# Nathan: The physics of Yoenis Cespedes’ truly amazing throw

From SABR member Alan Nathan at Baseball Prospectus on June 11, 2014:

When I woke up on Wednesday morning and checked my overnight Twitter timeline, I found considerable buzz about an incredible throw made by Oakland A’s left fielder Yoenis Cespedes on Tuesday night.

With the game between the A’s and the Angels tied 1-1 and Howie Kendrick on first with one out in the bottom of the eighth, Mike Trout hit a fly ball to left field that fell in for a hit. When Cespedes misplayed the bounce and the ball rolled into foul territory, Kendrick kept on running. Cespedes eventually fielded the ball, over 300 feet from home plate, then uncorked a perfect strike on the fly to nab Kendrick at home plate. Prompted by several calls on the Twittersphere for a “physics analysis” of this amazing throw, I decided to forget about what I had been planning to do concentrate on this analysis instead. So, here we go.

What I wanted to do was come up with a way to determine the full trajectory of the throw. To do that, 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. Now, I should point out that ESPN reported somewhat different numbers, D=300 ft and T=2.78 sec. I am pretty confident about the T, and perhaps less confident about the D, since I had to estimate the distance from the foul pole. But ESPN had to do that also. In any case, I’ll proceed with my numbers and comment later on doing the same analysis with the ESPN numbers.