The Math Behind Intentionally Walking Juan Soto

At my old job, my boss occasionally held idea sessions. He wanted everyone to participate, and the point wasn’t to come up with something actionable, just to brainstorm. No suggestion was too ridiculous – sure, it might get picked apart in discussion, but the whole point was to suggest weird stuff and see what came out of it. Still, I can safely say that none of those judgment-free-zone ideas sounded quite as zany to me as “let’s intentionally walk the guy in front of Aaron Judge.”

That didn’t stop Stephen Vogt on Tuesday night. With runners on second and third base and one out in the bottom of the second inning, Vogt didn’t let Juan Soto hit. He put up four fingers to send Soto to first. His reward? A bases-loaded encounter with Judge, the best hitter in baseball. Obviously Vogt had a reason for his decision. I ran the math to see how well that reason agrees with theory.

In a vacuum, it’s pretty clear why this intentional walk was bad: It loaded the bases with only one out, increasing the chance of a big inning, and it did so with the presumptive American League MVP at the plate. But there were two reasons to do it. First, it took the bat out of Soto’s hands, and Soto is himself a phenomenal hitter, particularly against righties. Second, it created the chance for an inning-ending double play, which would have been a huge boon to the Guardians’ chances (they already trailed by two). If you squint, you can kind of see it; maybe these two choices are equal. It didn’t matter in Game 2, because the Yankees won going away, but if the Guardians come back to win the series, they’ll be facing New York’s best hitters in important spots again, so what Vogt chose to do Tuesday night might help us guess what he’ll do in the future.

I decided to work backwards to figure out what I would have done in this situation. First, I took projections for Judge and Cade Smith, who was summoned from the bullpen for this matchup. I adjusted both of those projections based on regressed platoon splits. Smith doesn’t have a ton of major league data to work with, but he’s pitched to an observed reverse split, and I forecast him to have roughly neutral platoon matchups going forward. Judge is about 5% better against lefties than righties, roughly average for a right-handed hitter.

With those projections and a modified log5 model, I came up with a grid of modeled outcomes. That looks like this:

From there, I calculated what each of those outcomes would do for Cleveland’s win probability. For example, a home run would make it 6-0 Yankees, and more or less end the game (5.4% Guardians win probability). A strikeout would make things much better (23.5% win probability). A groundout could either score a run or produce a double play, with roughly equal likelihood. Here’s what that looks like with all the win probability numbers filled in:

In aggregate, I get an 18.1% chance of Cleveland winning the game when Smith stepped in to face Judge. That’s largely because of a good chance of striking Judge out; most of the ball in play outcomes are pretty rotten for the Guardians. In reality, Judge hit a sacrifice fly, which was almost exactly the average outcome – our game odds gave Cleveland a 17.7% chance of winning after the plate appearance.

That’s a rough spot for the Guardians, obviously. But we’re not comparing it to 50% – they were already trailing and already had the dangerous part of the Yankees lineup coming up with runners on base. Things were already bad. To compare it to the alternative of pitching to Soto, I had to do some similar analysis. First, I created a matchup grid for Soto against Smith. I picked Smith instead of a lefty because I can’t imagine Vogt would want to use a worse reliever in such a big spot; Smith was the only Guardians reliever warming up, so this seems like a good bet. In any case, here’s the outcome likelihood grid for Soto against Smith:

From there, I just did some plug-and-play math. For each potential Soto outcome, I adjusted the base/out state, then used my grid of Judge’s potential outcomes from up above to further progress the game state. For example, after a Soto strikeout, I re-ran the Judge numbers with runners on second and third and two outs. After a Soto double, I re-ran the Judge numbers with a runner on second, one out, and a four-run deficit. I did this for all of Soto’s possible outcomes so that I could figure out how likely the Guardians would be to win in each case.

Some of these were easy — an unintentional walk is the same as an intentional walk, for example. Some are tricky – a groundout doesn’t always score the runner, so I’m guessing there. Maybe Smith would pitch Soto differently based on the base being open; maybe he’d pitch Judge differently based on what happened in Soto’s at-bat. These are just generalizations, with plenty of margin for error. But still, it’s worth doing the math, so I did.

Here’s the result of all that math, the likelihood of the Guardians winning, accounting for the fact that a Smith/Judge matchup will follow Soto’s at-bat:

Those are pretty intuitive results: If Soto gets a hit, the Guardians are worse off than if they’d just walked him. If he makes an out, they’re better off than if they’d walked him. Thank you, I’ll be here all week. But the really interesting part is that when you sum all of those up, you get a 19.1% chance of winning the game, a full percentage point better than the projected win probability after an intentional walk.

That feels strange, because Soto’s projected outcomes are strong there. We’re talking about a .267/.425/.428 batting line, a near-.400 wOBA. Intuitively, walking someone with results that good to set up a double play feels like a smart idea. The problem is that many of Soto’s best outcomes are walks. That’s what’s so tough about him: Plenty of plate appearances that would normally end in a strikeout or weak contact become walks thanks to his elite batting eye. That makes Soto a nightmare in spots where a baserunner is valuable. But when the pitcher’s alternative is intentionally walking him, those unintentional walks simply don’t matter. If you face Soto and walk him, no big deal! That was your backup plan in the first place.

All that said, the total increase in Cleveland’s win probability isn’t outrageous. One percentage point of win probability isn’t nothing, but it’s hardly a massive effect. It’s definitely small enough that other factors could make intentionally walking him a good decision, even if the math disagrees in a vacuum. For example, the Yankees were pretty likely to win anyway. Vogt also had something going for him that I can’t quantify for this exercise: Soto didn’t face Smith, so he isn’t building up a mental catalog of his pitches. The Guardians plan on using their bullpen a lot, so preserving a little mystery there has value. Down 2-0 in the series, there isn’t much room for error; every matchup between Smith and Soto is going to be meaningful. If you think that Smith is going to face Soto multiple times with the game on the line, maybe the added value offsets what the Guardians lost by forgoing a chance to get Soto out.

As is always the case when you’re splitting something so minutely, there’s a chance my math is wrong here. A little error could go a long way given the tiny effects we’re searching for. Additionally, the composition of both the Yankees and Guardians leans in favor of taking a risk; the Guardians are underdogs, so I generally like strategies that increase variance for them. But even with that caveat, I’m pretty surprised by the outcome. My initial guess was that thanks to Soto’s proclivity to walk even when you don’t want him to, pitching to him would be a far better idea than walking him. But his power and platoon splits, along with the fact that Smith is such an elite reliever that his outcome grid against Judge isn’t abysmal, make the math work, or at least make it close. So good job, Stephen Vogt. You did something that sounds completely crazy – issuing an intentional walk to load the bases for literally Aaron Judge – and I can’t even say for certain that it was a bad decision.