Pirates SS Cole Figueroa gets that swing plane
right, squares up, and is rewarded with a double.

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

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.

Physics of Knuckleballs

Baptiste Darbois Texier, Caroline Cohen, David Quéré and Christophe Clanet
New Journal of Physics 18, July 2016

Red Sox knuckleball pitcher Steven Wright.

Zigzag paths in sports ball trajectories are exceptional events. They have been reported in baseball, volleyball and soccer. Such trajectories are associated with intermittent breaking of the lateral symmetry in the surrounding flow. The different scenarios proposed in the literature (such as the effect of seams in baseball) are first discussed and compared to existing data. Then experiments are performed on zigzag trajectories and a new explanation is proposed based on unsteady lift forces. In a second step, ind tunnel measurements of these unsteady lift forces are exploited to solve the equations of motion for various sports and deduce the characteristics of the zigzags, pointing out the role of the drag crisis. Finally, the conditions for the observation of such trajectories in sports are discussed.

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.

The Intrinsic Value of a Batted Ball

Glenn Healey, The Hardball Times, March 17, 2016

Heat map showing weighted on-base average (wOBA) as a function of vertical and horizontal launch angles, for exit speed equal 93 mph.

This article is the best attempt yet to develop ''outcome-independent batting metrics", based on the characterics of the batted ball. Prof. Healey applies a Kernel Density Estimation technique to HITf/x batted ball data from the MLB 2014 season to construct a continuous probability distribution of outcome probabilities as a function of the three batted ball variables: exit speed and vertical and horizontal launch angles. He uses these distributions to construct wOBA as a function of these variables, an example of which is shown in the above image. There is a wealth of information contained in images such as these and you need to read the article to learn about some of the interesting insights that result. Technical details of the mathematical approach can be found in a companion article.

How Do Hitters Perform With Their Eyes Wide Shut?

Michael Richmond, Sons of Sam Horn, February 24, 2016

This is an excellent article by Michael Richmond, physics professor at Rochester Institute of Technology. The article is a popular summary of the experiment reported in the peer-reviewed article Contribution of Visual Information about Ball Trajectory to Baseball Hitting Accuracy, by Takatoshi Higuchi, et al. The essential experimental result is that occluding the batter's view during the final 150 ms of the pitch flight time had essentially no effect on the batter's ability to square up and hit the ball on the sweet spot. In effect, the batter could shut his eyes during that last 150 ms without adversely affecting his ability to hit the ball. This result was long suspected; now for the first time we have actual experimental evidence. You can read all about the experiment and the implications either from the original article (which is a bit technical) or from Michael's excellent summary.

Robert Adair talked this subject in his presentation Batting and Thinking [audio file] at the Science of Baseball Symposium, part of the AAAS annual meeting in February 2000. He discusses the process whereby a batter observes, processes, decides, and swings the bat. As you listen, you should also look at this excellent graphic , courtesy of the NY Times. Adair goes into much detail about this topic in his famous book, The Physics of Baseball. See also this short video clip Hitting a Major League fastball should be physically impossible

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. .

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.