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

USA Baseball and member organizations announce new youth bat performance testing program

On August 7, 2015, USA Baseball and its member organizations (including Little League) announced new bat performance standards for youth baseball, to be implemented starting in 2018. The new standard, which will replace the current BPF 1.15 standard used by many of the youth baseball organizations, is very similar conceptually to the BBCOR standard used in college and high school baseball. Both are based on the ball-bat coefficient of restitution, with performance limits set by the highest performing wood bat.

You can learn about the physics of bat performance standards from my article Regulating the Performancs of Bats, published in The Hardball Times Annual 2015

Download StatCast Batted Ball Data

This a link to Daren Willman's site baseballsavant.com. Go there to obtain StatCast batted ball data for the 2015 season, including batted ball speed, launch angles, and distances. Also included are all the pitch data. Want to know who hits the ball hardest. Download the data and you will find out. The above plot (updated July 12, 2015) shows the relationship between fly ball distance and batted ball speed, with the color indicating the density of fly balls in that region of the plot. For a given speed, there is a broad range of distances, primarily due to different vertical launch angles, which were not recorded. However, there is a maximum distance for a given batted ball speed shown by the solid black line. That line extrapolates to about 535 ft at the largest recorded batted ball speed of 120 mph. However, there seems to be some indication that the data "rolls over" at the highest speed (>105 mph). More data will be needed to confirm whether or not this is actually the case.

A Tale of Two Dingers

My analysis of the two tape-measure home runs hit by Alex Rodriguez on April 17, 2015, published on April 23 in The Hardball Times. The analysis makes extensive use of StatCast, the new system used by MLB for tracking the ball and all the players on the field. It also makes good use of data from ESPN Home Run Tracker. The figure shows the trajectories of the two home run, one of which traveled over 470 ft, the other about 490 ft..

An Analysis of a Broken Bat Home Run

On March 30, 2015, Red Sox slugger Mike Napoli hit a dinger over the Green Monster at Fenway South in a Grapefruit League game versus the Twins. You can see the homer here. While the event was certainly unusual, was it a remarkable show of strength by Napoli? Conventional wisdom says that he had to work harder than normal to get such a well-hit ball, given that the bat broke. As Red Sox color announcer Jerry Remy said, "That will give you an idea of how strong Napoli is." So, is conventional wisdom correct? Was Napoli impeded by the broken bat, thereby requiring an extra effort to "muscle the ball" while it was in contact with the bat? The answer to both questions is a resounding NO. Go to the link to read my analysis.

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.