunting with no outs and a runner on 2nd base, this percentage is 42.64%, which is greater than not bunting (36.53%). In summary, while we would be expected to score more runs in a particular inning without bunting, it is more likely that a team scores any runs when bunting. What?!
Essentially, by preserving the out and not bunting, teams increase their chances of having a "bigger" inning and scoring a larger amount of runs. However, by giving up the out and valuing having a runner 90 feet away, it is more likely that at least 1 run score. Hence, the reason why you see many more teams bunt in extra innings in this situation, as opposed to during normal play.
Now, adding more stipulations to our simulations to having runners score from second when a single is hit or from first when a double is hit would probably increase this percentage for Team No Bunts. However, these simulations still gives us this valuable insight. The analytics tell us that the sacrifice bunt will continue to be phased out of MLB, and rightfully so. However, there still is and will always be a place for the sacred sacrifice bunt. And, who knows, maybe an important playoff game or World Series game will be decided by that old relic that is the bunt.
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