There’s some very informative commentary from Ike at his blog on how the reconstruction algorithm of PITCHf/x works and how that affects measurement error in the data.
He also has a couple of previous posts on the PITCHf/x topic.
It’s nice to see a fellow Sooner and, as best I can tell, a fellow OU Physics alum writing on this topic.
Fast Balls 
September 21, 2007 at 9:28 am
Had no idea you were a fellow Sooner.
BOOMER!
I’m really only just getting started with this stuff, so who knows when my thoughts are way off…It’s been a while since I’ve thought in terms of classical physics.
September 21, 2007 at 10:19 am
I think that Ike is wrong in his description as to how the PITCHf/x tracking works. The link to the paper he quoted on my web site is not a description of how the tracking works but rather a description of a different tracking system. Some comments:
1. It is definitely not true that lower speed points are more accurate than higher speed points. What matters is the shutter speed, not the frame rate. While the frame rate is only 60/sec, the shutter speed is much faster so that there is no blurring of the image at high speed. I have seen the videos (when analyzing Bonds’ 756th home run) and I can see with my own eyes that there is no blurring.
2. Each of the two cameras determines a pixel location (u,v), from which the actual ball coordinates (x,y,z) are determined based on the camera calibrations.
3. The x,y,z positions for each frame are then fitted to a 9-parameter (constant acceleration) function. Velocities and accelerations are not directly measured. Only positions are measured and they are used in the fitting procedure to get velocities and accelerations.
4. The fitting is an unweighted fit (and I know, since I have done it myself), meaning that all points on the trajectory receive equal weighting. The final points on the trajectory are no more accurate than the initial points, except insofar as the camera calibration *might* be more accurate near home plate. I emphasize *might*.
5. I have checked carefully about the constant acceleration fit to the data. That is, I have calculated a “true” trajectory using a model for the Magnus force and drag. I then do a 9-parameter constant acceleration fit, which describes the data very well. I am going to tidy up that calculation when I get a chance and post it on my web site. One additional item in this regard. When analyzing the pitch for Bonds’ record-breaking home run, I used the (x,y,z) information along with my least-squares fitting routine to extract the drag and lift coefficients along with the spin axis. I then did a 9-parameter fit to the (x,y,z) data and used that to extract the drag and lift coefficient and spin axis. When comparing the two sets of results, they were very similiar (and within the overall accuracy of the system).
6. The best experimental data I know about the spin decay rate comes from measurements on golf balls. If I make the necessary scaling to apply to baseball, I find that the time constant for spin decay is about 25 seconds. That means the spin changes by no more than 2% in the 0.5 seconds between pitcher and batter. A negligible effect.
7. When I analyzed the Bonds data, I digitized the images by hand to get the pixel coordinates of the ball for each frame. The PITCHf/x system is much more sophisticated and uses some pattern recognition routines to automatically scan the images and find the coordinates, with sub-pixel accuracy. In effect, for a blob that is larger than one pixel, you can find its “center of gravity” to better than one pixel using these techniques.
8. The experts at Sportvision tell me that the main inaccuracies in the system (besides “operator errors”, which occur from time to time) are camera calibration errors due to the movement of the camera. They try to correct for these “on the fly” by using fixed markers on the field as their reference (e.g., the first and third baselines).
September 21, 2007 at 12:16 pm
Thanks Alan,
I figured I was probably wrong in some of that…I was only going off of the information I could find easily available.
One of the things I worry about though is that it seems to me that a constant acceleration fit to position tends to get the initial (and final) velocities wrong, as well as the accelerations, which can make a difference when calculating a thing like pitch break.
September 21, 2007 at 3:16 pm
Ike…send me your e-mail address and we can carry out this discussion off-line from the rest. Over the weekend, I am going to have a very close look at what can go wrong with the 9-p fit, specifically as it relates to the initial and final parameters. My gut feeling is that it might have implications for the initial and final positions but not for the velocities. But, I will hold off any further speculation until I do the calculation. You can reach me at a-nathan@uiuc.edu.
September 21, 2007 at 8:55 pm
Can’t wait to see the results.