A beta version of a new Trajectory Calculator is now ready. This version is fully 3-dimensional and utilizes drag and lift coefficients that have been optimized using Statcast data. Feeback is welcome.

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

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.

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.

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.

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.

To hear from Ted Williams himself about the science of hitting, click here. Particularly note the discussion starting at about 12-1/2 minutes into the video, where Ted talks about 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, 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.