Nathan: How far did that fly ball travel?

From SABR member Alan Nathan at Baseball Prospectus on January 8, 2013:

In my line of work, I get asked questions from all sorts of different people, such as reporters, kids doing science fair projects (and their mothers), and diehard baseball fans. Some recent examples: How much farther will a fly ball travel in Denver? What’s the deal with those BBCOR bats? Is the baseball juiced? Should the Red Sox trade Jacoby Ellsbury? Okay, I confess that no one has (yet) asked my opinion on that last question. However, one question that I get asked quite often is the following: Can we predict the landing point of a fly ball just after it leaves the bat? That’s what I want to talk about in this article.

Let me try to sharpen up that question a bit. Suppose we have data telling us the velocity of a fly ball just after leaving the bat, so that we know the batted ball speed, vertical launch angle, and horizontal spray angle. How well does that information determine the landing point? Such a question might arise, for example, in a batting cage situation. You measure the batted ball velocity—perhaps with a portable HITf/x or TrackMan system—and immediately tell the batter that he just hit a 385-ft home run, without the ball ever leaving the batting cage. But is this really possible? In a simpler, gravity-only world—I like to refer to it as the “Physics 101” world—it most definitely is possible. Under such conditions, once the initial velocity is known, the ball follows a trajectory that is completely predictable, landing in a location that can be calculated precisely with no more knowledge than one learns in the second week of Physics 101. End of discussion, right?

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Originally published: January 8, 2013. Last Updated: January 8, 2013.