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

Optimizing the Swing: A Physics-Based Approach

Alan Nathan, Presentation at 2019 SABR Analytics Conference

Color contour plot relating exit velocity and launch angle to attack angle and centerline angle. The dashed red line indicates where the attack and centerline angles are equal. The blue curves and colors are exit velocity contours and the black dashed lines are launch angle contours.

In this presentation (audio link), I present the results of various experiments on oblique ball-bat collisions and show how they are used to predict batted ball parameters from the swing parameters, as shown in the figure. Then I start to address the "reverse engineering" problem, whereby one tries to determine the swing parameters, especially the attack angle, from the batted ball parameters. The issue of timing enters if the attack angle of the bat differs from the descent angle of the ball, and this issue is investigated quantiatively. Finally, the question is addressed whether it is advantageous to alter the swing to sacrifice exit velocity to gain some extra spin on the batted ball. Further links related to this topic can be found by clicking here.

Baseball Aerodynamics

Airflow around a spinning baseball. The ball is moving from right to left and is spinning with backspin. Note that the wake behind the ball is deflected downward, resulting in an upward force on the ball.

This is a link to the website of Prof. Barton Smith, aka NotRealCertain. Barton, a Professor of Mechanical and Aerospace Engineering at Utah State University, is an expert on sports ball aerodynamics and especially on the use of the technique known as Particle Image Velocimetry to study air flow patterns around the moving object.

Pitch Movement, Spin Efficiency, and All That

Alan M. Nathan, The Hardball Times, August 27, 2018

This article takes a critical look at how movement is determined from measurements of the trajectory. Two techniques are investigated. Technique 1 is that used currently by Statcast/Trackman. Technique 2 is based on one that I investigated over 10 years ago. I show that Technique 1 results in systematic deviations of the movement from the exact values whereas Technique 2 does much better. The underlying physics behind Technique 2 is discussed here; click here for the spreadsheet template described there.

The Physics and Timing of the Outfield Bounce Throw

Andrew Dominijanni, The Hardball Times, August 21, 2018

Andrew (@ADominijanni) does a wonderful physics-based analysis quantifying the relative merits of the on-the-fly vs. bounce throw from the outfield.

A Humidor at Chase Field: What's Up With That?

Alan Nathan, The Hardball Times, April 17, 2017

Chase Field, home of the Arizona Diamondbacks.

As has been reported in the media, a plan is afoot to install a humidor at Chase Field, home of the Arizona Diamondbacks. Prompted by these reports, I decided to dust off my old analysis from 2011 that successfully postdicted the reduction in home runs when a similar humidor was installed at Coors Field. The new calculation combines physics with statistical analysis to predict a 25%-50% reduction in home runs that would result from storing baseballs in a humidor rather than in the very dry climate of Phoenix. This result has attracted some attention in the media as well as a followup article by Andrew Perpetua which tends to support the 50% (as opposed to the 25%) reduction.

The DBacks management postponed use of the humidor to the 2018 season, so it is very useful to compare home run production in 2018 to that in 2017. Professor David Kagan's Humidor Tracker does exactly that and is updated at the end of each home stand in the 2018 season. Other articles with the early returns from the 2018 season can be found here, here, and here.

Finally, I gave a presentation on this topic at SABR48 in Pittsburgh, June 21, 2018. The slides can be downloaded here

Trajectory Calculator

This is a link to a page describing the latest version of my Trajectory Calculator, which is now fully 3-dimensional and utilizes drag and lift coefficients that have been optimized using Statcast data.

Effect of Temperature on Home Run Production

With the start of the 2017 World Series in Los Angeles and with tempertures well into the 90's, I did a "back-of-the-envelope" calculation of how a change of temperature affect the home run production. I find that, on average, an increase of temperature by 1-deg F increases fly ball distances by about 0.33 ft, leading to approximately 1% more home runs.

Fly Ball Carry and the Home Run Surge

Alan M. Nathan, The Hardball Times, August 24, 2017

Result of the carry analysis

This article reports the results of an analysis of trajectories at Tropicana Field for the 2015-2017 season to determine if there is any change to the carry of a fly ball. Since the Trop is a domed stadium, atmospheric effects are constant and any change in carry can be attributed to changes in the drag properties of the baseball. A five foot increase in carry is found for 2016-2017 relative to pre-ASG in 2015, as shown in the figure. A more technical version of this article can be found here.

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. Early in the 2017 season, three new articles about this issue have appeared: As Home Run Rates Rise, MLB Offers Evidence That the Ball Isn’t Juiced by Ben Lindbergh, Juice the ball. Or don't juice it. Just tell us! by Sam Miller, and Let's Assume the Ball Isn't Juiced ... by Russell Carleton.

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.

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, Spin That Curveball, The Next Collin McHugh?, Mother May I?, and especially What We Know About Spin Rate, in which he has done some analysis using the concept of useful spin.