# Help With the Physics Behind PITCHf/x

I’ve been digging into the PITCHf/x data over the past few weeks and stumbled across something I can’t quite figure out. When I first started using the data, I didn’t realize that px and pz were where PITCHf/x is mapping the final location of the ball; undeterred I set out to Google to jog my memory on the basics physics formulae that can map time using initial velocity, final velocity, distance and constant acceleration.

Step 1 was to calculate final velocity for every pitch from -50 feet to 0 feet. This was a simple formula that is SQRT(vy0^2-2*50*ay). Initial velocity squared less acceleration * yo2 * distance. Based on y0 being 50 feet from home plate.

Step 2 was to calculate time based on initial velocity and final velocity. I cross-checked my numbers to using the Start_Speed and End_Speed (which don’t match up to to vy0 for some reason) and got basically the same number.

Step 3 was to calculate xFinal based on Time, ax and x0 (ditto for zFinal). Strangely, my zFinal was a little lower (about .17 feet) than the PITCHf/x pz value and .015 more to the right than the px value. That might mean that they are measuring z and x 50 feet from release point, rather than at home plate.

I need to know if (a) my math is wrong (b) pz and px are wrong (c) ax and az are wrong.

Any help would be appreciated!

Eli Ben-Porat is a Senior Manager of Reporting & Analytics for Rogers Communications. The views and opinions expressed herein are his own. He builds data visualizations in Tableau, and builds baseball data in Rust. Follow him on Twitter @EliBenPorat, however you may be subjected to (polite) Canadian politics.

Guest
AC_Butcha_AC

I just read your article and didn’t look anything up cuz I’m in a hurry but for whatever reason I think I remember that the measurment starts at 55ft away from home plate.

Guest
Matt P

“For PITCHf/x data, the starting point for pitches, in terms of the location, velocity, and acceleration, is set at 50 feet from the back of home plate. However, 55 feet seems to be the consensus for setting an actual release point distance from home plate, and is used for all pitchers. ”

http://www.fangraphs.com/community/estimating-pitcher-release-point-distance-from-pitchfx-data/#comment-234157

Guest
Alan Nathan

Dave Kagan, a regular contributer to THT, wrote an article that has all the details about px,pz and much more. See http://baseball.physics.illinois.edu/KaganPitchfx.pdf.