Baseball Therapy: Now With 50 Percent Less Math

Time to do a little less #GoryMath. Really.

On these pages here at Baseball Prospectus, it’s common that we spend a good amount of time agonizing over methodology and coming up with (let’s face it) rather convoluted ways in which the game of baseball can be understood better. There’s nothing wrong with that in the abstract. We always strive for the best understanding of the game—or as good scientists, the best understanding of anything, really—that we can find. Nope, nothing wrong with that in the abstract.

But there’s more to baseball (and life) than the abstract. I’ve argued in the past that the field of Sabermetrics is sorely lacking in what can be called “translational” research. How do we get from those lovely mathematical proofs to seeing something that’s actually put into action? It’s one thing to say that managers are using their closers inefficiently (and we can prove it!) to getting them to actually use their closers more efficiently.

The standard reason that’s always been given for “their” lack of speed in embracing New Age strategies was that… well, I guess we’re just too smart for them. (Pardon me while I pat myself on the back for having a Ph.D.) They don’t quite get the #GoryMath.

Wait, who exactly is it that doesn’t get the #GoryMath?

Warning! Gory Mathematical Details Ahead!

Let’s take an old Sabermetric bug-a-boo with a well-known solution. It is accurate to say that MLB managers, as a whole, are mathematically inefficient in how they use their closers. Insofar as the closer is usually the best reliever in the bullpen, it’s silly to save him to protect a three-run lead in the ninth, but not to bring him into a one-run game in the eighth inning or into a bottom of the ninth, tie game situation. But that’s how closers are actually used. In fact, managers should be using their best reliever at the point in the game where they will face the greatest leverage. Why hasn’t it happened?

Let’s for a moment assume that managers are a) smart and b) rational. The nice part about these assumptions is that they are both true.

The standard form of these arguments is to propose a model that is different from the current “traditional” closer usage (Model A), and then make some perfectly reasonable (or at least not all that unreasonable) assumptions about what might happen in the alternate model. For example, we might begin with a model (Model B) in which a manager makes a simple change like using his closer for two innings in a one-run game and letting his eighth inning guy handle the three-run saves in the ninth instead. Or perhaps Model C where he uses his closer in a tie game on the road. Or Model D where he simply “uses his closer at the highest point of leverage in the game. As my wife says “Totes obvs.”

You get extra credit points if you create a table like this:

Then comes the exasperated sigh of why, oh whyyyyyy, given this table, do managers continue with Model A when this table is right here. I’ll give you a hint, it’s not stubborn pride. It’s that the table is missing a column. We’re good at making the “extra wins” column, but very bad at remembering that a good cost/benefit analysis should also consider the costs.

Take Model D, using the closer at the point of highest leverage in the game. First off, while it’s mathematically correct to say that this is the optimal strategy, it’s a little more complicated than that. “The point of highest leverage” might be obvious in hindsight, but let’s say that it’s the seventh inning, runners at second and third with one out and a two run lead. Obviously a pretty high leverage situation, but is there another one coming down the road that might be higher? In real time, a manager has no way to know that. It’s plausible to create an algorithm which says something like “If this sort of situation appears in a game at this time, then the chances of a greater leverage situation appearing later in the game are at least low enough that the expected value… blah blah blah."

Consider how complicated that algorithm would have to be. Not impossible, mind you, but not something that can be written in two sentences. It takes a lot of bandwidth to deal with that sort of algorithm. That’s not meant as a sleight to managers. That’s just humanity. Then there’s the fact that it’s not like relievers can just be brought in fully ready at the click of a mouse button. Bases empty can become second and third in a matter of minutes and the proper reliever might not even be standing up. Plus, there’s evidence to show that relievers are more wild when they are dealing with a “sudden” save situation.

But beyond that, what would it cost a manager to have to be thinking about this leverage-based algorithm? There’s only so much that a manager can keep in his head at one time. He may have to think about pitch sequences to “politely suggest” to tilt the at-bat toward a groundball that would trade a run for an out. Maybe he’s also thinking about defensive positioning or strategizing how many outs he has left in his bullpen and whether it makes sense to go to the closer now against this particular batter or not. Trying to think about that complex algorithm would take away from his ability to do all of those things, and what the game plan is against this particular batter might be more important than who is doing the pitching against him.

Then there are models like B and C which are easier to put on an index card and may indeed be mathematically more sound. But again, let’s talk about the cost that goes along with those models. It’s easy for me the internet guy to suggest those models, especially when the manager has to do all the tough work like explaining to the closer that some of the save situations that were formerly “his” will now be going to someone else. Maybe the closer is cool with that and understands the research. Maybe he’s thinking about how this will affect on his next arbitration hearing. Maybe he’ll be kinda sour about that and become a grade A headache for the next two months. If the benefits of this new strategy are only a fraction of a win over the course of a season, is it really worth upsetting the whole clubhouse dynamic?

Oh yeah, the manager also gets to deal with the media on the night when the strategy goes haywire (there will always be a night when it does) and the team loses a tough one. You don’t have to do that. It’s not that any of these costs are insurmountable. The cranky closer might be mollified if the manager talks to him about his strategy in advance. The media can be politely told that they aren’t in charge. And maybe it’s worth putting in the effort to clear the way for the strategy (and for the manager to just get over it and do it), but it’s rare to see a column in that table attempting to quantify the effort that’s needed.

To put it into terms that those of you who are fans of #GoryMath might appreciate.

It looks like we’re only doing 50 percent of the math that we really need to do. When suggesting a strategy, you want the one with the best expected value in terms of runs or wins. If you’re suggesting a strategy that’s not likely to be adopted, then that lack of adoption is part of the expected value. A good mathematical accounting of a strategy will account for how it is likely to work in the real world, rather than how it works if everything were perfect. Sometimes, it’s better to advocate for the strategy that’s not as mathematically strong, but is more likely to actually be used.

Managers get the idea of leverage and it’s not a mystery to them. They’re just working from a different data set. I think the fact that we see so little adoption of these non-traditional bullpen usage patterns (and other Sabermetric favorites) is a testament to the fact that at the very least, managers believe that the cost column is rather big. It’s entirely possible that the reasons why they believe that are entirely irrational. Fine. Congratulations on being super-rational. But if there’s one thing I learned from my days as a therapist, it’s that it doesn’t matter if the person is being irrational. That’s their reality and sometimes you have to work within it.

If we’re to go beyond the abstract, Sabermetrics needs to understand what’s in that “cost” column and come up with ways to address those issues, rather than just leaving it to the manager to clean up that mess. How do you get the rules for the strategy boiled down to where they fit into ten words? What’s the best way to get a closer on your side when it comes to not being so tied to the save rule and to embrace the concept of the high leverage reliever, rather than the save collector? Are there workarounds?

Apparently, no one’s done that one yet, but that’s the real work left to be done.