View from the batter’s box

My article at Hardball Times on Danny Herrera’s screwball includes views of his pitch trajectories as seen from the right-handed and left-handed batter’s boxes.

I mentioned in the References section that I did some trigonometry to transform the coordinate system from plate view to batter’s box view.

Here is what I did.

The pitch trajectory is shown as the dotted black line. Any point on the trajectory can be calculated using the initial position, velocity, and acceleration provided in the PITCHf/x data, along with the equations of motion. Only the x-y plane is shown above since no transformation was done to the z axis. The coordinates in the PITCHf/x coordinate space are x and y, shown in black.

The coordinates in the batter’s box view are x’ and y’, shown in red. The y-axis in the batter’s box view runs along a line from the batter’s head to the pitcher’s approximate release point (the average x value of his pitches at y = 55 feet). The x-axis in the batter’s box view is set perpendicular to this new y-axis.

The origin of the batter’s box view is offset 2.8 feet in the x direction from the origin in PITCHf/x coordinate space. I calculated 2.8 feet from the center of the plate as the approximate location of the batter’s head, based on a video frame capture in Marv White’s presentation at the PITCHf/x Summit. I chose not to offset the origin in the y direction for simplicity, although I also believe this does not introduce any significant inaccuracy. The batter’s head is typically within a foot or so of y=0.

First, I calculated the quantity m, the distance to the baseball, shown by the blue line. This distance m = sqrt ( y^2 + ( x + 2.8 ft)^2 ).

Next, I found the value of the angle alpha. The angle alpha = arctan ( 55 ft / ( x0 + 2.8 ft) ).

The angle (alpha - theta) = arctan ( y / ( x + 2.8 ft) ), which allows us to calculate the angle theta.

The angle theta = arctan ( 55 ft / ( x0 + 2.8 ft) ) - arctan ( y / ( x + 2.8 ft) ).

The batter’s box coordinates x’ and y’ can be found from the angle theta and the distance m. The new y’ = m * cos (theta), and the new x’ = m * sin (theta).

I am happy for you to use my method for batter’s view transformation if you provide attribution in the form of my name and/or a link to this website.

 

Random fun with PITCHf/x

This has nothing to do with anything except me reveling in the things you stumble upon in the PITCHf/x data set. I was looking at some Roy Oswalt data from last year. When I looked at his August 18 start, I noticed he had thrown his fastball at two distinctly different speeds.

When do you think Oswalt pulled his left oblique muscle?

You’re right. From the AP game recap:

Oswalt said he first felt something near his rib cage on his last pitch of the third inning, a curveball to Geoff Blum. Oswalt batted with two outs in the fourth and beat out an infield RBI single to give the Astros a 3-0 lead.

“I went through the fourth and told them I want to stay out there and see if I could get through two more innings,” Oswalt said. “Made it through the fourth and thought I could have made it through the fifth.”

No revolutionary analysis there, but I thought it was a fun tidbit.

 

Status of the catalog

Last year I diligently kept a catalog of articles written about topics related to PITCHf/x or using PITCHf/x data. Some of you have noticed that I have been negligent in updating that catalog this year. My last full update was January 15, and I did a partial update on March 1.

A new update is now in progress behind the scenes. Since the article list now exceeds six hundred articles, I’m working toward a database solution to better track them all. Hopefully, I’ll be able to unveil something within the next few weeks. In the mean time, Harry, if you would quit writing more than an article per day, that would help a lot. I should just rename my catalog the Cubs f/x Index.

 

THT: Cust 2008

During March I did an in-depth study of Jack Cust’s surprising 2007 season. Recently I’ve been wondering why he was struggling so mightily in 2008. I did an update to the study and published the results at The Hardball Times.

Edit:  I posted to THT Live about Cust’s performance over the last couple days.  I don’t intend to imply that I can divine the end to a player’s slump or the beginning of a hot streak.  It’s more of a case of me musing out loud about and trying to learn how the PITCHf/x tools fit into the scouting/performance picture.

 

Correcting the PITCHf/x data

Ike Hall has a really good post on data corrections at his new blog.

I’m still in the process of reading through it, but he now has concrete data that confirms what I have believed all along on the basis of the pitcher data I’ve seen, that a uniform correction factor for each park for the whole 2007 season was not adequately addressing the real source(s) of error in the data.

 

BP Radio interview

I was interviewed about PITCHf/x by Will Carroll of Baseball Prospectus Radio.  You can listen to the interview on the BPR site.

 

Typical spin and Valverde

I posted an analysis of Jose Valverde’s early-season troubles on THT Live yesterday.

Also, Dan Brooks (Jnai) has been doing some very good work with PITCHf/x over at the Sons of Sam Horn discussion board. His PITCHf/x wiki is well worth checking out.

As part of the discussion of Dan’s work at the Book blog, I made a chart of pitch speed vs. spin deflection angle for a typical right-handed pitcher.

 

Standing on the shoulders of giants

We are like dwarfs sitting on the shoulders of giants. We see more, and things that are more distant, than they did, not because our sight is superior or because we are taller than they, but because they raise us up, and by their great stature add to ours. –John of Salisbury

The two men who inspired me to take up PITCHf/x analysis have both now moved on to work for major league clubs. My hearty congratulations go out to Dan Fox, the new Director of Baseball Systems Development for the Pittsburgh Pirates. The Pirates are getting a good man.

Previously, Joe P. Sheehan took an internship with an undisclosed major league club. I am excited for him and fully expect to see his name in bigger roles in the not-too-distant future.

I quote John of Salisbury not to claim superiority for my work over Dan’s or Joe’s, but to the extent that I have been successful in uncovering new territory, a great deal of credit goes to Joe and Dan for inspiring me and for laying out the groundwork in the nascent PITCHf/x field. I appreciate both of them, and I’m encouraged to see their work being recognized by major league clubs.

 

Joining Hardball Times

I’m sad to say that I am leaving the Statistically Speaking blog at MVN and excited to let you know that I will be joining the team of writers at The Hardball Times.  I haven’t written any articles yet for THT, but I’ll let you know when I do.