The greatest hitter of all time, hitting a
home run in his final at bat, September 28, 1960.

Welcome to my site devoted to research on the physics of baseball. My particular research interests are two-fold: the physics of the baseball-bat collision and the flight of the baseball. I have done quite a bit of independent research in both areas. I am also heavily involved with several areas of practical interest to the game. One is characterizing, measuring, and regulating the performance of non-wood bats, an area for which I have served on committees advising the NCAA and USA Baseball. Another is exploiting new technologies for tracking the baseball, such as PITCHf/x, HITf/x, and TrackMan, for novel uses in baseball analytics. But this site does much more than catalog my own work. It attempts to provide links to much of the high-quality work done over the past decade or so on various aspects of the physics of baseball. If readers know of a site that I have overlooked, please contact me.

Recent Research Highlights

Ancient Baseball Physics:
The Physics of Baseball From Yesteryear.

One article, Science Explains Babe Ruth's Home Runs, appeared in during the 1920 season when Ruth hit 54 home runs, nearly doubling his own single-season record of 29 from the previous year. The article talks about the physics of hitting a home run, a subject we know a lot more about now than we did nearly 100 years ago. As a result, there is some wrong physics in the article. I discuss all of that in my analysis. My thanks to Greg Rybarczyk (@hittracker) for calling this article to my attention.

Another interesting article, Spitball Myths, appeared in a 1919 issue of Popular Science Monthly and discussed the physics of both curveballs and spitballs. Some of the physics is right, some is not. But it makes for an interesting read. The right stuff: spinning balls curve, although the explanation given in the article is not quite right. The wrong stuff: The author doesn't recognize the role of the seams in a ball curving. In fact, the seams play a huge role in the "swing" of a cricket ball. But the author is right that the primary purpose of lubricating the surface of the ball is to reduce the friction between fingers and ball, which reduces the spin. Other links to Popular Science articles about spitballs can be found here. Thanks to Cliff Otto for sending me the article.

Oblique Collisions of Baseballs and Softballs with a Bat

Jeffrey Kensrud, Alan Nathan, and Lloyd Smith. accepted for publication in American Journal of Physics (October 2016)

Bat robot making contact with a softball on a tee.


Experiments are done by colliding a swinging bat with a stationary baseball or softball. Each collision was recorded with high-speed cameras, from which the post-impact speed, launch angle, and spin of the ball could be determined. Initial bat speeds were in the range 63-88 mph, producing launch angles in the range 0-30 degrees and spins in the range 0-3500 rpm. The results are analyzed in the context of a ball-bat collision model and the parameters of that model are determined. For both baseballs and softballs, the data are consistent with a mechanism whereby the ball grips the surface of the bat, stretching the ball in the transverse direction and resulting in a spin that was up to 40% greater than would be obtained by rolling contact of rigid bodies. Using a lumped parameter contact model, baseballs are shown to be less compliant tangentially than softballs. Implications of our results for batted balls in game situations are presented.

Spinning Out of Control

Alan Nathan, Fangraphs, October 26, 2016

Joc Pederson spinning out of control.

During the 2016 NLCS, Game 5, 5th inning, right-hand-batter Kris Bryant hit a long fly ball to nearly straightaway centerfield. Centerfielder Joc Pederson, normally an excellent outfielder, badly misplayed the ball. In this article, I analyze the trajectory of the batted ball to show that the ball sliced toward right field. I then show that it was not a particularly unusual trajectory in that fly balls hit to centerfield usually slice toward the opposite field. Finally, I discuss the physics that leads to the slicing movement.

Exit Speed and Home Runs

Alan Nathan, The Hardball Times, July 18, 2016

Home runs are up significantly in 2016.

In this article, I take a deep dive into the increase in home runs in MLB during the first half of 2016. This increase can mostly be accounted for by an increase batted ball exit speed for balls hit in the angular range 200-350, the "sweet spot" for home runs. Does that mean the baseball is "juiced"? Read the article and especially the Addendum to get my view. I gave a talk about this at the 2016 Saberseminar and the slides are available here. Finally, I discussed this topic in some detail on a BP Toronto podcast, August 25, 2016, with my interview starting at approximately 21:00.

For another point of view, see the excellent article Are Juiced Balls The New Steroid?, by Ben Lindbergh and Rob Arthur.

Going Deep On Goin' Deep

Alan Nathan, The Hardball Times, April 6, 2016

Sunset over Coors Field in Denver, where the ball really flies.

In this article, I use Statcast fly ball data from the 2015 season to investigate how fly ball distance depends on exit speed, vertical launch angle, and elevation. The Coors Field effect is quantified. Indirectly, this analysis is used to determine the effect on fly ball distance of temperature, relative humidity, and wind. A perhaps surprising result is the weak dependent of distance on the rate of backspin, in agreement with earlier findings reported in this article.

Optimizing the Swing

Alan Nathan, The Hardball Times, November 11, 2015

Optimizing the Swing, Part Deux: Paying Homage to Teddy Ballgame

Alan Nathan, The Hardball Times, December 24, 2015

These articles report the research I have done to find the optimum swing parameters for a batter. The two parameters I am trying to optimize are the swing plane (also known as the attack angle) and the ball-bat offset, which is related to how well the ball is "squared up". In the first article, I used the best models available for the ball-bat collision and for the flight of a baseball through the air to find the parameters that lead to the longest fly ball distance for both a fastball and a curveball. I find than an optimally hit fastball travels a little farther than an optimally hit curveball. I also find that a downward attack angle will not lead to the largest distances. Finally I find that the swing strategy for hitting the longest fly balls is different from the strategy for getting on base with high percentage. In the second article, I used the same ball-bat collision model to find the exit speed and launch angle for a given offset and swing plane, then link onto Statcast data to find the probability of a safe hit or home run. I then investigate with issue of timing and the role that plays in optimizing the swing plane.

To hear from Ted Williams himself about the science of hitting, click here. Particularly note the discussion starting at about 12-1/2 minutes into the video, where Ted talks about swing plane.

All Spin Is Not Alike

Alan Nathan, Baseball Prospectus, March 31, 2015

The forces on a spinning baseball.

This article describes how to use Trackman data to separate the spin of a pitched baseball into a part that leads to movement (the "useful" spin) and a part that doesn't (the "gyrospin"). It is shown that fastballs and changeups are consistent with all their spin being useful, whereas breaking pitches (including cutters) have varying but significant degrees of gyrospin. The ratio of useful to total spin might be a helpful diagnostic for pitchers, especially those who throw breaking balls. Random measurement error in the movement means the type of analysis discussed in the article should only be used for averages of collections of pitches rather than for individual pitches. For those of you interested in technical details, you can read all about them in my unpublished companion article.

Jeff Long has written several articles for Baseball Prospectus, here, here, and here, in which he has done some analysis using the concept of useful spin.

How Far Did That Fly Ball Travel? (Redux)

Alan M. Nathan, Lloyd Smith, Jeff Kensrud, Eric Lang, Baseball Prospectus, December 9, 2014

This article is a followup to a previous article How Far Did That Fly Ball Travel? published in Baseball Prospectus on January 8, 2013. It is an account of our experiment at Minute Maid Park in Houston, January 2014. The object was to measure the distance of fly balls projected into the outfield with a fixed initial speed of 96 mph and vertical launch angle of 280. In an ideal world, all baseballs would land at the same place. But as the figure shows, there is great variation in the distance, depending not only on the type of baseball (NCAA, MiLB, MLB) but even which baseball of a given type. Interestingly, the data also show very little variation in distance for backspin rates in the range 2200-3200 rpm. An important conclusion is that variation in fly ball distance is due much more to ball-to-ball variation in the drag (for example, due to small differences in surface roughness) than to variation in spin. Further evidence for ball-to-ball variation of drag comes from PITCHf/x data, about which an article will be written soon. Further evidence for MLB home run distances being nearly independent of spin will also be presented in a future article.

NOTE: If you are not able to access the Baseball Prospectus article, you read it here.