For Your Enjoyment, a Home Run Rate Refresher

Here’s a question for you: does Mike Trout hit more home runs against bad pitchers? The answer is yes, of course, but we can parse the question a little differently to make it more interesting. How about this one: does Mike Trout hit more home runs per fly ball against pitchers who are home run-prone? That at least has some intrigue.

Here’s one way you might do this study. Take every pitcher in baseball and group them into quartiles based on their home run per fly ball rate. I’m using line drives and non-pop-up fly balls to make a slightly different rate, but the idea is the same. With the pitchers bucketed like so, simply observe Trout’s home run rate against each quartile:

But before Tom Tango pulls his hair out, let me add something important: This is a bad way to do this study. There’s a big problem here. Trout’s home runs and the pitchers’ home run rate aren’t independent of each other. If Trout tags a guy for a few home runs, that pitcher’s home run rate goes up. If Trout doesn’t hit any out against a pitcher, that pitcher will tend towards the stingiest quartile. Even if Trout’s home runs were randomly distributed across pitchers, this data would tend towards shape.

So if we want to get an uncontaminated look at this, we need to use a sample that isn’t influenced by Trout’s own exploits. There are two options: strip out Trout’s at-bats, or use a previous season’s data to group the pitchers. For now, I’m simply going to use 2018 home run rates, though with it being the offseason and all, I’ll likely go back and try the other method at some point as well.

Okay, so now we’ve got a method. One quick note: I excluded all pitchers who didn’t throw in the majors in 2018 from the sample. You could try to estimate their rate from minor league or previous major league numbers, but I deemed it cleaner to simply ignore them altogether. How does Trout do against each group as determined this way?

No more signal now! That looks more or less like random noise to me. But Trout is just one player, and the sample size is small. Let’s answer a bigger question: do batters hit more home runs per fly ball against bad pitchers? I repeated the study with every batter in baseball who hit a fly ball this year.

A few notes on my methodology here: I wanted to get an equal sample of each group. If Aaron Judge, say, faced mainly pitchers from one quartile, that quartile might show higher power numbers due to Judge. So I weighted each batter’s data by the smallest sample they had. If a batter faced 8, 13, 25, and 32 pitchers in each group, for example, they’d get a weight of 8 in each quartile. In this way, each sample has the same weights from each batter.

With that done, we can look at the data, but boy, there’s nothing to see there:

Batters didn’t really hit more home runs in 2019 against pitchers who were more homer-prone in 2018. There’s a general upward tilt, and the sample size is large enough (6,472 air balls per quartile) that we can be somewhat sure that the slope is not due to a measurement error, but the size of the effect is miniscule. The edge to facing a pitcher who’s particularly homer-prone, as compared to particularly stingy, is only 2%.

Next, let’s repeat the study, only in reverse. Rather than look at each hitter against four quartiles of pitchers, we’ll look at each pitcher against four quartiles of batters. As before, we’ll group batters based on their 2018 rates and throw out batters who didn’t record any fly balls in 2018. For this run, I also got rid of pitchers batting, because otherwise the entirety of the least-powerful batters was made up of pitchers, and that’s not really what we’re testing here.

What do the data show? Well, they show a difference, that’s what:

If you face the bottom tier of batters, you don’t give up many home runs, even if they get the ball in the air. Face the best guys, and balls leave the yard at more than double the rate of the weaklings.

That’s really logical, and I’m not trying to present something new here. The point, instead, is that batters have the most to say about home runs. You probably know this intuitively. If you look at Joey Gallo’s stats, you don’t say “oh boy, high HR/FB%, he’s probably due for some regression.” You say “Yup, he’s big.” If you look at a pitcher’s numbers, you might see that same HR/FB% and intuitively assume he’s been getting unlucky.

This fact, that the most- and least-homer-prone pitchers aren’t all that different in terms of home run rate, is the reason that people cite xFIP as often as they do. Expecting each pitcher to have a league average rate of home runs per fly ball isn’t exactly right — there’s slope, after all — but it’s closer to right than wrong.

That’s all I’ve got for you today. Probably you already knew it, even. But every so often it can be useful to revisit the basics, to make sure that assumptions like “home runs even out for pitchers” still make sense. Luckily for us (and for them), they do.