Recently, Tigers fans have been fuming with some of the recent sacrifice bunts ordered by their fearless leader Jim Leyland. One very curious bunting incident occurred on August 3, when our savior Alex Avila was ordered to lay down a bunt in the fourth inning to move up Jhonny Peralta and Ryan Raburn to 2nd and 3rd. Was this the correct move? When are there situations when it is appropriate to bunt?

As a man of baseball tradition who plays by the books, Leyland may not put much thought into the numbers, but we sure will here! This may not be as fancy as charts and graphs, but will hopefully provide some insight and entertainment. We will examine when it is an appropriate situation to bunt, and how bunting has affected the Tigers recently.

**When is it appropriate to bunt?**

We will first look at bunting from the perspective of win probability. It is fairly safe to make a conclusion that bunting in a close game becomes relatively more effective as the game progresses, as the possibility of future runs scoring is gone, giving the possible run scored by moving up the runner more value. We will thus examine the prospect of bunting in the 9th inning with the score tied.

We use this WPA Calculator from the Hardball Times to make these calculations. Note that this calculator essentially assumes a homogenous lineup of batters, so bunting may be more effective than this calculation yields if a weak batter attempts a bunt.

First, we will consider moving the runner from first to second with no outs. We will assume the low run environment of 3.0 runs per game, just for the sake of giving bunting a chance to prove effective in this scenario. However, we see that if the bunt succeeds, the WPA of this play is -0.0075, so this strategy does not pay off. From this perspective, even in the most dire of situations, bunting to advance a runner from first to second is poor strategy.

There may be something to gain from advancing the runner from second to third in this run environment, as the WPA of a successful bunt is 0.0283. However, we also have to see what happens when the bunt fails, which we will assume is a fielder's choice that results in a man on first. This play has a WPA of -0.1738, which is a lot to lose. In order for this play to be worthwhile, you would need to be at least 86% sure that the bunt would be successful. For reference, the average bunter from 2005 had a success rate of 77% (ref), so a very good bunter would be required to make this worthwhile; no team had a bunt success rate of at least 86% in that year.

The most fruitful situation for bunting comes from advancing runners on first and second to second and third. The WPAs are described in the table below, along with looking at different run environments. For reference, 4.5/game is about the MLB average now.

These results show that bunting may be a viable strategy with runners on first and second, especially with a good bunter. Remember that we did these calculations only for the 9th inning though, and with the score tied. The numbers change when the bunting team is down a run, and it turns out that bunting is not quite as effective in this situation, but still viable.

So what can we conclude from this WPA analysis? In the proper run environment, that is, with strong pitching or weak hitting, a bunt may be a viable option. Also, it its most effective with runners on first and second, although this has been known for some time.

**Run Probability**

The problem with the assumptions we make is that we are assuming a certain run environment in a certain inning. While fair assumptions, let's make another set of assumptions that are more primed to the ultimate purpose of bunting: scoring one run. The intuition used here is that bunts generally lower the expected number of runs in exchange for lowering the variance. The added out may harm the average number of runs scored, but it also may lower the chance of a very low and very high scoring inning, which could improve the probability that at least one run may score.

To do this, we will use this run expectancy chart provided by Tango. We are interested in the 1993-2010 table which gives the chance of scoring at least one run at a given base/out state. We will be interested in the shaded values: yellow values are our possible situations, green values are successful bunts and red are unsuccessful, with the orange value being ambiguous.

Base Runners | ___ | 1__ | _2_ | 12_ | __3 | 1_3 | _23 | 123 |

0 outs | 0.293 | 0.441 | 0.637 | 0.643 | 0.853 | 0.868 | 0.866 | 0.877 |

1 out | 0.172 | 0.284 | 0.418 | 0.429 | 0.674 | 0.652 | 0.698 | 0.679 |

2 outs | 0.075 | 0.135 | 0.230 | 0.237 | 0.270 | 0.288 | 0.280 | 0.334 |

Like before, we calculate the break even point. Here, I use the acronym RPA to measure the gained probability that a run scores.

By this metric, we see fairly similar numbers as before, the situation with man on 2nd slightly improves, and 1st and 2nd is a little worse off compared to the average run environment. I calculated the break even rate here for 1st just for laughs.

One thing you may have noticed throughout this article: I only consider two particular outcomes, the expected bunt outcome, and an out with the same base state. There are of course, many possibilities with a sacrifice bunt, both better and worse than these situations, so while these stats may not be exact in this sense, they should prove to be a guide to finding how effective sacrifice bunting is.

**How has it affected the Tigers?**

After looking at all of these bunting situations in the 9th, we now look at the Avila sacrifice bunt on August 3 in the 4th inning, a call that was highly debated after the game. Since there was a 3-2 lead for the Tigers, using the second model where the goal is to get just one run is not very applicable, so we analyze this play with WPA. According to the Fangraphs game log, this surprisingly had no effect on the game, with a WPA of 0. While this seems to make the play seem not so bad, we should also consider this:

- WPA assumes an average lineup, and Avila has been well above average this year.
- The Rangers have a strong offense, and sacrifice bunting will reduce the variance of runs scored for that inning. This reduces the chance of having a big inning, which is more valuable in higher run environments.
- Our next batters were Betemit and Jackson, neither are better than Avila.
- Bullet points make everything better.

So after all this statistical analysis, I use my better judgment to show that this bunt was in fact, a bad play. Oops.

More recently, Jackson bunted in the 8th against the Orioles with a one run lead, advancing Betemit to 2nd with one out. Despite how bad of a play we made out the sacrifice at first to be, this play had a mostly harmless WPA of -0.013, but that is probably a factor of already having a lead late in the game.

You'd be hard pressed to find a sacrifice bunt with the Tigers where our WPA has actually increased this season, outside of the bunter reaching. So what's the lesson here? Numbers make a good case in showing that in most cases, the sacrifice bunt is not a good decision. Keep in mind that numbers don't always paint a complete picture, and remember to keep track of what you assumed to get those numbers. Hopefully the front office continues to take the advice of BYB and sends Leyland a memo, but even so, I have a feeling he'll accept that advice as if a six-year-old girl were critiquing his lineups.