Yordan Alvarez, Baseball’s Kobayashi Maru

Every time Yordan Alvarez has stepped to the plate against the Mariners this week, I’m reminded of Star Trek. There’s an in-show famous training exercise known as the Kobayashi Maru, one every single officer candidate tries. The goal is to rescue a ship named, you guessed it, Kobayashi Maru. It’s famous because you can’t beat it. No matter what you try, you fail. The test isn’t about succeeding; it’s about how you handle failure.

That’s the energy Alvarez is bringing to the plate in the ALDS right now. He always seems to step into big spots — Jeremy Peña has done a great job getting on base in front of him — and delivers runs in droves. He’s 4–8 with two homers and a double and has accounted for seven RBI on those hits. Bring in Robbie Ray to face him? He doesn’t care. Refuse to enter the strike zone? He doesn’t care.

In the bottom of the eighth inning last night, Scott Servais attempted a new Kobayashi Maru solution. With Peña on first base and two outs in a one-run game, he chose to walk Alvarez intentionally. That put a runner in scoring position for Alex Bregman, hardly a weak hitter. Bregman singled home that insurance run the Astros were aiming for, the Mariners didn’t score in the ninth, and that was that.

There’s no succeeding in this situation, but let’s run through the math to see whether Servais’ maneuver had promise. The raw numbers present a daunting hill to climb. Ignoring the identity of the pitcher and batters, the difference between having a runner on first and a runner on second in that spot is meaningful. The road team wins roughly 13.7% of the time in the first scenario, as compared to 12.6% in the second. One percentage point might not sound like a lot, but that’s a meaningful chunk of the Mariners’ remaining chances at a win.

Next, we can plug in projections for Andrés Muñoz, the pitcher, as well as Alvarez and Bregman. I’ll use a method I frequently use for these by looking at individual outcome frequencies: how often Alvarez projects to get a single, double, homer, and so on against Muñoz, and the same for Bregman. Here, for example, are Alvarez’s outcome frequencies against generic opposition after removing intentional walks:

Alvarez, as you might expect, projects as one of the best hitters in baseball, with gargantuan extra-base power. He’s also displayed no platoon splits whatsoever in his career; with a bit of regression thanks to having only 557 career plate appearances against lefties, we can estimate a platoon edge of around 5% of wOBA. Bregman is no slouch either, but he has a much larger platoon split; after regression, he projects for roughly an 8% wOBA improvement against left-handed pitchers.

On the other side of the coin, Muñoz has shown reverse splits in a tiny sample. Even after a healthy dose of regression, he looks like a righty who is bothered less than normal by lefties. I’m not particularly surprised by that given his pitch mix; he has a sharp slider, the kind that demonstrates small-ish platoon splits overall, and dominates with a fastball in the triple digits. You could convince me of a lot of things about his skill against lefties, because the sample size so far has been tiny, but “really good against everyone” makes a lot of sense to me.

With the individual splits for each player in hand, the method is simple. First, we look at the potential game states after a Bregman at-bat with runners on first and second. Next, we look at the potential game states after an Alvarez at-bat with a runner on first followed by a potential Bregman at-bat.

With Bregman batting and runners on first and second, I get that the Mariners had a 13% chance of winning the game. That’s better than the naive expectation for their situation; Muñoz is a really good pitcher, one of the best in baseball. Even against a great contact hitter, he projects to rack up enough strikeouts to make things tough on the Astros. Bregman’s best chance at success is to run into a single.

That’s what happened in the game. What might have happened if Muñoz pitched to Alvarez? We’ll never know, but using the same math as before, the Mariners stood a 13.7% chance of winning the game when Alvarez stepped to the plate but before he walked. In other words, walking him slightly decreased the team’s chances of winning, though by less than the naive expectation. And it’s not because Bregman is a better hitter than Alvarez, or a better matchup for Muñoz, or anything like that. Just in wOBA numbers, my method projects a .305 wOBA in an Alvarez/Muñoz confrontation, miles higher than the .250 I get for Bregman/Muñoz. That’s a huge gap; it’s just not enough to make up for having a runner on second base.

This answer felt inevitable when I started doing the math. With a great pitcher on the mound and two very good hitters coming up, you should almost never walk the first one. Muñoz gave up nine extra-base hits this year over 248 batters faced, roughly one per seven appearances; it’s really hard to beat him without stringing together singles.

But maybe my Alvarez projection is light. I used numbers that projected him as one of the best four hitters in baseball, but any projection will necessarily assume he can’t keep up his current tear. Just for fun, I started increasing Alvarez’s projection to see how good of a hitter he’d have to be for this walk to make sense.

Bad news for Servais fans: he’d have to be ludicrously good. I reached a break-even when I gave Alvarez a .580 wOBA; there’s been exactly one season in baseball history (1920 Babe Ruth) better than that. If you’re more of a slash line person, this equates to a .467/.563/1.011 line. Put another way: you shouldn’t walk someone in a tight game when doing so will move a runner into scoring position, no matter what.

If you want to play devil’s advocate, Alvarez has actually exceeded that slash line so far in this series. If you ignore the free pass, he has a .500/.500/1.375 line in these two games. If Servais could know with full certainty that he was getting that distribution of outcomes (25% home run rate, for example), the walk made sense. But if you think Alvarez has a true-talent 25% chance of hitting a home run in a given time at the plate, even for a short span of time, I have a bridge I’d like to sell you in Brookyln. That’s just not how baseball works. No one is ever that likely to succeed, or that likely to fail from the pitcher’s standpoint.

Did you really think I would write an article about this intentional walk and say anything other than that it was a bad idea? It was crazy! Walking a run into scoring position while trailing by one is wild, particularly when the next guy to bat just put up a 136 wRC+ season. If Servais had a sabermetric advisor sitting next to him, I’m sure he would have counseled against it.

Still, I find myself sympathizing. Did you really want to face that guy again, the towering presence who had accounted for eight of Houston’s 11 runs in the series to date? The one who makes baseball bats look like matchsticks and who just hit an effortless 370-foot backbreaking home run against your ace on a pitch that never sniffed the strike zone? If you could find some way to avoid him, wouldn’t you?

The numbers aren’t always sympathetic to human emotions. If I were Servais, I might have broken, too. You can let Yordan Alvarez beat you for only so long before you have to do something different, even if it’s something wrong. That’s why you’d design a test that no one can win: you want to see how the test-taker fares under pressure. There’s no greater pressure in baseball at the moment than seeing Alvarez step into the opposing batter’s box. Unless Seattle can pull off a miraculous comeback, the Kobayashi Maru will be awaiting Houston’s opponent in the ALCS. Good luck, cadets.