Like many of you, I was minding my own business on Saturday, March 29, when I got a text from a well-connected friend asking me what the deal was with the new bats that the Yankees were using and whether they were responsible for all those home runs. Of course, having been preoccupied with other things, I had no idea what he was talking about. But I very quickly found out, as I have since been bombarded with questions from people I haven’t heard from in ages, as well as interview requests from the media. As I write this, a week has passed, many articles have been written, and lots of people have weighed in on these new bats. But while this article will appear rather late in the discussion, I am hopeful it will provide some new insights into the so-called torpedo bats. And as I am want to do, I will discuss what I have learned from a physics perspective.

Before getting into my quantitative analysis, I first want to discuss the torpedo bats more qualitatively, as they were presented in a recent FanGraphs article by Davy Andrews. With a beautiful image that pretty much tells the whole story, Davy shows three different regions of a typical baseball bat: the skinny handle (“total garbage”), the sweet spot zone, and the 3-4 inches at the tip (“more garbage”).

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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.” Read the rest of this entry »

Podcasts hosted by athletes — I don’t know about all that. But I did enjoy a recent clip from Mookie Betts’ podcast where he was talking to Cal Raleigh, who was comparing Zack Wheeler — perhaps the best pitcher in baseball — to his batterymate Bryan Woo.

“[Wheeler] is kind of like Woo,” Raleigh said. “He glides down the mound. And it’s so effortless. Some guys just have that natural glide down the mound, easy, and [the ball] just gets on you.”

Coincidentally, in a conversation in late August, Phillies minor league pitching coach Riley McCauley made the same comparison.

“[Woo] is very Wheeler-ish,” McCauley told me. Read the rest of this entry »

The month of April is now complete and the verdict is in: The in-play home run rate for the 2022 season is down from recent seasons, as shown in Figure 1. Much has already been written about this feature by a variety of authors, including Jim Albert, Rob Arthur, Eno Sarris and Ken Rosenthal, and Bradford Doolittle, Alden Gonzalez, Jesse Rogers and David Schoenfield, and various reasons have been proposed for the relative dearth of home runs. Some argue that the baseball has been deadened, resulting in lower exit velocities and therefore fewer home runs. Others have suggested that the drag on the baseball has increased, perhaps due to higher seams. Yet others have argued that it is the effect of the universal humidor.

In this article, we will address the issue of reduced home run rates and hopefully add more light to the discussion. Specifically, we will examine home run rates during the month of April for the 2018-22 seasons, excepting the ’20 season for which there was no major league baseball in April. Here is our approach. Read the rest of this entry »

Every now and then, something happens in a major league game that arouses my interest as a baseball physicist. In the sixth inning of the recent American League Wild Card game, the Red Sox were up 3-1. With Aaron Judge on first and one out, Giancarlo Stanton hit a laser of a shot that bounced high off the left-center field wall at Fenway, barely missing a home run. As it happened, Judge was thrown out at home plate, while Stanton took second on the throw. It was truly a game-changing play. But what I really want to talk about is Stanton’s shot, particularly the distance the ball would have gone had it reached field level unobstructed. That is the usual meaning attached to “home run distance.” Although not normally done, I want to apply it to a single.

As it turns out, there is a wealth of data available that allows us to figure this out. First, we know the Statcast measurement of the launch conditions:

The most important of these parameters, exit velocity and launch angle, are publicly available. Of lesser importance to the calculation are the spray angle, spin rate, and spin axis. Note that the ball is hit very hard and, typical of Stanton, at a somewhat low launch angle. For both those reasons, the spin rate is not particularly large and the spin axis indicates nearly perfect backspin (i.e., very little sidespin). Note also that the small negative spray angle means the ball was hit slightly to the left-field side of center. Read the rest of this entry »

I guess it wouldn’t be baseball in these trying times without a debate about the state of the ball. This year’s rendition started in February when Eno Sarris and Ken Rosenthal of The Athletic reported that they obtained an internal memo Major League Baseball had sent outlining changes to the baseball that would “reduce offense slightly in the 2021 season.” Specifically, Rawlings loosened the tension of the ball’s first wool winding, reducing the weight and bounciness of the ball as measured by COR, or the coefficient of restitution.

How would the new ball affect the league’s offensive environment? At that point, we could only speculate. Included in Sarris and Rosenthal’s article is a cautionary tale from the Korean Baseball Organization, which experienced a crash in league-wide offense after minor reductions to the ball’s COR. But the article also cited Dr. Meredith Willis, who believed that because MLB intended to reduce the ball’s COR along with its weight – the KBO actually increased the weight of its ball by one gram – the effects would be less severe. As for MLB, its memo included an independent lab that found minor decreases in fly ball distance with the new ball.

Then came spring training, and along with it the first uses of the new baseball. As March closed out, Rob Arthur and Ben Lindbergh published an article for The Ringer entitled “The New Baseball Still Seems Juiced.” Using data from spring training games, they made two key observations: (1) home run per contact rate had increased, not decreased, from last spring, and (2) the new ball seemed to have a high drag coefficient. “Higher drag should translate to less carry and fewer home runs,” Arthur and Lindbergh wrote. “Yet the higher-drag balls also have a higher home run rate on contact, because they have a substantially higher exit speed.” If the ball’s COR was really reduced, they added, the opposite phenomenon should occur. Read the rest of this entry »

Editor’s Note: This research was completed while Charles Young was still a student at University of Illinois, Urbana-Champaign.

It’s hard to imagine that an obscure property of the baseball known as the “drag coefficient,” a quantity well known to physicists but hardly to baseball people, would become part of the baseball vernacular. But it has, thanks in no small part to the rapid increase in home runs in major league baseball over the past several years and the conclusion of many people that that increase is due to changes in this otherwise elusive drag coefficient (C_D). In fact, the committee of scientists and engineers commissioned by MLB to determine the causes for the recent surge in home runs found that the principal reason was a reduction in drag coefficients between 2015 and 2017. In a follow-up report, the committee found that the decrease in home runs in 2018 and the increase in 2019 were due, in part, to changes to C_D.

One remarkable finding was that a change in the average C_D value of a baseball by as little as 0.01 (about 3%) would change the distance of a fly ball on a typical home run trajectory by four to five feet, leading to an increase in home run probability of about 10-12%. Equally interesting was the finding that the ball-to-ball variation in C_D within a given season was large compared to the small shift in mean value needed to explain the home run surge.

While the primary focus of recent research has been on the evolution of mean values of drag coefficients, we are aware of no serious studies of how the ball-to-ball variation in C_D has evolved over the years, the focus of the present article. We start with a simple discussion of drag and what it depends on in Section II. Next, in Section III, we discuss several caveats related to the method used to determine C_D values from publicly available pitch-tracking data. Then in Section IV, we get to the heart of the analysis before getting to the principal results in Section V. A summary is given at the end.

II. What is the Drag Coefficient?

When a baseball travels through the air, it collides with air molecules, in effect pushing them out of the way. With each collision, the ball loses a tiny bit of speed, though not nearly enough to result in any measurable difference to the speed of ball. But there are many such collisions, with the net effect being that the baseball slows down significantly. For example, a pitched baseball loses about 9-10% of its speed over the roughly 55-foot distance between release and home plate, so that a ball released at, say, 95 mph is only moving at 86 mph as it crosses home plate. The effect on a fly ball is even greater, since the path length is longer and the ball experiences many more collisions with air molecules, resulting in a huge loss of distance. In fact, a typical 400-foot fly ball in the presence of air would travel over 700 foot in a vacuum if otherwise hit identically. That’s a huge effect. The larger the drag force, the more the ball slows down and the less it carries. Conversely, the smaller the drag force, the more it carries. Read the rest of this entry »

Back in early 2013, I wrote a guest article for Baseball Prospectus entitled “How Far Did That Fly Ball Travel?” In that article, I posed a seemingly simple question: Can we predict the landing point of a fly ball just after it leaves the bat? A more precise way to ask the question is as follows: Suppose the velocity vector of a fly ball just after leaving the bat is known, so that the exit velocity, launch angle, and spray angle are all known. How well does that information determine the landing point? I then proceeded to investigate the question, at least for home runs, with the aid of HITf/x data for the initial velocity vector and the ESPN Home Run Tracker for the landing point and hang time. Using a technique described in the article, that information was used along with a trajectory model to reconstruct the full trajectory and extrapolate it to ground level to determine the fly ball distance. The answer to the question was immediately obvious: The initial velocity vector poorly determines the fly ball distance.

This conclusion led naturally to the next question: Why? One obvious reason is variation in atmospheric conditions, especially wind. However, the data revealed that the variation in home run distance for given initial velocity was as large in Tropicana Field, where the atmospheric conditions are expected to be constant, as in the rest of the league. So that was eliminated, at least as the primary culprit.

The article then went on to consider variation in two other parameters that play a role in fly ball distance: backspin ω_b and drag coefficient C_D. Neither of these parameters were directly measured. Rather they were inferred, along with the sidespin ω_s, in the procedure used to recreate the full trajectory. The analysis showed the following:

• For a given value of C_D, distance increases as ω_b increases. This makes sense, since larger backspin results in greater lift, keeping the ball in the air longer so that it travels farther.
• For a given value of ω_b, distance decreases as C_D increases. Again this makes sense, since greater drag is expected to reduce the carry of a fly ball. Interestingly, this was the first appearance in print of a suggestion of a significant ball-to-ball variation in the drag properties of baseballs.
• There was a moderately strong positive correlation between C_D and ω_b, suggesting that the drag on a baseball increases with increasing spin, all other things equal. Although this effect is well known for golf balls and had been speculated for baseballs in R. K. Adair’s excellent The Physics of Baseball, to my knowledge this is the first real evidence showing the effect for baseballs.
• Given that both lift and drag increase with increasing ω_b and that they have the opposite effect on distance, it was tentatively concluded that at high enough spin rate there would be no further increase (and perhaps even a decrease) in distance with a further increase in spin.

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