A remarkable photo of the ball-bat
collsion (from Champaign News-Gazette)

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

Bats: They're Not Just Flying Mammals. The Science of the Baseball-Bat Collision.

Slides of my talk at the 4th annual Saberseminar, Boston University, August, 2014.


Marco Scutaro "squares up" and hits a line drive single in 2012 NLCS.

In the presentation, I talked about general features of the baseball-bat collision, including how the batted ball speed depends on pitch and swing speed. Also discussed are the role that vibrations play in determining the "sweet spot" of the bat; the factors that contribute to bat performance; the reason why aluminum generally outperforms wood; and the use of science to regulate the performance of bats, especially as applied to the so-called BBCOR bats used by the NCAA and high schools.

The Physics of a Truly Amazing Throw

an article I wrote for Baseball Prospectus on June 11, 2014.


Trajectory of Cespedes's amazing throw, from release on the left to catch on the right. The red dots show the position of the ball at half-second intervals. The bar at 300 ft shows the location of the ball when caught by the catcher.

The article is an analysis of an amazing throw by Oakland A's leftfielder Yoenis Cespedes the previous day, thowing out a runner at home plate with a perfect strike carrying about 300 ft on the fly. Note the comment I posted on the article where I used updated information to re-analyze the trajectory. Using a total distance of 300 ft and a hang time of 2.80 sec, I find that the ball was released with a speed of 101.5 mph and a vertical launch angle of 10.0 degrees. The correct trajectory is shown in the plot just above.

In a followup, my student Eric Lang has analyzed some other historic throws in an article, A Physics Comparison of Great Throws From Years Past, published in The Hardball Times, June 24, 2014. A composite plot of the Cespedes throw plus seven others is shown below.


Trajectories of eight amazing throws.

Simplified Models for the Drag Coefficient of a Pitched Baseball

an article written by Dave Kagan and myself and published in the May, 2014 issue of The Physics Teacher.

We show a variety of techniques for determining the drag coefficient from PITCHf/x data. These techniques should be suitable for classroom instruction in introductory physics courses and is an excellent way to introduce to beginning students the concept of air resistance for projectile motion.

The New MLB Tracking System


Jason Hayward runs 80.9 ft along a nearly
straight-line path to make a spectacular diving catch.

At the Sloan Sports Analytics Conference in Boston on March 1, 2014, MLBAM made a presentation about a new tracking system that will effectively track everything on the field: the pitched and batted baseball and all the players. Although not officially announced, it is my understanding from discussions with people in the know that the new system is a merger of radar and video technology, taking full advantages of the strenghts of each. Doppler radar is the natural technology for tracking the baseball. Video is the natural technology for tracking the players on the field. Together, they offer a powerful tool that has the potential to revolutionize baseball analytics. A great example of how the tracking technology might be used in broadcasts is shown in this clip. The new technology is a partnership between Trackman for the Doppler radar and Hego for the video. The new system will be installed at Miller Park in Milwaukee, Target Field in Minnesota, and Citi Field in New York for 2014, with a rollout to 29 USA parks (with Toronto still under discussion) for 2015. It is still not known how much, if any, of the data will be publicly available. As I learn more about this new technology and the MLB plans for rolling it out, I'll be posting at this site.

Modern Techniques for Evaluating Hitting


Batting Average for Balls in Play (BABIP) versus batted ball speed and vertical launch angle.

Link to slides of a talk I gave at the August 2013 Saberseminar at Boston University. The slide above shows that if a ball is hit hard (> 90 mph) and at a launch angle in the range 10-12 degrees, it will result in a hit almost 100% of the time. The data are from the April 2009 release of HITf/x.