## A new PITCHf/x chart

For a long time, I've been frustrated by spin movement (Magnus effect) charts because they don't genuinely show how much a pitch actually moves. These charts perfectly demonstrate how the spin of the ball changes its path, but they don't show how velocity adds a vertical element to the pitch's movement.

Take this chart for example. These are the pitches thrown by Texas Rangers LHP Derek Holland during September and October of last season.

Even though they are much slower pitches, Holland's change ups are located in the exact same place on the graph as his fastballs. If his fastball and change up start with the same trajectory, the change up will always cross the plate lower than the fastball. I wanted to capture this on a chart, so I put gravity back into the equation.

Using Gameday's physics data (initial position, initial velocity, acceleration), I calculated how long each pitch was in the air. Keep in mind, though, that PITCHf/x starts at 50 from the plate and ends just in front. The mapped data covers only about 48 1/2 feet.

With the flight time for each pitch, I calculated the drop caused by [sea-level] gravity. After converting this number from feet to inches, I added the vertical spin movement. Here's how it turned out:

Success. The change ups now appear below his fastballs. The chart reflects not only gravity's effect on a pitch, but it also helps separate pitches by velocity, making identification a little bit easier.

This chart does not replace virtualizations by any stretch of the imagination, but I think it does show how different two pitches can be from each other even when spin movement alone can't show it. Taking this a step further could lead to a "hitter's decision" chart that would represent how different the pitches look at a certain time or distance from the plate.

The gravity charts are now available for all pitchers in TexasLeaguers.com's PITCHf/x Database.

[[Update: On April 24, 2010, the Spin Movement w/Gravity charts were updated to reflect gravity's effect from y = 40 to y = 1.417. This change was made based on the information that can be found at Alan Nathan's PITCHf/x site: MLB Extended Gameday Pitch Logs: A Tutorial]]

## Reader Comments (7)

Mike Fast used to do a very similar thing (possibly the same thing) when he wrote for StatSpeak. The articles are gone now, however.

I figured I couldn't possibly be the first one to do this, but I couldn't find something like this anywhere else. Thanks for the note.

Very cool Trip, I like this much better than the standard spin deflection charts, and you are correct that this is much better for identification. Can you possibly share the formula you used to add gravity to the movement? I have little background in physics and would likely not be able to reproduce what you've done here.

Dan: I looked around and though I didn't find anything specific, I think the charts Mike did involved normalizing pitch movement to the pitcher's fastball. I could be wrong.

Nick: I used the quadratic formula to solve for 't' in the standard acceleration equation: 1/2*ay0*t^2 + vy0*t + y0, where y0 is the starting point of the tracking for a given pitch. ay0 and vy0 are given by PITCHf/x and represent the pitch's initial forward acceleration and velocity, respectively.

Using the value of 't' -- which is the amount of time it takes the baseball to go from 50 feet away from the front of the plate to 0 (the plate's front edge) -- it's easy to calculate gravity's effect on the height of the pitch -- 1/2*a*t^2.

Since some pitches start at y=55 and others start at y=50, the graphs will show "bonus" gravity effect when y=55. I haven't compared them to see how big of a difference it makes, though.

Here we go:

http://fastballs.wordpress.com/2010/04/18/tales-of-the-curve-an-analysis-of-erik-bedard/

Thanks, Dan.

His first chart is a little off, I think. His landmarks are off by 90°. 0° is straight forward spin (12-6 curveballs), not spinning toward righties. 180° is straight backward spin ("rising" fastball), not spinning toward lefties.

I just asked Mike how he was calculating his gravity effect since my values seem to be much larger than his.

After speaking with Mike and reviewing Alan Nathan's tutorial (which I should already have memorized...), I have changed the gravity calculation to reflect the path of the ball from y = 40 to y = 1.417.

If I understand that part of the tutorial correctly, I may need to adjust my pitch virtualizations as well.