Updating the Pinch Hit Penalty, with a Few Rules of Thumb

Pinch hitting is hard. Baseball is a rhythm game, and pinch hitters are denied any semblance of routine. They’re on the bench, swinging a bat back and forth to get the blood pumping in their arms, and then just like that, they’re in the game. They might have been daydreaming about what they plan on ordering from room service, and here’s Jacob deGrom throwing 92 mph sliders. Good luck!

That’s the classical conception of a pinch hitter, and it explains why Tom Tango, Mitchel Lichtman, and Andrew Dolphin found a significant pinch hitting penalty in The Book. They found a 24-point wOBA penalty for pinch hitters, which is a large cost. That’s roughly equivalent to the platoon advantage a lefty gets when facing a right-handed pitcher.

That’s a pretty striking difference. When your team gets a lefty batter up against a righty pitcher in a big spot, it feels great. Imagine that pitcher being replaced by a left-hander. Feels pretty awful, right? That’s the same swing in effectiveness you get when a batter pinch hits rather than batting regularly.

You don’t always hear about this effect on broadcasts, because there are other decisions that go into pinch hitting. You’re getting a diminished version of whichever hitter you select, but other advantages can still tip the scales in a batter’s favor.

Platoon advantages matter. As I mentioned, going from left-on-left to right-on-left is worth as much as the pinch hit penalty, and that’s before considering the hitters; a powerful righty slugger replacing a banjo-hitting lefty shortstop is a no brainer, and you can imagine situations — your star hitter on his day off replacing a utility infielder — when the move makes sense even without picking up a platoon advantage. Christian Yelich, off the bench, is still a better hitter than Eric Sogard, regardless of who’s pitching.

That’s the conventional sabermetric thinking, anyway. The Book was published in 2006, a lifetime ago when it comes to player preparation. Hitters weren’t sitting on the bench drinking soda and smoking cigarettes, but short of that, it hardly resembled current baseball. Players now are treating the game like a science; they have dedicated warm-up routines, terabytes of video, and purpose-built pitching machines. Think you might be coming in to face a slider-happy reliever? You can swing at sliders in a cage under the stadium for 20 minutes to get ready.

To that end, I wondered if the pinch hitting penalty had changed. It’s poor form to assume old relationships in baseball still hold; they often do, but there’s nothing predestined about a pinch hitting penalty, and without checking, we can’t know if things have changed.

To look for changes, I decided to roughly replicate the pinch hitting study from 15 years ago. I took every pinch hit appearance where a right-handed batter faced a same-handed pitcher, to avoid platoon effect confusion. I looked at the results of those pinch hit appearances, and compared them to what we’d expect those same batters to do if we used their non-pinch-hitting seasonal lines.

For example, there were 1,622 right/right pinch hit matchups in 2019. After removing batters whose only plate appearances were pinch hits, 1,594 remain. In those plate appearances, batters compiled a .284 wOBA. If each batter had instead produced at their non-pinch-hit seasonal level, they would have put up a .295 wOBA. Thus, we can say that the observed pinch hitting penalty comes out to 11 points of wOBA.

A single year of data doesn’t say much. Two standard deviations of wOBA on 1,594 plate appearances is around 25 points of wOBA. Pinch hitting might be a huge penalty, or it might help batters, and our sample isn’t really big enough to say either way for certain. You might say, if you’re fond of sounding like an AP Statistics textbook, that using only data for 2019, we failed to reject the null hypothesis that pinch hitting has no effect on batter performance.

But let’s not talk like textbooks. That’s not a reasonable null hypothesis. Our priors are that a pinch hitting penalty does exist. There’s an equally valid null hypothesis that the pinch hitting penalty comes out to roughly 25 points of wOBA, and we couldn’t reject that either.

It’s a little early in the infinite (?) offseason to head down this particular Bayesian rabbit hole. Instead, let’s just look at a few more years!

So much for a convenient trend. If the pinch hit penalty has gone away, it’s all happened in the last year. That’s a silly conclusion, though. The right conclusion, to me, is that the penalty is there, just the same as ever. Change the technology all you want; it hasn’t had much of an effect on batters’ ability to go from 0 to 100 mid-game.

With that in mind, I thought it might be useful to come up with some pinch hitting rules of thumb. Useful to teams? Maybe not — managers already have their own calculus for pinch hitting, and one article isn’t going to suddenly change their mind. But maybe this will help you reason through pinch hitting decisions better, or at least let you know if that anguished screaming sound you made when Joe Journeyman stepped into the on-deck circle was merited.

First, if it’s a pitcher, it’s a good pinch hitting decision. We aren’t taking knock-on pitching effects into account here — we can save that discussion for a later date. From a pure value at the plate standpoint, you can’t ever get mad at a manager for pinch hitting for a pitcher.

With that out of the way, you should next think about platoon advantages. Is your manager going from a bad handedness matchup to a good one? If so, that’s a mark in their favor. How much of a mark depends on the handedness. If you’re bringing in a right-handed batter to face a southpaw, a situation which will come up more often given the three-batter minimum, you’re in luck; lefties hit for a .308 wOBA and 88 wRC+ against left-handed pitchers, while righties checked in at .331 and 104 respectively.

What does that mean in practice? Well, if two opposite-handed batters have the same overall skill level, you’d expect the righty to perform roughly 25 points of wOBA (or 15 points of wRC+) better. The math doesn’t quite work like that, because lefties are better hitters on average than righties and also face a higher proportion of opposite-handed pitchers than righties do, which means that their true-talent line is further from their lefty-on-lefty line.

But look — we’re approximating here. Rules of thumb, and whatnot. And there’s your rule — if a righty batter is a better overall hitter than the lefty he’s replacing, and he’s giving you the advantage, that’s a good switch. One example down, and three to go.

Next, what if you’re replacing a righty with a lefty to get the platoon advantage? This doesn’t work quite as well for you, because righties aren’t as disadvantaged by same-handed pitchers as lefties. This one comes out to 15 points of wOBA, or 10 of wRC+ — and probably a little smaller after accounting for the hitter populations.

So, here’s our next rule of thumb: for a lefty to replace a righty and gain the platoon advantage, he needs to be meaningfully better than the player he’s replacing. Replace a 100 wRC+ guy with another 100 wRC+ guy just to get a left-handed bat in, and you’re giving up edge. If the lefty is 10 points of wRC+ better than the righty he’s replacing, it makes sense. In between, it could go either way depending on pitcher and batter specifics.

What if you can force a pitching substitution with your pinch hitting? If you have a lefty at the plate facing a lefty pitcher, and can bring in a righty to face a righty pitcher, you’re getting a small edge. But it’s a minuscule one — the pinch hit penalty overwhelms it. You’d need a batter at least 15 points of wRC+ better, and perhaps closer to 20, before the decision starts to make sense. Don’t get cute hunting matchups.

Last, basically don’t pinch-hit with a same-handed batter unless a few factors line up. Your batter needs to be 20-ish points of wRC+ better for it to be clearly a good decision, and if you have that kind of batter on your bench, they’re best saved for a high leverage situation. To pinch hit for a same-handed batter, you need a great hitter and a big spot. Otherwise, it’s overthinking.

These are merely rough guidelines. While batters mostly don’t have platoon skill, some pitchers do. Against a lefty who is incredibly tough on lefties (or a righty-killing righty), teams should be more willing to pinch hit to gain the platoon advantage. Forcing the other team to make a substitution can be valuable if the pitcher coming in is much worse than the pitcher on the mound. And situation matters; bringing in a 5% strikeout rate pinch hitter to replace a 25% strikeout rate batter with a runner on third and fewer than two outs is probably a good call, even if the wRC+ numbers don’t line up.

But for the most part, these rules will get you where you need to go. Gaining the platoon advantage? Fine, though you won’t get a huge pickup unless you have a great pinch hitter. Not getting the platoon advantage? Don’t do it! Fifteen years on, the math of pinch hitting looks basically the same as it did in 2006.