First-Batter Walks: The Sequel

Last week, I investigated something that I’ve long wondered about: are relievers particularly prone to wildness on their first batter of the game? I didn’t find much of an effect, and I also got tons of valuable feedback about further avenues for investigation. Do base/out states matter? Does handedness matter? Do intentional walks skew the data?

Aside from the last one (a definite yes), I haven’t explored all of these avenues yet. I did, however, answer another question I was curious about, one that ties into the general theme of reliever walk rates. I’ll tell you upfront that I found a confusing result, and that I’d love to hear anything I’ve missed or avenues for further investigation.

Here’s the question I’m answering: when a reliever walks the first batter he faces, what does that tell us about the rest of his appearance? All of us have seen this in practice, and we probably all know the existential dread it engenders. Great, he doesn’t have his command today. How many walks are coming up? Is the lead safe? Will the team even stay in the game long enough for a new pitcher comes in?

To explore this possibility, I examined every game thrown by a reliever since the beginning of the 2015 season. I split each reliever’s appearances into two subsets: every appearance where they unintentionally walked the first batter they faced on one hand, and every other appearance (except intentional walks, I threw those out) on the other. This gave me a sample of 1,085 relievers across more than 80,000 appearances.

From there, I looked at how each reliever did after the first batter they faced in each subset. That’s a confusing sentence, so let’s look at an example. We’ll use Fernando Rodney, because it’s always fun to use Fernando Rodney. Beginning in the 2015 season, Rodney made 44 appearances where he walked the first batter he faced. He also made 275 appearances where he didn’t walk the first batter he faced.

In the 44 walk-first appearances, he faced 145 subsequent batters and unintentionally walked 10.3% of them. A quick note: from here on out, every walk rate I quote will exclude intentional walks, both from the numerator and denominator. I simply threw them out of the sample. Of course, his overall walk rate for the appearance was still atrocious, what with the walk starting every single one and all. In fact, he walked 31.2% of batters in those appearances — 100% against the first batter, then 10.3% on subsequent ones.

When Rodney didn’t walk the first batter, he faced 811 further batters and walked 10.1% of them. Combine that with those 275 non-walks to start the appearances, and that comes out to a 7.6% walk rate. Here, then, we have two clearly different samples: one where Rodney walked 31.2% of his opponents and one where he walked 7.6% of them.

Here’s the thing: after that first batter, his walk rates were nearly identical! It’s relatively clear that his overall walk rate was worse when he walked the first batter, but that’s entirely down to the fact that we specifically selected a sample with walks in it. After that first batter faced, he walked just over 10% in each sample, roughly what you’d expect from a pitcher with a career 11.4% walk rate.

I can flat-out guarantee you that it didn’t feel that way at the time. An opening walk feels like a disaster. And hey, though Rodney was remarkably even between his two samples, he’s just one example. Just because this one pitcher in particular performed roughly equally in the two subsets doesn’t mean all pitchers do.

I weighted each pitcher by the lesser of their two appearance totals. That was almost always the times they walked the first batter, naturally, but just to be safe, I took the lesser of the two. For each pitcher, I created a walk rate differential — simply the difference between their non-first batter walk rates in the two conditions. From there, I came up with the overall population change in walk rate.

Why do it this way instead of simply looking at the overall population walk rate in each instance? Simply put, that wouldn’t work. The two samples aren’t the same. Pitchers who walk the first batter have higher walk rates, on average, than pitchers who don’t walk the first batter. You don’t have to just believe that on faith, because I ran the numbers. In the first-batter-walk sample, pitchers ran a 13.3% walk rate. In the sample of pitchers who didn’t walk the first batter, the walk rate was a comparatively low 9.5%.

That’s not meaningful, though, because as I said above, the samples aren’t the same. We’re not asking whether a first-batter walk means more walks are coming, ignoring everything else. We’re asking this question: for a given pitcher, does a walk to the first batter he faces portend an elevated walk rate for the remainder of his appearance?

That question is why I looked at each pitcher’s differential walk rate across the two conditions — it keeps the proportion of each pitcher in each sample constant. That allows us to measure what we’re looking for rather than capture the fact that wilder pitchers tend to walk more batters — good, great, not what we’re looking for.

With that preamble now completed, what are the results? I won’t lie to you — they shocked me. The average pitcher runs a lower walk rate over the balance of their appearance when they walk the first batter than when they don’t. It’s a tiny margin — 0.15 percentage points — but don’t get caught up in the exact details. The key here is that first-batter walk doesn’t tell us much of anything about how the remainder of the outing will go.

This finding stunned me, so I spent a while looking for explanations. My first thought: maybe the act of walking the first batter changes the game in a way that makes future walks less likely. Having a runner on first, just by itself, might entice pitchers to challenge the next hitter now that first base isn’t open.

To handle this, I adjusted each pitcher’s walk rate based on the base/out states they faced. I tried a simple adjustment — simply adding or subtracting walk rate for each batter faced based on how different that situation is from league average. That moved the results slightly — after this adjustment, the sign of our finding flipped. Adjusting for the situations they find themselves in, pitchers have a higher walk rate in appearances where they walk their first batter — by a still-tiny 0.2 percentage points.

There’s room to wonder about that adjustment, because I’m not taking score into account, or the identity of the pitcher and batter. I’m also skeptical about potential selection effects; perhaps in appearances where the pitcher starts off well, their managers give them enough opposing batters that they eventually tire and start to walk more batters despite starting out with better command of their stuff.

Finally, there’s one massive problem with using walks as our indicator variable. Say a pitcher walks the first batter he faces, then compensates by throwing meatballs right down the middle to the next batter. The next batter promptly homers, a terrible outcome for the pitcher — but one that wouldn’t show up in this test. By looking only at walks, we’re missing a key question about pitcher performance. Having no command doesn’t only mean issuing walks.

These are all potential problems with my findings, and I’m hoping that you will help me find more. Consider this an interactive article — I’d love to hear things I missed, because this puzzle of pitcher walk rates is an itch I can’t stop scratching. I feel like the answer is in there, somewhere, and I simply haven’t happened upon it yet. It can’t be that pitchers walk batters at a roughly equivalent clip regardless of whether they started off with a walk or not — even though the evidence is squarely pointing that way at this point.

So let me know what you think, either in the comments here or wherever you normally talk to me (hi Dad!). I won’t rest until I dig a little bit deeper into this puzzle. Or, fine — I will rest, in the normal seven-to-eight-hour nightly increments, but I’ll think a lot about walks before bed. With any luck, we’ll even arrive at a satisfactory answer!