ESPN Home Run Tracker :: How HitTracker Works

How HIT TRACKER Works

The Problem: Estimate the True Distance of a Home Run: When a batter hits a long home run, people want to know how far it traveled. Unfortunately, in the past it has been difficult to determine this distance with accuracy when the ball does not complete its trajectory all the way to the ground, i.e. when it strikes a light tower or other tall structure, or even when it lands in outfield seats that are elevated above field level. Hit Tracker determines the true distance a home run travels by recreating the precise trajectory the ball followed during flight, and extending that trajectory all the way back to field level to allow “measurement” of the home run.

How Hit Tracker Works: Hit Tracker is a spreadsheet tool that takes as inputs atmospheric information and observation data, and gives as an output the true distance that the home run traveled, along with the initial speed of the hit off the bat and the precise angles at which the ball left the bat. It does this by creating as a starting point an initial “best-guess” three dimensional trajectory for the home run, and then modifying that trajectory, a little bit at a time, until the trajectory matches the observed data from the actual home run event. An example follows:

Hit Tracker Example: A player hit a “walkoff” home run at Fenway Park on May 10, 2005, the ball striking one of the light towers above the left field wall and seats before caroming back onto the playing field. How far would this home run have traveled if it had not struck the light tower or any other obstruction?

Atmospheric data: Hit Tracker accounts for all the atmospheric factors that significantly influence the flight of a batted ball: wind, temperature, altitude and spin. Wind speed and direction, temperature and altitude must be specified by the user, based on the conditions at the time of the home run. The spin of the ball is determined by a series of assumptions related to the direction and speed of the ball as it leaves the bat. So, for the particular home run in question, the atmospheric data would be entered:

Wind: in from RF at 5 mph
Temperature: 57 degrees F
Altitude: 21 ft. above sea level
Spin: automatically calculated

Observed data: To determine the trajectory of a batted ball, Hit Tracker uses two points: an initial point, which is always assumed to be about 3 feet above home plate, and a final point, which is a point typically near the end of the ball’s flight. For this “final” point, Hit Tracker needs to know the location of the final point and the time of flight of the ball to reach the final point. On the home run in question, the location of the point of impact of the ball against the light tower was determined using a scale model of Fenway Park, and the time of flight was measured with a stopwatch, yielding the following data:

Distance from home plate: 314 ft.
Vertical distance above field level: 43 ft.
Horizontal angle: 7.4 degrees to the right of the left field line
Time of Flight: 3.20 sec.

Initial trajectory: To determine the trajectory that the ball followed, Hit Tracker begins by making a “best guess”. The inputs to this best guess trajectory consist of three parameters:

SOB: the initial speed of the baseball off the bat
VLA: the vertical launch angle; small for a line drive, large for a popup
HLA: the horizontal launch angle; the direction on the field, e.g. right-center field

Given these three initial parameters, Hit Tracker constructs the complete trajectory for the initial guess, breaking the flight of the ball into small increments of time (1/100th of a second) and applying the forces acting on the ball during flight:

Gravity
Wind resistance
Magnus force - the force due to the spin of the ball (what makes a curveball curve)

Figure 1: “initial guess” trajectory and impact point of actual home run

In the case shown here, the initial guess trajectory point for 3.20 seconds is a bit high and a bit short compared to the actual observation point (with the horizontal angle not shown here, but also taken into account), so the initial trajectory needs to be changed. Using a proprietary method, Hit Tracker rapidly adjusts the three inputs (SOB, VLA, HLA) until the Hit Tracker trajectory point for 3.20 seconds matches the actual observation point. Once this occurs, Hit Tracker has reconstructed the actual trajectory the ball followed in flight; the true distance of the home run is then read from the Hit Tracker trajectory, representing the actual distance the ball would have traveled had its flight not been interrupted.

Figure 2: “initial guess” trajectory, final trajectory and impact point of actual home run

Summary of Hit Tracker results: For the home run in question, the final values for the three input parameters are as follows:

SOB (Speed off Bat): 107.9 mph
VLA (Vertical Launch Angle): 26.6 degrees
HLA (Horizontal Launch Angle): 12.3 degrees to the right of the left field line

These inputs to the ball trajectory, combined with the atmospheric data, result in a true distance for this home run of 372 ft.

Screenshot of Hit Tracker:

Figure 3: Hit Tracker screenshot

Other Applications: Hit Tracker can also be used as part of a scouting and player valuation system by extending analysis to all outfield flies in addition to home runs. For additional information, see below:

Additional Information: For more information on Hit Tracker, please contact Greg Rybarczyk via email at grybar@hittrackeronline.com.