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If you made a list of the top six or seven stories from the first week of the 2016 season, I suppose that Trevor Story would be the top, uh, you know. Spaces 2 through 6 or 7 would be taken up by Bryce Harper’s hat, John Gibbons’ choice of gametime attire, Kyle Schwarber’s injury, Andrew McCutchen hitting in the no. 2 spot for the Pirates, Noah Syndergaard’s 95 mph slider, and perhaps Stephen Strasburg’s slider that doesn’t actually exist.

I don’t expect that anyone’s talking about Arodys Vizcaino of the Atlanta Braves. Vizcaino who was (re-)acquired from the Cubs prior to the 2015 season in exchange for Tommy La Stella, (re-)arrived in the big leagues in July of last year and by August, he was accumulating saves—well, what saves there were there to be accumulated on a team that finished with 95 losses—and striking out more than a batter an inning. That used to sound a lot more impressive, but let’s give credit where it’s due. Vizcaino is rather gifted in getting 7-year-olds keeping score to write the 11th letter of the alphabet in the appropriate row and column. That’s always a good quality to have in a reliever.

What’s interesting about Vizcaino isn’t Vizcaino (although I’m sure he’s a perfectly lovely human being). There are plenty of relievers with high strikeout rates nowadays. The interesting part is how the Braves have decided to use Vizcaino. In years past, Vizcaino would have been anointed as the Braves “closer,” not that the Braves project to be in contention this year, but every team has a few leads to protect now and then. Vizcaino would have been brought into the ninth when that lead was fewer than three runs. Most of the time, he would have protected that lead, and he would have collected a save for his troubles. Even on a bad team, by the end of the year, he could have had 30 S’s after his name.

There’s been an Avogadro’s Number of articles written about how the rigid “ninth inning only” closer is a horribly inefficient use of the guy who is supposed to be the best reliever on the team. And this year, the Braves(!) are finally going to do something about it. They’ve told Vizcaino that he is their ace reliever and that he will pitch to protect a close lead. The Braves innovation? Before the eighth inning, manager Fredi Gonzalez will look at who’s due up for the opposing team. If it’s the heart of the order, Vizcaino will go in and pitch the eighth. Someone else (on Opening Day, it was Jason Grilli) will handle the ninth against what is likely to be inferior competition and hopefully notch the “save.” If the 7-8-9 guys are due up for the other team in the eighth, Grilli will pitch to them, hopefully with Vizcaino ready to protect a still-extant lead in the ninth inning.

The plan is beautiful in its simplicity. Vizcaino still has a defined role and has some certainty around when he’ll pitch. There will be none of this "coming into the middle of the sixth inning because the iPad said so." Most nights that he pitches, he’ll throw one inning and then go take a shower. If he got hurt or couldn’t pitch one night, there are plenty of other guys in the Braves system or on the waiver wire who might not be as good, but are at least conditioned to throw one inning and leave, so spare parts—always a problem in baseball—are plentiful. And on top of that, the “new” role is being framed in terms of honor. One of the important pieces about the design of the modern bullpen is that it creates a hierarchy of roles, with the “closer” at the top. Whether that’s mathematically how you might design a bullpen, it fits nicely with how male culture works. In this case, the top of the hierarchy isn’t defined by pitching the game’s ultimate inning, but by pitching against the other team’s best hitters. The rest of you, if you want his gig, get better at pitching.

Sure enough, on Opening Day with the Braves facing off against the Washington Nationals, Fredi Gonzalez got to use his new strategy. With the score tied 2-2 going into the eighth inning and the Nationals scheduled to send Anthony Rendon, Bryce Harper, and Ryan Zimmerman (their 2-3-4 hitters) to the plate, it was Vizcaino coming in from the bullpen. Vizcaino issued a walk to Harper, but otherwise deposited a goose egg on the Washington side of the scoreboard. Job done!

It probably also helps that the other guy in the eighth-ninth tandem, Jason Grilli, who will be asked to handle some ninth-inning situations, has done so before. Of course, on Opening Day in the ninth, after the Braves took the lead in the bottom of the eighth, Grilli came into the ninth and coughed up the tying run. It’s hard to get a good read on whether the well-referenced “closer mentality” exists or not. We can imagine though that pitching the ninth inning comes with the added psychological burden of “well, if I screw up in the eighth, the offense might bail me out in the ninth, but in the ninth, it’s all on me.” Whether or not that’s “real” or not, it’s at least comforting that Grilli has shown that he isn’t affected.

No, this isn’t the perfectly optimized bullpen, but is it an improvement over the ways things are now?

Warning! Gory Mathematical Details Ahead!

When we investigate this one, it’s important to pause and make sure that we’re doing it right. This one sounds easy, but it’s not. For one, we’re used to modeling outcomes in terms of the number of runs that a strategy would either produce on offense or allow on defense. There’s nothing wrong with that per se, but too often, we model those runs the way that WAR does it, using runs that have been stripped completely of context. The thing about bullpen usage is that often, the context that a pitcher is brought into is the entire point of the strategy. The fact that we have closers in general is a tip of the cap to the fact that—while it’s never a good idea to give up a run or two—giving them up in the ninth inning of a close game is a particularly bad idea, because you might just lose the game.

It’s also easy to think of the problem as an exercise in aggregate probabilities. For example, using the Braves’ Opening Day situation, at the time that Gonzalez made the choice to go to Vizcaino in the eighth inning, the only thing that was certain was that Rendon, Harper, Zimmerman, Daniel Murphy, Jayson Werth, and Wilson Ramos would all have a chance to bat at least one more time. While it was too early in the season to get a bead on what the 2016 versions of each player might look like, we have a track record on all six and could create some reasonable probabilities for what to expect.

If we accept that Vizcaino is a better pitcher than Grilli (even leaving aside the details of whether Vizcaino/Grilli has a particular pitch in his arsenal that Bryce Harper is particularly vulnerable to), we might assume that matching up Vizcaino with Rendon/Harper/Zimmerman (and possibly Murphy) will dull their edges a little bit, at least relative to Grilli. But, Grilli will still have to pitch. Let’s over-simplify this for a moment. Let’s assume that the Nationals will all perform at their 2015 levels, and Vizcaino is good enough that hitters will hit 10 points below their general OBP (completely made up). Against, Grilli, hitters will perform at their average. Here’s the expected OBP for each hitter.

Nationals Batter (2015 OBP)

Vizcaino pitches 8th, Grilli 9th

Grilli pitches 8th, Vizcaino 9th

Rendon (.344)



Harper (.460!!!)



Zimmerman (.308)



Murphy (.322)



Werth (.302)



Ramos (.258)



* – before you write it in the comments, yes… I know someone could get a hit. This is an illustration. Keep reading.

If you sum those up, they are exactly equal. We would expect exactly as many on-base events whether Vizcaino pitches the eighth or ninth. So, the strategy has no benefit? Au contraire!

The trick to understanding this one is in modeling Vizcaino and Grilli’s actual jobs: getting three outs, ideally before a run crosses the plate. We know that in an encounter between any pitcher and hitter, what ends up happening is a mixture of their two talent levels (and a healthy dose of randomness). Despite the old saw that good pitching beats good hitting, it’s actually more likely to be the reverse. For most of the base outcomes of an at-bat (strikeout, walk, groundball vs. fly ball), it’s about a 2-to-1 split between the batter and pitcher in terms of whose variance explains what happens. Despite the imbalance, it still means that the pitcher isn’t completely helpless and he does have a good amount of say about what happens, even if it isn’t the majority. Good pitching can blunt good hitting a bit.

But good pitching doesn’t have to completely dominate in order to succeed. Consider for a moment that even the best hitters make outs 60 percent of the times that they come to bat, and last year, an average hitter made an out more than 68 percent of the time. A pitcher’s job is to get three outs. The offense’s job is to score runs, though absent a home run, to accomplish this they usually need two or three guys to do something other than make an out.

When you model it like that, there are consequences that need to be taken into account. Let’s use “two guys don’t make outs” before three outs are recorded as a proxy for scoring a run. If we assume that everyone in the lineup has an “effective” OBP of .290, the chances of two or more out of four guys not making an out (because if only one out of four does, the inning is over) are 33.1 percent. Here’s a table showing what that looks like with other OBPs.

Effective OBP

Chances of “scoring”













As you climb the ladder, each probability number gets a little further apart from the last one. This shouldn’t be surprising to anyone. It’s the entire reason why the good hitters are listed close to one another (and near the top of the lineup) in general. The best way to score runs in baseball is to “bunch” good events together, and bunches are more likely to occur in a row of three or four good hitters.

In our overly simplistic world where we assume that Vizcaino knocks 10 points off of the other team’s OBP, but where we can only use that super-power for one inning, we want it to be in the inning where the better hitters will be coming up. When you take the edge off of better hitters, you reduce the chances of a cluster of hits/walks happening by more than if you take the edge off of bad hitters. Mathematically, it makes sense.

Of course, a second look at the numbers shows that the amount that you actually save by the new strategy is tiny. Using Vizcaino against the good hitters in the eighth might save 1.78 percentage points worth of a chance of the other team scoring vs. the 1.70 percent of a chance he would shave off of lesser hitters in the ninth. The math here is admittedly a little slapdash, but it’s pretty clear that the effect size is actually pretty tiny. The Braves might have 40 save situations this year, and we’ll assume 20 of them where Gonzalez would employ Vizcaino in the eighth rather than the ninth. Even if each time Fredi Gonzalez uses this more efficient strategy, it nets out one-tenth of 1 percent less chance of a blown save, then over the course of a season, that means a 2 percent chance that the Braves will net out one less blown save than they otherwise would have gotten. I won’t swear to that exact number, but we’re talking about a small fraction of a win here.

Using Vizcaino based on who’s coming up, rather than the inning is the mathematically sound thing to do. It’s just… well, that’s all you really get out of it.

Is That All There Is?
In the past, I’ve evaluated other “more efficient” closer models and found them to indeed be more efficient, just not that much more. For all the critiquing that we do of managers and their bullpen strategies, there’s just not a lot to be squeezed out of this one. In this case, the Braves are doing the mathematically proper thing, and they might as well do it because it costs them nothing to do, but this isn’t the move that’s going to get them five extra wins. Sorry, Atlanta. (Then again, most managerial stratagems moves actually have limited on-field value when you do the math.)

Baseball fans have a penchant for obsessing over who gets saves (I blame the fantasy people) and saves still get pitchers paid. What we’ve learned over the past decade or so is that Jerome Holtzman’s creation is neither a good indicator of how good a pitcher actually is or what his impact was on the game in which he got the save. The save mostly tells us when a pitcher was on the mound, i.e., the ninth inning. That’s different than saying that a good reliever isn’t a good thing to have or isn’t worth paying for. But the question of whether he’s good or not shouldn’t be measured in how many games he saves.

At the risk of sounding like an episode of Effectively Wild, imagine what baseball would be like if suddenly, everyone forgot that the save rule existed. There would still be a bunch of one-inning-and-done guys around and some of them would be a few standard deviations better than the mean. Would managers still use them only in the ninth? If there was still pressure to hold a guy back for a save ninth-inning situation, it would probably come in the form of how psychologically horrible it is to let a game get away in the ninth inning like that. There’s probably some validity to that. But, I think that there would be an equal pull on managers to rationally say “Well, if the other team is sending up the heart of the order in the eighth, the game is really going to be won or lost there.” And that’s the beauty of the Braves system. They’re playing the game like the save rule doesn’t exist and that the only important thing is actually winning the game. Which… y’know…

If the Braves can make this one work, then perhaps we can look forward to a world where teams don’t manage to the save rule and the “closer” as we know it returns to being a relief ace, even if he’s just a one-inning relief ace. But it’s possible that the Braves are pioneering something worth copying, even if no one was paying attention to it because of all the other stuff going on this week.

Thank you for reading

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Nice piece! (even though I was silently hoping that the conclusion would show a greater effect)

As you allude to, it's kind of amazing that it's the Braves that are doing this. One the one hand, they've got nothing to lose by trying it out this year, but historically they've skewed a little more traditional (at least in terms of their front office-speak). It will be interesting to see if the strategy expands, or at least sticks around, once the team is better.

The A's have done this with Doolittle and Madson already this season as well.
Mathematically, it makes sense! Those truly meaningful words seem to be missing from the "book" of baseball that so many old school baseball men still adhere to. I go back to Earl Weaver, and long before that as well. He understood the modern concept of the game when everyone else was still living in the dead ball era. He eschewed the bunt completely and his managerial philosophy of pitching, defense and 3-run homers looks like the game as it is played today. It is no coincidence that teams that are at the forefront of the mathematical approach to actually playing the game, the Astros and Pirates in particular, are ascending, while teams with dinosaurs in charge such as the Angels are falling behind.
Great article. Really good food for thought.
This is not a new idea. SABR guys have been talking about it a lot and Kevin Cash did it against Boston last year bringing in his closer in the 7th to face the middle of the order, his 8th inning guy in 8th, and 7th inning guy in 9th in a tie game and it worked... It's a great idea.