The “Back to the Basics” series is designed to explore the foundation principals of statistical  analysis across the four major American sports. The series will provide readers with an  understanding of how teams approach roster construction and why certain decisions are made both on and off the field. Readers will also be directed to additional information sources, such as websites, books, or even magazine articles that could substantially increase their knowledge of the subject at hand.​

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Bunting and Run Expectancy in Baseball

In this post, I attempt to uncover why "sabermatricians" have such a negative view on sacrifice bunting in baseball. Finding the answer involved diving into a number of concepts, ranging from base-out situations to run expectancy. In the end, I found that the answer is more complicated than initially expected. Going beyond the most basic answer dictates that sacrifice bunting isn’t always a bad thing. However, teams that choose to sacrifice bunt are giving away outs, which often decreases an offenses chance of producing runs. 

The argument against the sacrifice bunt may be best portrayed by examining Tom Tango’s original Run Expectancy Matrix. The Matrix examines both the likelihood of scoring a run and the average number of runs a team scored given various base-out situations and eras of play. (The run-expectancy matrix developed by Tom Tango has been fiddled with and re-engineered by a number of statisticians on the web, but the original is still the best [in my opinion] visual tool available for explaining this concept.)

The chart above describes the average number of runs scored when given various base/out situations. The Base Runners section depicts all possible base runner situations. For example, 1B _ 3B indicates that there are runners on 1st and 3rd.  We can determine the average number of runs scored based on the base out situation by finding the corresponding "Out column" to the right of the Base Runner section. Returning to our previous example, if there are runners on 1st and 3rd with no outs, an offense will score, on average, 1.853 runs. 

Tango’s Matrix was not predictive in nature, but rather an average of data compiled over the stated period of time. However, the large sample size allows the table to be used as a tool for analyzing in-game decisions even today. This table is based on league averages, but it can be adjusted and tweaked based on the offensive nature of each MLB team.

The issue with the sacrifice bunt is that a team decreases the expected number of runs it can generate by giving up an out.  For example, by succesfully sacrifice bunting a runner on 1st to 2nd, a club actually decreases the number of runs it expects to score in the inning from .941 to .721.

This type of decrease in expected runs is consistent throughout the table as long as the following assumptions are made: (1) runners only advance one base; and (2) each batter is considered an average MLB hitter. (Please note that assumption 2 concerns an average hitter as opposed to a replacement level hitter.) The general argument is that when a team chooses to sacrifice bunt, it is decreasing the number of runs it is expected to score in the inning. The tradeoff of the out is not worth advancing the runners.

However, as sports economist Andrew Zimbalist points out in a recent podcast, “[w]hat’s true on average isn’t necessarily true in every circumstance.”  Tom Tango’s research actually takes this into account in another table in his matrix which depicts the chances of scoring a run in a given base/out state.  Bear in mind that this means the table depicts the chances of scoring one run based on the given base/out state.

As you can see, this table shows that the sacrifice bunt actually can increase the probability of scoring one run in some base/out states. For example, if there are no outs and a runner on 1st, a team can increase its odds of scoring one run slightly by sacrifice bunting the runner over to 2nd and giving up the out. However, this is not true if the sacrifice would be the second out of the inning.

In no scenario does the sacrifice bunt increase the odds of scoring a run if you are going from one out to two. Again, this is under the assumptions that runners only advance one base and that each hitter is a league average caliber hitter.  

            

Now, this is examining the sacrifice bunt on its most basic level. There are scenarios when sacrifice bunting is a completely viable option for a club. An extreme example would be a pitcher sacrifice bunting runners over in most scenarios. The idea is that the pitcher is so far below a league average hitter that the odds of him adding an out which does not advance the runners is so great it is more beneficial to give up the out to advance the runner. For example, if the pitcher or pinch hitter comes up with a guy on 1st and no outs and strikes out, the odds of generating a run fall from .411 to .284.  However, had he sacrificed, the odds of scoring with a runner on 2nd and one out are almost 50% better than leaving a runner on 1st with one out [.418 v. .284]. Another scenario where sacrifice bunting may be beneficial is in late tie-game situations where a team is not necessarily concerned with generating as many runs as it can, but rather it is attempting to add just one additional run.

Therefore, a manager must consider at least the following factors when determining whether or not to call for a sacrifice bunt:

                                    (1) Game Scenario

                                    (2) Hitting Ability of Current Batter

                                    (3) Hitting Ability of Next Hitters

                                    (4) Bunting Ability of Current Batter [Odds of successfully sacrificing]

                                    (5) Baserunner Speed [Could he score from 2nd on a single?]

These are just some examples of how sacrifice bunting is actually a scenario by scenario decision. There are a number of different variables that need to be considered, many of which are outlined here. However, in general, giving up an out will decrease the number of runs a club can expect to score in a given inning no matter what the scenario is. Bear in mind that, throughout this post, we have been talking about the sacrifice bunt specifically. There are numerous other scenarios where bunting in general is beneficial. For example, this post from FanGraphs cites bunting for a base hit, a well-timed squeeze play, and beating an over shifting defense as additional scenarios where bunting could be beneficial.