Tracking Baseballs Using Video Technology:
The PITCHf/x, HITf/x, and FIELDf/x Systems

This page mainly contains links to articles on the PITCHf/x system for tracking pitched baseballs. In the near future, additional links will be added on the HITf/x and FIELDf/x systems for tracking batted balls and people on the field.

What the Heck is PITCHf/x? A superb article written by analyst Mike Fast (@fastballs) for The Hardball Times Annual 2010. This is a great place to start learning about what this new technology is all about and what it is good for. Mike is one of the premier PITCHf/x analyzers.

Determining Pitch Movement from PITCHf/x Data This is an article I wrote in October 2012 in which I discuss the concept of pitch movement, including how it is defined and how it is calculated using the PITCHf/x tracking system. I indicate why that technique does not exactly conform to the definition and further indicate how to correct it so that it does. I give some examples of how the improved technique can affect baseball analysis. A template in the form of an Excel spreadsheet is available to do the actual calculations.

Estimating Pitcher Release Point Distance from PITCHf/x Data This is a link to an article by Matthew Mata (Arcarsenal8) that appeared June 29, 2013 in FanGraphs. The article describes a procedure to determine the mean distance from home plate of a pitcher's release point by minimizing the area subtended by the distribution of transverse coordinates of the pitches as a function of home plate distance. As a added bonus, another outcome of the analysis is the pitcher's arm slot. The article describes some interesting mathematical and statistical techniques; nevertheless, the writing is very clear and the article should be accessible to many readers, even those without a mathematical background.

New Technologies in Baseball, a panel discussion of the latest developments in Sportsvision's PITCHf/x, HITf/x and FIELDf/x, and TrackMan's radar technology used to measure ball flight, presented at SABR40 in Atlanta, August 7, 2010. The panel members were Rand Pendleton (Sportvision), Rob Ristagno (TrackMan), Dave Allen (Fangraphs and Baseball Analysts) , Josh Kalk (Tampa Bay Rays), and myself. The zip file contains the talks that were presented by each of us.

An Introduction to FIELDf/x and A FIELDf/x Application: True Defensive Range, articles that were published in The Hardball Times Annual 2011. The first article is a brief introduction to the FIELDf/x system and is co-written by Greg Rybarczyk, inventor of the ESPN Home Run Tracker, and Kate McSurley of Sportvision. FIELDf/x is an enhancement to the pitch-tracking PITCHf/x system and uses multiple cameras to track everything on the playing field: the fielders, the umpires, the base runners, and the batted ball. The second article about True Defensive Range is written by Greg. It is the finest piece of publicly available analysis using FIELDf/x data that I have seen and is a must read for anyone interested in advanced fielding metrics. Thanks to Greg and to Dave Studeman, manager of The Hardball Times, for allowing me to post the articles here. Greg talked about this work at the annual PITCHf/x Summit in 2010 and 2011.

Yes, we can classify every pitch, an article by Dan Brooks (@brooksbaseball) appearing February 4, 2012 in The Hardball Times. In the article, Dan announces his new player cards, a collaborative effort with THT writers Harry Pavlidis (@harrypav) and Lucas Apostoleris (@DBITLefty). The pitch classifications are done by hand, a remarkable effort, and are almost surely the best available. The plots available for each pitcher are both informative and beautifully put together. This is great stuff by some of the best PITCHf/x analysts still unhired by MLB teams.

As of February 1, 2012, Mike Fast is no longer a free-lance analyst, having taken a position in the Baseball Operations department of the Houston Astros. Best wishes to Mike for success in his new position.

Here are links to some of the articles he has written.

Sportvision: This is the company responsible for the pitch-tracking technology, including the software used to reconstruct the trajectory in real time and render it for the broadcasters. They are also the people who created the virtual yellow first-down marker used in television broadcasts of football games. The Chief Technology Officer of Sportvision at the time the system was conceived and implemented was Marv White, an alumnus of the University of Illinois Department of Physics. Since March 2010, Marv White is Chief Technologist for Innovation at ESPN.

PITCHf/x Wiki An excellent wiki put together by Dan Brooks at the Sons of Sam Horn site. See also Dan's PITCHf/x Tool, which can be used to inspect and/or download data from a specific pitcher in a specific game.

The Effect of Air on Baseball Pitches An excellent tutorial by physicist Michael Richmond, specifically geared toward PITCHf/x users.

MySQL MLB Pitch FX Data: A link to Darrell Zimmerman's site for downloading the entire PITCHf/x data into an SQL database. If you know how to use SQL, this is far and away the easiest way to obtain the data. If you don't, then check the next link.

Databases for Sabermetricians, Part I, an excellent primer by Colin Wyers on SQL. This is how I learned whatever little I know about the subject.

Tracking an Object with Multiple Asynchronous Cameras is the patent application of Marv White and Alina Alt. This document discusses the various techniques that can be used to determine the trajectory in field coordinates (x,y,z) from the camera pixel information.

PITCHf/x Nine-Parameter Trajectory Model Fitting, a document written by Rand Pendleton of Sportvision giving the mathematical details that are used to convert pixel information into a constant-acceleration trajectory. The general technique outlined here can easily be extended to include arbitrary numbers of cameras or to utilize different physical models for the trajectory.

Effect of the Magnus Force in the PITCHf/x Tracking System : How to use the PITCHf/x data to get improved values for the break of the pitch due to the spin of the ball.

A Monte Carlo Simulation of the PITCHf/x System A statistical study addressing the overall accuracy of the PITCHf/x parametrization of the trajectories and the effect of random measurement error on derived quantities, such as the break of the pitch.

Determining the Drag Coefficient from PITCHf/x Data: This short paper, co-authored with Ike Hall, discusses the importance of getting the drag coefficient and shows how to extract it from the PITCHf/x data. It is also shown how to extract the lift coefficient and spin axis.

How to Link PITCHf/x to Retrosheet, article by Dan Turkenkopf.

Catalog of analyses posted on the web of PITCHf/x pitch logs, as compiled by The Hardball Times and updated regularly. This is your "one-stop shopping" site for some very nice articles. See also the excellent Pitch Classification Tutorial by John Walsh.

My own analysis of pitches in which I give a "physics" analysis in terms of drag and lift as well as a scheme for classifying pitch types. All the relevant formulas are given in this analysis.

HITf/x+Hittracker Analysis of a Home Run: An analysis I did using the HITf/x measrurement of the initial velocity vector and the hittracker measurement of the landing point and hang time to determine the full trajectory of a batted ball.

Second Annual PITCHf/x Summit. A gathering that took place July 11, 2009 in San Francisco. See also the related CBS story/video, which aired on July 26, 2009. Finally, have a look at the story about FIELDf/x by Alan Schwarz which appeared in the July 9, 2009 edition of the New York Times. Be sure to have a good look at the video (kudos to Mike Fast for doing the analysis that led to the video).

What Are We Learning from PITCHf/x. Powerpoint slides of a talk I gave at SABR38, the annual meeting of the Society of American Baseball Research, Cleveland, June 27, 2008. After the talk, Cory Schwartz of MLBAM did an on-camera interview with me, which can be viewed at here.

How Mariano Rivera Dominates Hitters Click on the link to see a NYT story from June 2010 about what makes Rivera the greatest closer in MLB history. Make sure you watch the remarkable video, which was put together using information supplied by the crack analysis team at Complete Game Consulting. Finally, look at the article Is Late Break Real?, where I examine the question of late break using a pitch by the great NYY closer Mariano Rivera as my primary example.

The Anatomy of a Pitch: Doing Physics with PITCHf/x Data. An excellent pedgogical paper by Dave Kagan (The Physics Teacher, vol. 47, pp. 412-416, 2009).

Template for Cd and Cl. This is a template for using pitchf/x data to calculate the air drag on the ball, the spin axis and estimate of the spin rate (in rpm) inferred from the movement, and the drag and lift coefficients (Cd and Cl, respectively). Click on the link to download the Excel file. The only input required are the 9-parameter fit to the pitchf/x trajectory into columns B-J, the gametime temperature (cell B3), elevation (cell B4), the relative humidity (B5), and the barometric pressure (B6). Improved values for the pitch movement are also calculated and are given in cells AH-AI. Since the drag is removed, these values are better representations of the actual movement than those given by MLBAM/Sportvision.