This is a story about failure. Like most stories about failure, it starts with an attempt to succeed. When I wrote about Kodi Whitley last month, I stumbled over his changeup. It’s phenomenally weird, the kind of pitch that almost no one in baseball throws. It doesn’t move much like any other changeup — it has more vertical break than anything in its same zipcode velo-wise. In fact, it almost resembles his fastball, only ten miles an hour slower.

I did the analytical equivalent of a shruggie — I said I’d need more data or video to have a conclusive opinion on it. But like manna from heaven, an email appeared in my inbox from noted Cardinalsologist and general site mensch Aaron Schafer. What if, he said, we analyzed changeups not based on their properties, but based on how they differed from a pitcher’s fastball? Maybe we could find a Whitley comp there, and maybe we could find something more general about changeups.

It won’t surprise you to know that I’ve gone down this approximate road before, though never with much analytical rigor. Those past times, I’d run out of steam after the first step, which I’ll now explain here. Take every pitcher in the majors who threw 100 changeups last year. For each pitcher, determine a dominant fastball type — whichever of a cutter, sinker, or four seam they threw most often. Now that we have a two-pitch pair, work out the velocity gap on each, then look at the whiff rate of the changeup.

So here’s the deal: that doesn’t really work. You can’t say that a big or small velocity gap is particularly good for getting swings and misses. The r^2 of velocity gap and whiff rate is a mere 0.073. In other words, most of the variation in missing bats can’t be explained by sheer velocity gap. It’s not some non-linear issue, either, where big and tiny gaps are both good but the middle mucks everything up. Take a look at the raw, ugly data:

There’s a very slight upward tilt: bigger velocity gaps seem to get more whiffs. But it looks mostly like noise, and it’s nowhere near being analytically interesting in my eyes.

When I’ve looked at this in the past, I’ve stopped there. Changeups aren’t well described solely by their velocity, you dingbats; let’s move on. But with little to write about this offseason (I’m not really a decade in review type, and we have better people for that), I decided to delve a little deeper.

First, I regressed more things against whiff rate. Vertical break gap, horizontal break gap, total movement gap; everything about how the baseball moves, essentially. They all came up empty. Not a single one was a better predictor than velocity gap, which we’ve already determined was okay at best.

Next, it’s time to look at composite predictions. How about a multivariate linear regression that incorporates movement and velocity differentials? You can probably guess the outcome, but I ran it anyway: nothing. The r^2 climbed all the way to 0.143, which is still terrible. You’d like to do better with so many variables, because we’re basically still not explaining any of the whiff rate variation.

What if we did the same thing, but used a non-linear regression estimation instead? We could be missing some weird combinatorial effect. Yeah — nothing. It’s just hard, frankly, to explain much more than 10% of the variation in whiff rate using horizontal movement, vertical movement, and velocity. There’s no trick, no one sneaky way to flip the numbers around that leads to a sudden revelation.

And that’s fine! If the only outcome of this article is that we all learn that there’s no simple test for changeup effectiveness, I could live with that. But before I completely throw in the towel and say that there’s nothing here, let’s talk about why there’s nothing here.

Changeups aren’t just slow fastballs. If that were the case, they would be a lot less interesting, and they’d certainly be less effective. When you watch a great changeup live, it’s not the break or the velocity that wows you — it’s the hitter losing a game of three card monte. The batter isn’t swinging at a breaking ball diving away from his bat; he’s simply not seeing what he expects.

What I think this means, from an analysis standpoint, is that there’s a lot going on in delivery and deception that we can’t capture just by looking at what happens after the ball leaves a pitcher’s hands. Arm action, consistency of delivery, deception — you can’t figure that out by seeing how much a ball spins or dips. Pitching is way more than movement and velocity, and no pitch more embodies that than a changeup.

In a way, that’s frustrating, because I’m not a scout. I can’t watch a pitcher in super-slo-mo and spot the key things that will either fool or tip off batters. I can’t study biomechanics and see if someone’s natural flexibility is going to make repeating their delivery easy. My skill lies more in smashing numbers into each other and seeing what comes out, and that simply doesn’t work all the time.

In another way, though, that’s great. Baseball would be pretty terrible if it were exclusively a game of numbers. A huge reason the game is so fun is because there are always more layers to peel back, always more things to find out or guess at. It would cheapen things a little, I think, if we could just look at a changeup’s vital statistics and know if it would be good.

Anyway, back to looking at a changeup’s vital statistics and seeing if it’s good. I had one last angle to try: angles. If you want to look for a pitch that’s hard for a batter to pick up, one thing you can look for is a well-mirrored pitch. Think of a hammer curve playing off of a rising fastball; one goes up, one goes down, and the hitter can tell what plane the pitch is on but not which way it’s going within that plane.

Changeups don’t play off of fastballs in the same way; they’re generally in the same direction as a fastball with some offset. But maybe there’s some angle of break that’s particularly difficult for batters to distinguish. Maybe changeups are best when they’re exactly the same as a fastball, say; or when they break at a 45 degree angle. The math on this isn’t hard; a little law of cosines here, a little actual Pythagorean theorem there, and you can work out the spin angle that a pitcher imparts on his pitches.

Just one problem: there’s still nothing there! I regressed angle against whiff rate the same way I did everything else, and got stone nothing yet again. In fact, angle isn’t even as good as break differential (directionless and measured in inches) when it comes to predicting whiffs. It truly seems like nothing in the pitch-level data is going to tell us how changeups work. This graph, yet again, looks like noise:

So there you have it: this is a story of failure. I stretched the data as far as I could with my feeble grasp of math and trigonometry, and I came up empty. Want to know if a changeup is good? Certainly don’t ask me! Or well, do ask me, but ask me after I’ve watched a lot of them, not based on some movement characteristics.

When Kodi Whitley is up next year, we can talk about his changeup. But until then, all we can say is that it’s unique, and that it seems mostly like it’s been working for him in the minors. There’s nothing wrong with that, and it’s refreshing to see that there’s not some easy trick to changeup analysis we’ve been missing all these years.