To Walk or Not to Walk

In my head, the playoffs have always had a unique relationship with analysis. Things are happening, always new and exciting things, and I feel a strong desire to know what’s skill and what’s luck, to sort out whether Adam Wainwright found the secret formula to pitching or whether he just had a good breakfast Sunday, while the Braves stubbed their collective toes on the hotel bed frame.

But for the most part, there’s not much to say conclusively about one pitching outing, or even a few pitching outings. The samples are vanishingly small in the postseason, and so I watch for the narratives and the drama, rather than trying to find an interesting line to analyze. Sure, I have opinions about the players in the playoffs, formed from a year of crunching numbers on their performances. But for the most part, I don’t use October to tell me new things about them.

If Patrick Corbin comes in and gives up six runs in relief, is he bad? Is he unsuited to relieving? Did he just not have it that day? I don’t know, and short of some velocity or spin rate smoking gun, I’ll probably never know.

Having said all that, there’s one thing I feel very comfortable analyzing. Managers still walk people intentionally in the playoffs, and maybe they shouldn’t. Dave Martinez and Mike Shildt succumbed to the temptation of making a difference over the weekend, and while neither decision ended up impacting the final accounting of the game, I was curious to see what those walks did to the teams’ chances of winning.

Let’s talk about Martinez’s decision first, because it’s much stranger. We’ll set the stage with all the essentials: in Game 2 of their series against the Dodgers, the Nationals took a 4-2 lead into the ninth inning, with Daniel Hudson taking the mound following a dominant inning by Max Scherzer. Justin Turner doubled to start the inning, but Hudson rebounded, striking out A.J. Pollock and getting Cody Bellinger to pop out to third.

Then things got weird. Max Muncy was due up next, and Martinez had a plan. That plan? Walk Muncy intentionally, putting the winning run on base and bringing Will Smith to the plate. It doesn’t take a beautiful sabermetric mind to know that this is a pretty wild decision, but let’s go through it just to make sure.

First, there’s the raw unadulterated win probability change. I used FanGraphs’ win probability inquirer to work out how much this move would cost the Nationals in an otherwise completely neutral context. Before the walk, the Nationals had a 94.7% chance of winning the game. Afterwards, that number fell to 90.2%.

That’s obvious. Walking a batter makes for more runners on base, and runners can score runs — we’re not simpletons here. The question, then, is whether the upgrade the Nationals received from facing Smith rather than Muncy recouped that 4.5% decrease in win expectancy. I’ll save you the suspense upfront — nope!

But let’s go through the math anyway. Normally, we could just look at wOBA to compare two hitters. Daniel Hudson has no career platoon split, and pitching platoon splits are pretty reliable at the sample size we have for him — he still has a below-average platoon split even after regressing somewhat towards the mean. Max Muncy also has no observed platoon split, but his is in a smaller sample and batter platoon advantages stabilize much more slowly, so his platoon advantage is likely around 3.8% or 13 points of wOBA (using some handy formulas from The Book).

Take the requisite projections and platoon splits for Muncy, Smith, and Hudson in this fashion, and use the odds ratio method to calculate expected pitcher/batter combinations, and Muncy projects to a .349 wOBA against Hudson while Smith projects to come in at a comparably poor .294 wOBA. That 55 points of wOBA is a big edge — something like the difference between facing 2019 Francisco Lindor and 2019 Leury García.

Per a handy post by Tom Tango, we can convert the wOBA to wins and vice versa. Do the math, and the Nationals would have needed to face someone with a wOBA 150 points lower to have this walk make sense. That’s not the difference between Lindor and García; that’s the difference between Alex Bregman and worst-qualifying-hitter Orlando Arcia.

Okay, so wOBA and win probability math says this walk was abysmal. We can do better, though, because wOBA isn’t quite right for this situation. Context-neutral stats like wOBA don’t perfectly capture what’s going on in a given situation, even if you adjust them for leverage. As a simple example, with a runner on third and less than two outs in a one-run game, wOBA will overvalue walks and undervalue contact. In the Nats/Dodgers situation, wOBA undervalues home runs, because it takes the average value of each outcome over all games, whereas a home run is exactly what the Dodgers needed.

To handle this, I went a little further into the math. I worked out the expected chance of each outcome for each player given the relevant platoon situation, then used the same odds ratio method for the two matchups. From there, I simply looked at the win probability in each end state. For example, if Muncy made an out, the Dodgers were done — the Nats would be 100% to win. If he hit a home run, the Dodgers would be tied, which works out to a 46.1% chance of Washington winning per our tool (in reality, it was probably lower given that the Dodgers are the better team).

I’m not going to show you the nitty-gritty details here, because ew math, but here’s an example. Muncy projects to hit a home run in 4.9% of his plate appearances against righties. Hudson projects to allow a home run in 3.2% of his plate appearances against lefties. The league average is 3.6%, which works out to Muncy having a 4.3% chance of hitting a home run in a given appearance against Hudson.

Plugging those values in, the Nationals were 94.3% likely to win the game when Muncy stepped in. That’s slightly lower than the naive expectation of our WPA inquirer, which makes sense: Muncy is better than the average batter. After the intentional walk, the Nationals were 89.8% to win the game. That’s a 4.5% drop, exactly what the generic numbers said. In other words: don’t walk Muncy!!!

That’s one intentional walk covered. Now let’s turn to Sunday’s Cardinals/Braves tilt, where Mike Shildt faced a slightly different situation. In a one run game with a runner on third and two outs, Shildt had the choice between facing Brian McCann or walking him to face Dansby Swanson. Once again, a manager chose to put an important runner on base to gain some ephemeral advantage.

The difference is, this one isn’t as bad as Martinez’s decision. Here, the Cardinals’ odds of winning the game fell from 86.9% to 83% in the generic case. 3.9% of a win is nothing to scoff at, of course, so it’s still a bad decision in the generic case. Let’s delve into the situation, though, to see whether this one was more merited.

First, we’ll do the wOBA method again. McCann has a greater than normal platoon split over a pretty big sample, and Carlos Martínez has an even larger platoon split over an even larger sample (and pitcher splits stabilize more quickly). On net, we’d expect McCann to produce a .316 wOBA against Martínez, while Swanson would project for an abysmal .252 wOBA. That’s a huge gap!

Next, we plug in the win probability change (.039 wins) and leverage situation and get that we’d need to see an 77-point wOBA gap between the two hitters to make it worth it. The actual gap is a mere 64 points, so it wasn’t worth it, but it was close. If McCann had been a slightly better hitter, or Swanson slightly worse, it might make sense.

Now, let’s add in the individual outcomes method. Before McCann came to the plate, and assuming no intentional walk, the Cardinals had a 87.7% chance to win the game, more or less in line with our naive expectation. When Swanson stepped in after the walk, the Cardinals were — wait for it — 87.6% to hold on. That’s right — the intentional walk did almost nothing.

This isn’t an intuitive result, so I ran through the math a few times. It comes down to a few things. First, McCann is basically a league average hitter against righties and Martínez is a league average pitcher against lefties. On the other hand, Martínez is one of the best pitchers in baseball against righties (expected .268 wOBA), while Swanson is below average against righties. Even more than that, Swanson gets most of his production from singles and walks, without much thump to speak of. Extra base hits are the way you get burned by this walk, and Swanson is not an extra bases kind of guy for the most part.

In the end, neither of the decisions mattered. Hudson walked Smith but struck out Corey Seager, and the Nationals won. Martínez gave up a first pitch double to Swanson, and the free baserunner the Cardinals gifted the Braves ended up scoring along with Swanson to make it 3-1 Braves, but the insurance run didn’t matter; the Cardinals didn’t score in the bottom of the ninth.

That’s merely what did happen, though. The math says that the Nationals absolutely shouldn’t have walked Muncy, while the Cardinals were pretty expected-value-neutral on their decision. Intentional walks are often bad, and data-savvy fans are rightly skeptical of them. That doesn’t mean they’re literally never the correct decision. Were I in Mike Shildt’s shoes, I still probably wouldn’t have walked McCann. But it was a close call due to Martínez’s extreme platoon splits, something that wasn’t obvious as I watched.