A remarkable photo of the ball-bat
collsion, from Cary Frye, @illiniphotog, May 2015

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

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

These articles appeared in the November 11, 2015 and December 24, 2015 editions of The Hardball Times and are the result of 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. .

Sports Ballistics

Christophe Clanet, Ecole Polytechnique, Palaiseau
Annual Review of Fluid Dynamics, 47:455-478 (2015).

Postion of different sports balls on the lift-drag phase diagram. The axes are the typical ratios of lift-to-weight (vertical) and drag-to-weight for the different balls.

This is a beautifully written article about the aerodynamics of sports balls, including the effects of gravity, drag, and lift. He treats such diverse topics as the peculiar trajectory of a shuttlecock (badminton), the famous Roberto Carlos free kick (soccer), paradoxical popups (baseball), knuckleballs (lots of different sports), and the optimum size of different sports fields. He does what every good physicist should do: He reduces each problem to its bare essentials, making the necessary approximations in order to identify the underlying physics for each of the examples. This paper is a must read for anyone wanting to learn a physicist's approach to the physics of sports.

Here are links to additional articles co-authored by Clanet, along with colleagues and students:

  • On the Size of Sports Fields

    This paper describes how the size of a sports field is related to properties of the ball (mass, diameter, drag coefficient) and the maximum velocity of the ball in the game.
  • The Spinning Ball Spiral

    This paper describes spiraling motion of a spinning sports ball, due to the increase in the curvature of the trajectory as the ball slows down due to drag. The model is used to analyze the famous free kick of Roberto Carlos.
  • The Aerodynamic Wall

    This paper describes trajectories in the limiting case where the drag force greatly exceeds the force of gravity. The formalism is applied to the trajectory of a badminton shuttlecock.

Oblique Collisions and the Spin of a Batted Ball

High-speed video of a ball making an oblique collision with a fixed cylindrical surface. Note that he ball, initially not spinning, hits the upper half of the cylinder and scatters upward with backspin.

Click on the above link to look at high-speed gif's of oblique ball-bat collision. These videos were part of an experiment to study the spin of a batted ball. You can read the resulting publication here or look at slides of a presentation by clicking here.

All Spin Is Not Alike

The forces on a spinning baseball.

This article appeared in the March 31, 2015 edition of Baseball Prospectus. The 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.

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.