Friday, June 13, 2014

How amazing was Yoenis Cespedes's throw to the plate? A physics analysis


I need two critical pieces of information: How far did the ball travel (D), and how long was it in the air (T). To answer both questions, I replayed the video over and over again until I was satisfied that I had a good estimate of both D and T.

First, we know that the distance to the left-field foul pole in Anaheim is 340 ft. I estimate from the video that Cespedes was about 20 ft from the foul pole and just inside the LF line when he unloaded the ball. I also estimate that the ball was caught by A’s catcher Derek Norris about 2 ft from the corner of home plate. Thus I find that D=318 ft. Next, I used several different camera angles to time the throw with a stopwatch. I found amazing consistency with that process, arriving at T=3.17 sec. ...

I made certain assumptions about the drag coefficient and the amount of backspin on the ball. The specific assumptions are not terribly important, since the final result is not all that sensitive to reasonable changes in those assumptions. Based on the video, I assumed that the throw was released from a height of 6 ft and was caught at a height of 5 ft. I then simply adjusted the release speed and vertical launch angle to make the trajectory be 5 ft off the ground and 318 from release after 3.17 sec. I find that the ball was released at a speed of 97-99 mph and at a launch angle of 12-14 degrees. ...

How accurate did Cespedes have to be to nab the runner at home plate? The replay shows that there was very little margin for error. How does that translate in the accuracy of release? ...

I found that a ±1 degree change in horizontal angle would lead to a horizontal deflection of about ±6 ft at home plate, probably making it impossible to nail the runner. I found that at ±1 degree change in the vertical angle would change the height of the ball at home plate by ±5 ft, meaning the ball would have hit the ground just in front of the plate or nearly gone over the catcher’s head. So we can safely conclude that Cespedes’s margin of error was less than (but comparable to) ±1 degree in each direction.
--UIUC physics professor emeritus Alan Nathan, Baseball Prospectus, on quantifying amazing