The Physics of the Rarified Air of Spring Training

The blue planet has finally moved along its orbit past the days when the sun’s direct rays only brighten the southern hemisphere. Now our sweet orb has eased into a more egalitarian position where the equator has its time in the spotlight. In less cosmic terms, it is time for the sense of renewal only spring training can provide.

The veterans are taking the month to adapt their offseason regimens to the rigors of 162 games and hoping for a precious few more. Meanwhile, hundreds of young ballplayers get to don the uniform of the big club while they vie for a coveted spot on an affiliated team, nurturing the small chance they could make it to The Show.

The air is indeed rarified. Coaches, players, and even we physicists know rarified air has a profound and measurable effect upon the National Pastime. So, let’s look at the air in both Florida and Arizona.

The table below illustrates the simply delightful weather for both the Grapefruit and Cactus leagues. With the exception of relative humidity, the climates are remarkably similar in March.

In 2016, Alan Nathan summarized the effect of air on a fly ball in “Going Deep on Goin’ Deep.” He stated that a ten degree increase in temperature would result in a 3.3-foot increase in distance for a typical fly ball, so the temperature variation between the leagues will make little difference.

The same can be said of the humidity, because a 50 percent increase only results in a 0.9-foot change in distance. The wind might make a bit of difference, because a five mph wind will change the distance by about 19 feet. So, the difference here would result in about eight feet. However, the direction of the wind could be in, out, or across the field so, the wind-related variation from Grapefruit to Cactus is something of a wild card.

There must be something funny about the way the air across Florida interacts with the ball compared to Phoenix because the ballparks are different. Below is a table indicating the distance to center field for each park in each league, courtesy of Ballparks of Baseball.

You have probably guessed the reason the Cactus League parks are on average larger than the Grapefruit League venues. Phoenix is at an elevation of about 1,100 feet, while Florida is a couple of decades away from being below sea level.

Nathan’s work tells us that fly balls should travel an extra six feet for every thousand feet of elevation. It is a lovely coincidence that this matches the difference in average center field distance between the two leagues.

One might therefore expect the number of homers in the two leagues to be roughly the same. Here are the numbers for 2017 from FoxSports.com.

There are many more at-bats in the Cactus league, which is probably due to fewer rainy days. So one should expect more dingers in Arizona even though there are 15 teams in each league. Overall, there are still 10 percent more homers per at-bat in Phoenix even with the larger stadiums. Here are a couple of possible explanations. I’m sure more will be added in the comments section.

• 1. This one year of data is just unusual for some reason.
• 2. The wind blows out more often in Arizona than Florida.
• 3. The pitching is also affected by the difference in the elevation.

As a physicist, the possible explanation that most interests me is the pitching question, so you’re stuck hearing about it. As we know from the mad scientists of baseball and their continuing evil experiment at Coors Field, not only does the mile-high air affect the flight of fly balls, it also limits the break on pitches. There should be a smaller, but nonetheless appreciable, drop in break due to the thinner air in Arizona compared to Florida.

Clayton Kershaw throws the standard, if exceptional, repertoire of a four-seam fastball, a slider and a curve. Using a model of the trajectory of the flight of a pitch and some data from the MLB database, we can calculate the change in position of each pitch at the plate due to the rarified air of Phoenix. The results for the change in horizontal position (∆x), the vertical position (∆z), and the total position change (∆r) are shown in the table below.

Since a four-seamer has mostly backspin, it will rise less in the thinner air of the Cactus League, which it does, as the 0.64-inch decrease in the height (∆z) shows. Kershaw’s slider, unlike many, has substantial backspin as well, and it also rises less—0.40 inches in this case. His curve, which has topspin causing it to drop, is also less effective in that it crosses the plate 0.42 inches higher in Phoenix.

These differences are rather large. That is to say they are an appreciable fraction of the diameter of the bat, so they could account for batters’ extra power in the Cactus League. After all, if your fastball loses over six-tenths of an inch in hop, and your curve loses over four-tenths of an inch of drop, you’re going to have some trouble on the mound.

Of course, one could argue against this explanation by pointing out that elevation changes are a standard problem that big league pitchers solve every day (except in Denver). Excluding the Rock Yard, the average elevation of major league parks is 357 feet, and they vary from nine to 1,082 feet in elevation. Still, losing around half-an-inch of break can’t make a pitcher’s life very easy.

Regardless of whether the limited break on pitches in the Cactus league explains the difference in long balls, at less we’ve examined the physics associated with the rarified air of spring training. Good luck, Rook!

References and Resources

• Ballparks of Baseball, Spring Training Ballparks
• Alan Nathan, The Hardball Times, “Going Deep on Goin’ Deep”