The Baseball Moves Differently in the Cactus League

There isn’t much for a baseball writer in the dull days of late February. Someone added a new pitch? The pitching nerds are all over it. Somebody else set a new career high for exit velocity? I’m not sure that merits more than a tweet and/or skeet. Statistically responsible baseball writers have long concluded that attempting to find signal in the noise of spring training stats is a futile exercise.

Thankfully, Effectively Wild came to my rescue. On Episode 2288, Ben and Meg discussed the peculiar case of Justin Verlander, who is pitching in the Cactus League for the first time in his career. After allowing a home run off a hanging slider, he sought consolation from his new teammate, Logan Webb.

“I was told not to overconcern yourself with pitch shapes here and the movement of the ball because it’s tough,” Verlander told Maria Guardado of MLB.com after his start. “It’s my first spring training in Arizona, so everyone was like, ‘Hey man, it’s a little different out here.’ I’ve heard it from everyone. But I think you still need to be honest with yourself.”

There it was — a beautiful post topic, dropped directly into my ears. Pitch shapes? Science?? A spring training angle??? I set about investigating straightaway: How does pitch movement differ between the Grapefruit and Cactus Leagues?

The question matters more than it might seem at first glance. Every day of spring, analysts and pitch modelers dig into the fresh data, assessing the quality of a prospect’s stuff or the viability of a veteran’s new pitch. If there really is a difference between the two sites, some sort of adjustment needs to be factored into “stuff” grades for pitches thrown in Arizona versus those thrown in Florida.

So what’s the truth? In short: Pitches do move differently in the Cactus League. Over the last four spring trainings — so, stretching back to spring of 2022 — curveballs and knuckle curves have dropped nearly an inch less in Cactus League ballparks compared to those thrown in Grapefruit League ballparks. On the flip side, four-seam fastballs drop a half-inch more in Cactus League games than Grapefruit League games:

The main reason? Florida air is denser than Arizona air. (All the science facts to come are thanks to Alan Nathan’s blog post “Baseball At High Altitude.”) The Magnus force — which acts on a spinning baseball — is proportional to the density of the air. When the air is less dense, the Magnus force is weaker. That means pitches with backspin (like four-seam fastballs) drop more in Coors-like conditions; pitches with topspin (like curveballs) drop less. The Cactus League isn’t quite like Coors, but it’s the closest thing that exists in professional baseball; the air density in Cactus League ballparks in February is lower than all other non-Coors parks.

There are three central factors that influence air density: Elevation, temperature, and humidity.

The thinness of the Arizona air is largely due to the elevation of the greater Phoenix area. (Every ballpark in the Cactus League sits around roughly 1,000 feet elevation.) Late February and early March temperatures in Arizona and Florida are roughly similar, but there is a significant difference in the humidity between the two states.

As you might imagine, Arizona is much drier than Florida. But humidity has a counterintuitive impact on air density. Because water molecules are lighter than air molecules, more humid climates actually have thinner air, meaning that the dry desert air should actually give a relative boost to pitch movement. The lack of humidity in Arizona thickens the air, offsetting to some degree the impact of the elevation.

It turns out humidity is not as influential as elevation. This Density Altitude Calculator gives some sense of the situation. If one were to pick a Cactus League city and a Grapefruit League city at random (Tempe and Bradenton, say), and input the average values for each location, the calculator informs us that there is roughly a 5% difference in air density. That figure corresponds neatly to the percentage difference in four-seam fastball induced vertical break between the two locations.

All of this made me curious about how Chase Field plays during the regular season. Every year, 20 or so games are played with the roof open. The rest are in an air-conditioned, fully enclosed stadium. How does the stadium play when the roof is open compared to when it’s closed? I assumed that closing the roof would increase the humidity and therefore decrease overall pitch movement.

The data, sadly, was inconclusive. Induced vertical break for four-seam fastballs for the two roof conditions (open versus closed) differed only slightly. Split by month, these differences technically met the threshold of statistical significance as measured by a two-sample t-test. But they were so slim, and which condition produced more IVB changed depending on the month:

The sample for any given month is small — as mentioned earlier, the roof is open roughly 20 times a year, and the vast majority of those times are concentrated in April and May, when the weather in Phoenix is at its most tolerable. Stretching the sample any further risked the introduction of confounding variables, including the decision to bring a humidor to Chase in the late 2010s.

There was one factor I hadn’t considered: The effect of wind. As Weather Applied Metrics’ Ken Arneson pointed out on Bluesky, the vast majority of pitches are thrown with a tailwind. In theory, eliminating tailwinds would lead to more vertical break than a stadium exposed to the elements. But the change in humidity between the two roof states, perhaps, is enough to muddy the results.

I did find a statistically significant relationship on one pitch specification: Velocity. But even this led to more questions than answers:

Pitches in thin air, like at Coors, do move marginally faster than those at other stadiums. The decreased drag force of these low air density stadiums means that pitches lose less of their speed as they approach the plate. I figured the same effect appears to be on display, to a lesser degree, in the closed roof setting at Chase Field, attributable to the increase in humidity from switching to an indoor environment. Sorted, right? Maybe not. Pitch speed is measured at the moment the pitch is released from the pitcher’s hand. Drag shouldn’t impact instantaneous velocity, only the velocity once it’s traveling through the air. Right? Anyone?

So the impact of the closed roof on velocity remains a mystery, for now. But that wasn’t the point of this whole thing. Forget the side quest — pitches move differently in the Cactus League than they do in the Grapefruit League! The more you know.