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“Doc, I had that dream again.”

“The one about the bullpen?”

“Yeah, I’m walking out of the dugout to go get my starter. We’re up 3-2 in the seventh and I’m waving for Andrew Miller.”

“I see …”

“The door opens up out in right field, but this time they start playing "Dark Star" by the Grateful Dead and Harry Pavlidis starts jogging out from the bullpen.”

“Who is Harr …”

“He’s not even left-handed, Doc! He’s not even left-handed!”

“OK …”

“And I’m yelling at the scoreboard operator guy to play something else, as if that will get Miller to come out of the ‘pen.”

“How are you feeling at this point?”

“Panicked. I spent all this time calculating the proper way to have a leveraged bullpen and all of a sudden, it’s undone because they send the wrong guy out. And I’m standing in front of 40,000 people in the middle of the ballpark and they’re all laughing at me.”

“That sounds unsettling.”

“What do you think it means, Doc?”

“Well, was Miller warmed up this time?”

“Beg pardon?”

“Was Miller warmed up?”

“Well, I don’t know, the dream started with me walking out to the mound. I mean if I’m waving for him, it makes sense that I would have warmed him.”

“Tell me what happened this time.”

“Well, Doc, Harry Pavlidis comes in and throws some warmup pitches and then on the first pitch, he gets the batter to roll the ball to the second baseman and we get out of the inning.”

“So, despite your stress, it all worked out.”

“Yeah, I guess.”

“What do you think the dream is trying to tell you?”

“Well, it’s not finished, Doc.”

“Oh?”

“After the ground out to second, I went down the dugout stairs and I just had to figure out what was going on. I meant to go to my office, but I ended up walking and walking down this dark hallway. And I was trying to talk myself through it. How did I mess up the leveraged bullpen thing?”

“Did you figure it out?”

“No, Doc. I walked down the hallway a while, and I came to a door that had a sign on it.”

“Interesting. Could you read the sign?”

“Yes, which is weird for me. I don’t usually read things in dreams. It said …"

Warning! Gory Mathematical Details Ahead!

This has puzzled sabermetricians for years. Why don’t managers use their bullpens more optimally? We know how to quantify game leverage. We know that runners at second and third with two outs in the seventh inning with a one-run lead is a more important spot than a clean three-run lead at the start of the ninth inning, so why doesn’t the closer (or whoever is the bullpen's best reliever) come into the tight spot in the seventh?

Modern bullpen strategy has tended to be inning-based. There’s a closer for those ninth-inning close games. There’s a setup guy for the eighth. There are guys who pitch in the sixth and seventh. And there’s the LOOGY. During the playoffs, managers tend to get a little more creative, mostly borne of the fact that they start mistrusting everyone but two or three guys and they just ask those three guys to pitch all of the time.

But why not make a change? When it’s getting hairy, why not bring in the closer? Managers have embraced the shift. They are making better lineups. They’ve stopped bunting so much. Is it really too much to ask them to do this?

I think the leveraged bullpen is a fantastic theory. It makes mathematical sense. What I’ve come to realize is that it's a perfect example of something that works great in a video game and not in reality. And frankly, I blame the video games. They never make you warm the pitcher up! (And the ones that do usually have that option turned off as the default.)

But before we get to that, let’s ponder another problem. Time is linear. The seventh inning unfolds before the eighth inning presents itself, which is in turn followed by the ninth inning (and if necessary, the 10th). We want the closer to come into the point of highest leverage, but this whole linearity thing presents a problem.

I looked for the highest leverage index point that happened in the seventh inning for each team in all games from 2012-2016, with the criteria that it needed to be above 1.5. Any games that were already blowouts were discarded. If a leverage index value of at least 1.5 appears in the seventh inning, I found that this was also the highest leverage point in the game (from that point forward) in 53 percent of cases. So, yes, our manager could bring his closer in here to pitch the seventh inning, but if he did and the goal is to try to get him into the highest leverage point of the game, there’s a 47 percent chance that this isn’t it.

So, if our manager hits the “closer” button now, he very much runs the risk of having a bunch of people like me whining that he hit it too soon. If he gets into the eighth inning without using the closer and then a situation with a leverage of 1.5 or greater appears, there’s still a 40 percent chance that yet another moment will appear in a later inning (either in the ninth or in extras) that will be a greater inflection point.

Should the manager bring in the closer at the first sign of trouble because the game might be won or lost right here or should he hold off a bit and maybe bring in his third-best reliever (if he’s not already out there)? The data points to the fact that this is essentially a coin flip decision. You could make the case that probabilitstically, the managers should favor pushing the “closer button” more quickly because in the seventh inning, he’d be right 53 percent of the time, but he’s going to be wrong a lot.

Plus, this kinda assumes that our manager has psychic powers. We’re assuming that the manager could hit the “insert closer” button at this point. When I do a retrospective look at what the highest leverage point was in the seventh inning, I have the advantage of hindsight to know that a relatively big moment happened. In other words, I can whine because I get to know what happened after the decision was/wasn’t made. I gotta say, all managers should manage that way. They’d be so much better at their jobs.

The problem is that when the seventh inning dawns in these games that eventually feature that high-leverage point in the seventh, there’s no way to tell that it’s anything other than a pedestrian medium-leverage seventh inning. But if our manager wants to have the “closer button” ready for pushing, that’s when he has to make the decision to get the closer warming up. Let’s prove that.

Warmup time varies from pitcher to pitcher. Some guys need more time than others, but for our purposes, we’re going to assume that our reliever needs three batters of lead time to get fully ready. (And yes, I know that at-bats are not a unit of time.) I looked at all cases in which the seventh inning ended up holding the highest point of leverage in the game for a team and where that point had a leverage index over 1.5. I then looked back in time to see what the leverage index was three batters earlier. In 47 percent of cases, the leverage index was below 1.0 at that decision point, and in 60 percent, it was below 1.2. There are a bunch of these seventh-inning, tight-spot scenarios in which the manager couldn’t reasonably have seen it coming.

Running that analysis the other way, I looked at all cases where, at the beginning of the seventh inning, the leverage index was somewhere between 0.8 and 1.2. Three batters later, I looked at the leverage index. In more than three-quarters of the cases, the leverage index was still below 1.5.

At the time a manager needs to make the decision to have his closer ready (i.e., tell him to warm up), we’re talking about a 75 percent chance that there’s not going to be a particularly high-leverage spot for him to work by the time he's ready. Even if one appears, it’s a 50-50 shot as to whether that’s the one spot in the game where we want him to be.

So yeah, our manager could have his closer warming at the beginning of the seventh inning if it looks like it might get a little hairy. And maybe he’ll be right one of those times, but most of the time the data tell us that he’ll be wrong. And if he’s wrong, he has a closer who’s gotten up and either has to be sat back down or perhaps brought into the eighth inning of a game that isn’t all that much in dispute, which is funny because the reason that we started yelling at the manager in the first place was that he was bringing his closer into a situation that wasn’t all that important.

Why The Modern Bullpen Will Persist

Using a bullpen strategy based on pitchers being assigned certain innings is tremendously inefficient and should be gotten rid of, except for the fact that the alternative is even more horribly inefficient and should be avoided at all costs. The leveraged bullpen is a great dream, but dreams don’t always come true. There will be times when our valiant manager will sense that something vile might be happening and have a high-leverage guy ready in a spot where he normally doesn’t have a high-leverage guy ready. That’s great on the day it happens, and I’m sure we’ll all take it as evidence that he’s surely capable of such feats (so why doesn’t he do it regularly!).

The reason that inning-based or matchup-based strategies persist is that managers have a pretty good idea of when the eighth inning is going to happen. If you want to play matchups, there is a handy, reliable guide on the dugout wall that details who is coming up to bat and when. There are some smaller tweaks that managers could make to the prevailing strategy that are still inning-based, including using the closer in tie games on the road (or tie games in general), and bringing him into the eighth or ninth inning, depending on what matchups might present themselves. However, when you do the #GoryMath, they actually wouldn’t add very much value.

Instead, I think that we need a small re-think on how we evaluate managers and their bullpen usage. We’re holding them to an ideal that isn’t really achievable. It’s time to put the idea of a leverage-based bullpen strategy to bed.