So You Want to Bunt in Extra Innings
Last week, an interesting question got me wondering about Billy Hamilton and the new extra-innings rules. As it turns out, he’s a valuable runner to have on second base! So valuable in fact, that he projects to gain his team roughly 0.3 wins in a 60-game season just by being fast.
For the Giants, that’s great. For the other 29 teams in baseball (or 28 if the Dodgers end up rostering Terrance Gore), that’s no help. What should their strategy be in extra innings? I had all these run expectancy tables, so I decided to dive in.
First things first: let’s set the parameters of this discussion. I’m going to be considering two decisions. First, does bunting to lead off the inning make sense, and does that decision change based on whether you’re the home or visiting squad? Second, assuming bunting doesn’t make sense, what about stealing third? Presumably you’d steal with one out, what with not making the first out at third base and all, so we’ll focus on those two decision points: bunting to lead off, and stealing if the first at-bat doesn’t produce any advancement.
The value of being a home team is immediately evident when looked at through this lens. Consider a situation where the visiting team scores two runs in the top of the inning. Right away, a bunt goes out the window. That’s a big edge; in 2019, and excluding extra innings so that walk-offs don’t interrupt a team’s run scoring, teams that reached the position of a runner on second base with no outs scored two or more runs 29.1% of the time.
In other words, nearly a third of the time, bunting the runner over serves no purpose at all; your team will need two or more runs just to tie, so the position of that runner is nearly immaterial. Getting to act after knowing how many runs your opponent scored is huge.
Let’s talk tactics for the home team first, then. They’re more straightforward. When the visiting team scores two or more runs, the strategy is obvious: just play baseball. There’s a small subset of these where bunting might later make sense — consider starting the inning down two, then having your leadoff hitter smack a double — but those happen so rarely that we can round them down to zero. Instead, let’s focus on the times where the visiting team scores zero or one runs.
To get an idea of how often a bunt moves the runner over from second to third base, I looked at every time a batter bunted with a runner on second base, and only second base, since 2008. I excluded bunts with two outs, since those are aiming for a different outcome, but there were luckily few of those. 70.8% of the time, things went as planned — a successful sacrifice bunt. Another 14.3% of the time, something good happens; a bunt for a single, an error, or an attempt on the lead runner that isn’t in time. The remaining 14.8% of the time, it’s a disaster; an out without advancement. More specifically, the lead runner is out 4.1% of the time and the bunt results in an out without advancement another 10.7%.
Quickly, you might consider changing this data to account for the fact that pitchers won’t usually be doing the bunting. That’s fair, but the bunting data for non-pitchers in that spot is thin, and the batter data might be non-representative; a decent percentage of the bunts in that sample were surprise bunt attempts rather than telegraphed sacrifices. If you’d like, you can mentally make bunts more likely to succeed for the rest of this exercise. Onward!
When the game is tied to start the bottom of the 10th, playing the game “straight up” results in a win 60.8% of the time — the percentage of innings where a team scores at least once. If the bunt succeeds, that number ticks up to 64.8%, a meaningful improvement. By counting the odds of scoring at least one run after each of the possible results of the bunt, we can work out the overall odds of scoring at least one run, given a bunt attempt:
| After | Odds of Scenario | Odds of Scoring |
|---|---|---|
| Lead Runner Out | 4.1% | 27.7% |
| Bunter Out, No Advance | 10.7% | 40.8% |
| Hit/Error | 14.3% | 84.3% |
| Sac Bunt | 70.8% | 64.8% |
After netting everything out, the result is clear. Given the first plate appearance being a bunt, and using the overall success rate for bunts with a runner on second, the home team will win 63.5% of the time it enters the bottom of the inning tied. That beats the 60.8% naive probability of scoring a run. A bunt is the way to go!
We can do the same thing for a one-run deficit, the only other margin that makes a bunt reasonable. This time we’ll simply use the same run probabilities, but assign the team a 50% chance of a win if they end the inning tied (it should be a little bit more than 50%, but we’re painting with a broad brush here). That looks like this:
| After | Odds of Scenario | Odds of Tie | Odds of Win |
|---|---|---|---|
| Lead Runner Out | 4.1% | 11.2% | 16.5% |
| Bunter Out, No Advance | 10.7% | 22.4% | 18.4% |
| Hit/Error | 14.3% | 40.9% | 43.4% |
| Sac Bunt | 70.8% | 44.9% | 19.9% |
That works out to a 43.2% chance of a win overall. Playing it straight results in one run 31.7% of the time, and two or more runs a further 29.1% of the time, for a net 45% win probability. When down one run as the home team, bunting to lead off the inning is a marginally bad idea.
Whether you play it straight up or start with a bunt, one scenario is bound to eventually come up: when the first batter of an inning makes an unproductive out, the runner on second has an opportunity to attempt a steal of third base. With one out, this can be a big deal; complete the steal successfully, and your team’s odds of scoring at least one run in the inning climb from 40.8% to 64.8%. There’s a reason that the saying is “never make the first or third out at third base” rather than “don’t be out at third” — getting to third with one out is enormously valuable.
That’s after a successful steal; after an unsuccessful steal, it’s bad times. Two outs and nobody on is, well, a tough way to score runs:
| Runs | Percent |
|---|---|
| 0 | 92.3% |
| 1 | 5.4% |
| 2 | 1.6% |
| 3 | 0.5% |
| 4 | 0.2% |
| 5 | 0.0% |
| 6 | 0.0% |
Armed with that knowledge, we can do the math to see how often a steal needs to be successful. In a tie game, it’s simple: successfully stealing raises your odds of scoring in the inning by 24 percentage points. Those wins are replacing ties, for a net win probability gain of 12 percentage points. In other words, a successful steal increases your odds of winning from 70.4% to 82.4%.
On the other hand, teams only score any runs at all 7.7% of the time when they face a two out, bases empty situation. That produces a total win probability of roughly 53.9%. Win 12 percentage points on a successful steal, lose 16.5 percentage points if caught; you need to be successful 58% of the time to make the math work. Given that runners were successful stealing third 74.4% of the time in 2019, going a little more often makes sense. How much more often? That’s up to teams to figure out, because there’s no formula for how much more often you’ll be thrown out when you run more often. Suffice it to say, though, that you should be far more willing to steal. In an early-inning situation, steals of third need to be successful 71% of the time to break even. Home teams should be running wild, in a relative sense, when the game is tied.
Switch the scenario from tied to down a run, and it stops making so much sense. Moving from second to third increases your odds of winning from 29.6% to 42.4%. Getting caught lowers your odds to 5%. That works out to a 66% breakeven rate; still lower than the leaguewide success rate, but not by enough that I’m confident saying a team should attempt meaningfully more steals. Every deficit beyond one makes a steal worse and worse.
Why did we spend so much time going through the home team’s decisions? Because they inform the visiting team’s decisions. Here’s a grid of the home team’s win and tie probabilities for a given deficit, assuming they bunt when tied and swing away when down, the optimal strategy:
| Deficit | Odds of Scenario | Tie % | Win % |
|---|---|---|---|
| 0 | 39.2% | 36.5% | 63.5% |
| 1 | 31.7% | 31.7% | 29.1% |
| 2 | 14.6% | 14.6% | 14.5% |
| 3 | 7.5% | 7.5% | 7.0% |
| 4 | 3.6% | 3.6% | 3.4% |
| 5 | 1.8% | 1.8% | 1.6% |
| 6+ | 1.6% | 0.8% | 0.8% |
The “Odds of Scenario” column shows how often the visiting team will amass a lead of that many runs, assuming no bunting. To work out the totals, you can simply multiply the odds of each scenario occurring by the win and tie probabilities given that deficit and add them up. In aggregate, that works out to 36.9% wins, 27.2% ties, and 35.8% losses for the home team. That’s a 50.7% win rate for the home team — that 0.7% edge comes from the correct application of bunting in the home half of the inning. With those odds set up, we can work backwards to find the value of a bunt for the visiting team. For example, after a successful bunt, the visiting team’s run scoring distribution changes, which makes the home team’s win probability look like this:
| Deficit | Odds of Scenario | Tie % | Win % |
|---|---|---|---|
| 0 | 35.2% | 36.5% | 63.5% |
| 1 | 44.9% | 31.7% | 29.1% |
| 2 | 11.2% | 14.6% | 14.5% |
| 3 | 4.8% | 7.5% | 7.0% |
| 4 | 2.4% | 3.6% | 3.4% |
| 5 | 0.7% | 1.8% | 1.6% |
| 6+ | 0.8% | 0.8% | 0.8% |
Sum those up, and that works out to a 52.9% win percentage for the home team after a successful bunt. Wait, uh, what? Getting the bunt down as planned doesn’t work? Bunting as the visiting team is bad! Why? Think of it this way: when the other team starts with a runner on second, you really need to score two runs to be comfortable with your lead. Bunting lowers your odds of scoring two or more runs from 29% to just under 20%. Don’t do that!
I’ll spare you the fancy tables for what happens when the bunt doesn’t work as planned. Instead, I’ll just present the unified table. After taking into account all possible outcomes of a bunt attempt and the likelihood of each score after that, here’s the final breakdown:
| Deficit | Odds of Scenario | Tie % | Win % |
|---|---|---|---|
| 0 | 36.5% | 36.5% | 63.5% |
| 1 | 40.5% | 31.7% | 29.1% |
| 2 | 11.8% | 14.6% | 14.5% |
| 3 | 5.9% | 7.5% | 7.0% |
| 4 | 2.9% | 3.6% | 3.4% |
| 5 | 1.2% | 1.8% | 1.6% |
| 6+ | 1.1% | 0.8% | 0.8% |
That works out to a 52% win probability for the home team, against their naive 50.7% odds that come from the visiting team simply playing baseball. Again: don’t bunt as the visiting team. It simply doesn’t do what you want it to do.
There’s one further matter: should you steal third? As the home team, the breakeven got quite attractive in a tie game. As a visitor, your odds of winning the game are a mere 33.6% with a runner on second base and one out. At the risk of repeating myself, that’s because scoring twice is where you want to be. The odds of scoring two or more runs after an out are quite poor.
We know from before that the visiting team wins 47.1% of the time after a successful sacrifice bunt (the inverse of the home team’s 52.9% win probability). That means a successful steal increases the visiting team’s odds by 13.4 percentage points — stealing third with one out is equivalent to successfully sacrificing the runner over. Unfortunately, making an out at third is about as bad as you’d expect — it lowers the visitors’ odds to a mere 6.1%. That breakeven, 67.2%, means that steals of third in extra innings, for the visitor, are no different than steals of third in regular innings. Do so at your own peril, and only if you’re likely to be successful.
There was an absolute ton of math in this article. Some of it was messy, and I’ve no doubt explained it poorly in parts. Here, then, are some rules of thumb to follow:
- Visiting teams shouldn’t bunt to lead off extra innings
- Home teams should bunt to lead off extra innings only in a tie game
- Visiting teams should steal third at the same rate they would in regulation innings
- Home teams should aggressively steal if the game is tied with a runner on second and one out
It’s really as simple as that! If your team follows those four rules, they’re doing extra innings right. If they don’t, they have some explaining to do to the probability gods.
Ben is a writer at FanGraphs. He can be found on Bluesky @benclemens.
Yeah, I was kind of worried about that. I think MLB is not going to be ready for the amount of Bunting this rule change encourages. Hopefully, it will be resigned to the dustbin of history following this season and we can look back on it the way hockey looks back on the animated puck gimmick.
How do you account for situations where the batter attempts to bunt and gets to a two-strike count without putting a bunt in play, and then makes an out while swinging away? It seems that these situations leave you with a negative result that is not quantified as a bunt attempt, although attempting to bunt was a large factor in the bad outcome.
That’s an unending frustration in looking at bunts. The data on bunt attempts isn’t great, particularly on bunt attempts that were pulled back and taken — foul bunts are easier to get data on. Additionally, the vast majority of our data comes from pitchers bunting, so it’s not perfectly relevant here. Perhaps teams have a better database of these, or perhaps it’s captured somewhere I haven’t seen; for now, I just shade bunting decisions a little one way — if it’s close, probably don’t bunt because of the prospect of bad counts. Bunting in a tie game isn’t close here, though — 3% of WPA is enormous for a decision like that. Not enough to make Mike Trout bunt, but it’s a bunch.
The Dbacks have Tim Locastro. The fastest man in baseball by baseball savant sprint speed. So I think he’ll at least be as effective as Billy Hamilton. In fact there are 30 MLB players with similar or faster sprint times as Billy so most teams should be able to start extra innings with a very fast players, especially since teams will now know that there is a lot of extra value in rostering them.
Yeah, but many of those players will already have already been in the starting lineup and thus not available to pinch-run. Hamilton gains more value here than he normally has in that he’s a lousy hitter who isn’t likely to be starting or pinch-hitting in any given game, so he’ll usually be available for this unique pinch-running role when the situation occurs.
That is true. Though Locastro is definitely still a bench player and teams will know the extra value in having a speedster on the bench for this specific situation.
How quickly do all these guys get to top speed? Hamilton still just LOOKS like the fastest guy I’ve ever seen on a baseball diamond, and I wonder if it’s because he has crazy fast acceleration or something.
It’s intuitive enough if you really spend time thinking about it, but having the numbers to back it up is excellent. Great post.
Instead of bunting why don’t hitters just use the lost art of hitting behind the runner to advance to 3rd.
Every time this happens the announcer praises the batter for “hitting behind the hitter”. I always assume the hitter is just trying to get a hit and the ball happens to go to the right side. It would be interesting to see an article on this. Take a guy who has a good reputation for doing this and see if he hits to the right at a greater frequency in this situation.
It’s a LOT easier to get down a successful sacrifice bunt than it is to purposely hit a ground ball to the right side of the field, especially for right-handed hitters.
I would think this, but if hitting behind the runner is a skill to some degree, we’d need to account for the chance the ball in play becomes a hit to understand its effectiveness.
I think we’ll see a lot more bunting than that. One item you can’t account for in a general evaluation like this is the quality of the batter. Trout or Yelich are up? Not bunting. Orlando Arcia or Mallex Smith or Yolmer Sanchez? Probably bunting (especially since Mallex could beat it out if the defense hesitates). Then you have your high-K power guys like Grichuk – do you roll the dice on him getting hold of one? Or do you have him lay it down before he strikes out and doesn’t move the runner up? Grichuk is at least LH and a pullh hitter so he might well move the runner over anyway if he puts it in play, but what if the hitter is a dead-pull RH hitter? That guy is going to have trouble moving the guy over*. I suspect managers will also look at recent performance – if a guy is struggling, they’ll have him sacrifice.
That brings up another question. Do teams start to favor lefties in extra innings hoping the other team will pinch-hit righties that might hit to the left side? Do RH hitters start to rediscover hitting the other way?
Lot of interesting things might come out of this experiment.
*Pujols would be the best example of a dead-pull RH hitter but there is zero chance the Angels will ask him to sacrifice – 1 career sac and that came in 2001. IN fact, had to go look it up – it was in the 6/16/01 game against the White SOx, bottom of the 7th, Cards up 3 and the 1st 2 in the inning had reached. Larussa had Pujols (who had a 1.079 OPS entering the game and was hitting 4th mind you) bunt them over. Sox walked Bonilla (remember when he was on the Cards?) and Craig Paquette brought home 2 with a single. I’m just going to guess that Pujols took it on himself to sacrifice and Larussa told him after the game to never do that again.
Or to put it more generally, there are a lot of player-specific variables that matter in the situation above and beyond the averages that go into run expectancy.
Managers gonna have to manage.
I was wondering about this last week and played around with some numbers and this tool (https://blogs.fangraphs.com/introducing-the-batter-specific-run-expectancy-tool/) that produces a run expectancy table that adjusts for the hitter’s wOBA (so not exactly the same question as the article, but along the same lines).
Turns out if you have Trout on deck, EVERYBODY should bunt UNLESS you have one of the ten best hitters in the game currently at the plate. The break-even point would be Nolan Arenado, but everybody worse than him should be bunting (the list of exceptions being Yelich, Bregman, Nelson Cruz, Bellinger, Rendon, Ketel Marte, Springer, and Soto).
If you have a league average hitter on deck, NOBODY should bunt except for the truly awful hitters. In 2019 there weren’t any qualified hitters that had a low enough wOBA to make the bunt worth it. If you’re good enough to be getting fairly regular playing time, you’re good enough to swing away in that situation
I don’t like the rule change, but if it gets more small ball in extra innings, that is a positive. The visiting team should play for the 1 run, get the lead and then shut them down in the bottom half.
The home team gets to lead off the inning with a runner in scoring position too though. Did you read the article?
Yes, so you want to make sure you get a run in the top half. That is why I said, then shut the home team down.
Except you’re not that likely to be able to shut them down unless you score at least 2 runs.
Shutting them down means not letting them score at all. Do you actually think that runs will be scored every half inning in extras just because someone starts on second?
I’m starting to think bluerum29 is just an expert troll.
Because I like small ball and pitching?
I find it interesting that a 63.5% vs 60.8% difference gets the conclusion “bunt is the way to go!” but a 43.2% vs 45% difference is just a “marginally bad idea”
wouldn’t you consider the 2.7% advantage extremely similarly to the 1.8% disadvantage?
secondly… you use “every time a batter bunted w/ a runner on 2nd”. isn’t it likely that teams will be strategizing/playing differently than in a typical game?
“every time a batter bunted w/ a runner on 2nd” must be chalk full of other games where the game is not in the 8th or 9th or extra innings, and tied or within a run or two! not exactly representative of the decisions a ML team will have to make this year, imo
As to the first point, that’s very fair. Probably should have just said it’s a bad idea. 1.8% is way too much to give up unless you have a really bad hitter at the plate.
As to the second point, they might be strategizing differently, but I’m not convinced that that should affect the bunt success rate. It affects the bunt *attempt* rate massively, but given that sacrifice bunts tend to be telegraphed, the defense doesn’t exactly have a lot of decisions to make. You’ll probably see an increase in attempts to get the lead runner, but I’d guess those don’t have a lot of impact, because they’ll be pretty split between some extra gets and a lot more 1st/3rd no one out spots. All of these rates definitely have uncertainty bands around them, though, until we start getting data on the actual situation.
I guess what I meant to say was that the teams’ strategies after the bunt or steal will be far different than they would be in a normal game.
If a team bunts a guy over to 3rd base to make 1 out in the 7th inning, in a 2+ run game, then the opposing team is just going to pitch to the next guy.
but here, especially if the home team is at the plate… they may be more incentivized to walk the next batter… or bring in a new pitcher… the game is on the line right now! etc… so I don’t think just representing the run expectancy of your typical inning with a bunt is accurate here
Oh yeah that’s totally fair. I’m not convinced that many of those strategies are effective — a runner on third with less than two outs isn’t easy to work around — but it could shave a percentage point or two off of the runner scoring for sure.
“Given that runners were successful stealing third 74.4% of the time in 2019…”
That’s a self-selecting sample though, right? (All data from Baseball Reference):
2019 Attempted Steals of 2B: 1970/2687 = 73.32%
2019 Attempted Steals of 3B: 293/372 = 78.76%
2019 Attempted Steals of 2B by Players who attempted at least 1 steal of 3B: 1287/1712 = 75.18% (+50 successes for 2687 attempts)
2019 Attempted Steals of 2B weighted by attempts to steal 3B: 78.09% (+128 successes for 2687 attempts)
2019 Attempted Steals of 2B by Players who attempted 0 steals of 3B: 683/975 = 70.05% (-88 successes for 2687 attempts)
Players who attempted to steal 3B were more successful at stealing 2B as group than those who did not. I agree that the 58% break-even rate is much better, but citing a good success rate for the league as a whole for stealing 3B isn’t really the way to go. It does push the level of success required to include athletic big guys who can steal bases rather than just base stealers.
Which manager will be the first to walk the leadoff man to create a double play possibility?
If the leadoff man is the team’s best hitter, that’s not a bad idea.
Especially if the home team is batting and the game is tied
Did you really mean “naive,” or did you mean “native”? I’m wondering if I’m missing something here.
I think it was “naive” in the sense of “innocent” or “untouched,” which, because English is funky, dovetails with a connotation of “native” as “initial” and “unspoiled” (so, indeed, either would have worked with the avg reader, though I prefer “naive” as probability can be “blind” or “dumb,” as in “naive,” but probability cannot logically be “native” to anything). Thanks; I’ll go back to my English teacher cave now after voting you, Coleridge’s namesake, up for asking a question about rhetoric 🙂
(our softball team in grad school was called “The Ancient Mariners”)
As someone who uses “native” quite a bit more than the average person, in the sense of “intrinsic” or something similar, I thought the same thing. I just chalked it up to math lingo. Perhaps someone can google this for us.
Ben, what I loved about this article is how you summarized at the end. Four lessons learned from all that tedious arithmetic. I can’t believe some franchise doesn’t pick you up to do similar stuff for them. It would be a huge loss for all your FanGraphs readers.
Sigh, once again you guys have posted a flawed bunt analysis by erroneously assuming that the leadoff batter is an equal hitter to the guy on deck (as well as the guy in the hole). If the guy on deck is a significantly better hitter than the leadoff man, then the various run expectancy odds for bunting go up across the board, and vice versa. You also have to consider just how good a bunter the leadoff man is.
Like any other point in the game, deciding whether or not to try a sacrifice bunt is decided more by what batters are due up rather than merely by raw probabilities!
A point I made higher up and one that gets overlooked way too often. It’s a shame that so many of the insights of sabermetrics end up getting boiled down to short simple mantras when the truth is they are not quite that simple:
Bunting is bad
Walks are everything
Ks don’t matter
RBI don’t matter
IBB are bad
Pitchers don’t control batted balls
and so on. . . .
I don’t think this is nearly the problem it once was. Too many arrogant predictions have been turned on their heads for the early uncomplicated statistical “certainties” to survive. All outs aren’t equal, all methods of reaching base are not equal, and the ability of a pitcher to produce a low BABIP is a repeatable skill (sometimes). I doubt you find any writers here that would disagree with this.
Another point: is the run expectancy with a runner on second the same if the guy who is pitching is the one responsible for that runner on second, versus not? My point being – it might be shown (or not) that if the pitcher who put the guy on second is still pitching, then run expectancy is higher than if the pitcher is new, the thought being that the runner on second is a possible indication that the pitcher is either off his game or not as good as the average pitcher. In the 2020 game, that runner on second is, of course, never there as a result of the current pitcher’s doing.
https://docs.google.com/document/d/1aLg4nfo-6szU3JbFqa6qmdcEcswKPmOc5Vm4QaFnokA/edit
“The value of being a home team is immediately evident when looked at through this lens.
…. Getting to act after knowing how many runs your opponent scored is huge.”
Your analysis ignores that the defense can adjust strategy also. For example suppose the home team in a tie game in extra innings gets a runner on third with one out. Walking the bases loaded and playing the outfielders way in could be good strategy. On the other hand if the visiting team gets in that situation the chance of giving up two or more runs makes it probably not a viable strategy for the home team.
Regarding Billy Hamilton:
Isn’t the rule that the last out batter from the last inning has to start on second? That means you can’t just pinch run a burner unless you bring him in to hit with 2 out which would be super stupid because even with 2 out you are not giving away an out in a the game in the 9th as there could be a solo homer.
You can pinch run for the player who would be starting on 2nd.
Btw a great thing to do might be bringing in a lefty pull hitter to hit with no outs and let him rip the ball. If he hits an extra base hit that is great and if he rolls over it and hits a grounder into the shift that is great too as it moves the runner to third. Just needs to avoid the K which of course isn’t easy these days.