The Three Batter Minimum Rule Barely Matters

The concept of one-out pitchers suggests a kind of dystopian future for baseball. Generic Matchup Righty Number One (let’s call him Adam Cimber for the sake of this sentence) comes in to get the first out of an inning. He’s replaced by Adam Kolarek to get a lefty, then Adam Ottavino to get another righty, and then, look, I’m out of Adams, but maybe Adam Wainwright was the starter?

In any case, it’s hard to imagine a more boring inning, a more surefire way to get Johnny and Jane Millennial to change the channel to Fortnite or American Gladiators or whatever it is the kids like these days. That, more or less, is the theory behind MLB’s newest rule change, a three batter minimum for relief pitchers that will go into effect for the 2020 season. The rule requires a pitcher to face three batters, or pitch to the end of the half-inning, with some exceptions for injuries.

There’s only one problem with that narrative: that all-Adam inning doesn’t exist much in the majors, even without a three batter minimum. In fact, the one-out relief specialist just isn’t much of a role in baseball anymore. I investigated the numbers to find out which teams would be most affected. To my surprise, essentially none of them were.

First, let’s talk methodology. I looked at every relief appearance that fit a few general rules. First, the pitcher had to face two or fewer batters. Next, there had to be a plate appearance that occurred after their exit but in the same half-inning — if they were on the mound when the last out was recorded, they didn’t count. Finally, it had to be before September 1. We want to look at baseball as it’s generally played, not baseball as it was played in September — particularly given the changing rules for expanded rosters. This might miss a few situations — the new pitcher picks off a runner, for example — but it broadly covers everything. First, a leaderboard of which pitchers were short-timers most often:

Alright, Oliver Pérez might need to find a new job in 2020; on the other hand, he also made 48 appearances that don’t fall into this framework, so maybe not. But for the most part, there’s no one on a roster solely to get one or two batters out. There are pitchers who do it from time to time, sure; as long as opposite-handed pitchers are at a disadvantage, managers will try to optimize their matchups.

But 21 appearances of Olly Pérez doesn’t figure meaningfully into the sum total of all the baseball played this year. There were only 489 appearances that fit these criteria last season. There were 2,190 games in my sample, which means that a now-disallowed short-stint reliever figured into about a quarter of last year’s contests. Budget two minutes for the extra pitching change, and that’s around 30 seconds saved per game. Not exactly getting that millennial audience back, now, are we?

But maybe averaging across the whole league misses the point. What if some teams are abusing the role, bogging down a few select markets? Let’s look at the leaderboard again, but this time break it down by team:

Okay, yeah, still nothing. If the Indians play an average opponent, the rule saves 0.42 pitching changes per game. If they play the Nationals, it’s just over half a change per game. We’re not talking about the indelible fabric of baseball; just an occasional minute in a game measured in hours.

Of course, even if the rule isn’t a big time saver, it could still make sense if it’s interesting strategically. Will getting rid of these (mostly) left-handed relievers lead to interesting strategic binds?

Yesterday, Sam Miller approximated the impact on Pérez by walking through his game log and approximating how he would fare against a changed batter mix (more righties, fewer lefties). While I wrote this article having missed Sam’s yesterday (sorry, Sam!), I kind of wish I hadn’t — his approach is more intuitive. I took a different tack; rather than break down each individual batter, I set out to create a reasonable upper bound for how much this rule change might affect a team’s win percentage.

For each relief appearance, I looked at the reliever who threw, then took the weak side of his platoon splits and compared it to the strong side to simulate not getting a handedness advantage. This probably over-penalizes teams; most of these specialist relievers are used for short bursts because they’re truly terrible against opposite-handed batting, and it’s likely that the team could find someone who is better overall if they were forced to play the weak side of the platoon.

But we’re looking for a ceiling, and I think this definition works for that. Armed with the penalty to wOBA for each pitcher, I took their average leverage index. From there, wOBA can be converted into runs, and runs into wins, so we can come up with an upper bound estimate for the change in scoring due to these new rules.

Let’s take Perez as an example. Let’s say he had a game where he pitched to a single batter with a leverage index of 2. His wOBA against righties was 94 points higher than it was against lefties last year. To work out how many runs this cost the Indians in expectation, we can simply divide the wOBA by a constant to convert it into runs. We can then multiply by leverage, because the 10 runs to a win conversion you do in your head is leverage-agnostic. It works out to a 1.6% (percentage point) decrease in win probability for the pitching team. Then we just add up every appearance in the same way.

As you might expect, the Indians stand to lose the most in this methodology. But even then, the top five teams aren’t affected that significantly:

There are lots of fuzzy parts in my math; the platoon advantages could be better regressed, or a more realistic estimate for new playing time distributions created instead of my arbitrary handedness penalty. But the point is, the numbers are tiny. In aggregate, it simply doesn’t matter much for any given team. And that’s an upper bound estimate — in all likelihood, teams will simply pivot away from players with such extreme platoon splits in the future.

In fact, that pivoting is actually the most interesting thing going on here. At the major league level, the competitive environment won’t change. Teams will either use their lefties for an extra batter or roster fewer lefties and more righties. In either case, it won’t matter much.

But while things don’t matter at the aggregate level, they absolutely do at the individual level. Perez, for example, might be out of baseball next year. Teams will have less incentive to sign and develop deception-first relievers who profile as specialists. Prospect LOOGY’s are already rare, but they will likely go extinct as a result of this rule change.

So in the end, is it worth it? Honestly, I can see arguments from both sides. It’s a tiny change that won’t affect competitive balance but will save a few minutes every couple games. You’ll definitely notice it the first time it happens, but it might fade into the background after that, because teams let pitchers face bad platoon matchups all the time; this simply tilts things a little more in the batting team’s favor.

But from a theoretical standpoint, I dislike how inelegant the rule is. For a narrow benefit (30 seconds and some tiny sliver of runs per game), the league is junking up the rulebook. And not with something like a slide rule, where you’re not allowed to headhunt, either — with an arbitrary constraint on a central rule of baseball — whoever you want to pitch can pitch as long as they haven’t already appeared in the game.

So next year, the first time you see a big spot where a specialist reliever doesn’t come in, by all means marvel at it. But by June, you will have forgotten, and baseball will roll on just like it always has, only with a new flourish in the rules where none previously existed.