Author Archive: Alan Nathan

Every now and then, something takes place in a major league baseball game that causes my inbox to light up. That’s what happened on October 4, when then-Padres first baseman Ty France hit a towering fly ball down the left field line during Game 1 of the NLDS at American Family Field. The ballpark has a retractable roof, which was closed at the time. As a result, the ball hit a roof cable in fair territory, slowing its progress to the point where it was caught on the warning track by Brewers left fielder Jackson Chourio. Since the ball struck the cable in fair territory, it was in play according to the American Family Field ground rules, so the caught ball was ruled an out. Nobody disputes those facts.

But here’s the question everyone seemed to be asking me: Had the ball not hit the cable, would it have cleared the left field fence in fair territory for a home run? Note that the fence is 342 feet from home plate and eight feet high. Note also that the ball was hit down the line. So the question of whether it would have been a home run reduces to two separate questions regarding the location of the ball once it reached 342 feet from home plate:

• Was the height of the ball greater than eight feet?
• Was the ball to the field side of the foul line?

Normally, given the exit velocity and launch angle, determining whether France’s ball would have been a home run would be easy. I would simply use my Trajectory Calculator with default values for the unknown parameters to calculate the full trajectory. Those default parameters are based on analysis of Statcast batted ball data from past major league seasons. However, this particular batted ball was somewhat unusual in that, while the exit velocity was a respectable 105.3 mph, the launch angle, 48.7 degrees, was considerably steeper than is typical for a major league home run. Had the ball been hit at close to the optimum launch angle of about 30 degrees, it would have carried over 400 feet, making the answer to our first question a resounding “yes.” But that is not what happened. Read the rest of this entry »

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”).

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 »

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.

Read the rest of this entry »

Every now and then, something occurs in a major-league game that just compels me to stop what I’m doing, switch gears, and go into analysis mode. It happened most recently in the top of the fifth inning of NLCS Game Five when Kris Bryant hit a fly ball to straightaway — but slightly on the left-field side of — center field. Center fielder Joc Pederson ran nearly straight backward initially facing toward right field. Then he suddenly and perhaps inexplicably spun around to face left field while still running toward the fence.

At the last minute the ball went just over the reach of his outstretched glove, on the right-field side of center field. The ball bounced on the warning track close to the CF fence, and when the dust had settled, Bryant was on second base with a double. Just to make sure everything is completely clear: Pederson was initially facing the right direction, then he spun around to face the wrong direction, then he spun back at the last second to the original direction, with the ball barely escaping his outstretched reach. Having spun around a complete 360 degrees, he clearly misplayed the ball.

Read the rest of this entry »