## Contributions to Variation in Fly Ball Distances

Back in early 2013, I wrote a guest article for Baseball Prospectus entitled “How Far Did That Fly Ball Travel?” In that article, I posed a seemingly simple question: Can we predict the landing point of a fly ball just after it leaves the bat? A more precise way to ask the question is as follows: Suppose the velocity vector of a fly ball just after leaving the bat is known, so that the exit velocity, launch angle, and spray angle are all known. How well does that information determine the landing point? I then proceeded to investigate the question, at least for home runs, with the aid of HITf/x data for the initial velocity vector and the ESPN Home Run Tracker for the landing point and hang time. Using a technique described in the article, that information was used along with a trajectory model to reconstruct the full trajectory and extrapolate it to ground level to determine the fly ball distance. The answer to the question was immediately obvious: The initial velocity vector poorly determines the fly ball distance.

This conclusion led naturally to the next question: Why? One obvious reason is variation in atmospheric conditions, especially wind. However, the data revealed that the variation in home run distance for given initial velocity was as large in Tropicana Field, where the atmospheric conditions are expected to be constant, as in the rest of the league. So that was eliminated, at least as the primary culprit.

The article then went on to consider variation in two other parameters that play a role in fly ball distance: backspin ωb and drag coefficient CD. Neither of these parameters were directly measured. Rather they were inferred, along with the sidespin ωs, in the procedure used to recreate the full trajectory. The analysis showed the following:

• For a given value of CD, distance increases as ωb increases. This makes sense, since larger backspin results in greater lift, keeping the ball in the air longer so that it travels farther.
• For a given value of ωb, distance decreases as CD increases. Again this makes sense, since greater drag is expected to reduce the carry of a fly ball. Interestingly, this was the first appearance in print of a suggestion of a significant ball-to-ball variation in the drag properties of baseballs.
• There was a moderately strong positive correlation between CD and ωb, suggesting that the drag on a baseball increases with increasing spin, all other things equal. Although this effect is well known for golf balls and had been speculated for baseballs in R. K. Adair’s excellent The Physics of Baseball, to my knowledge this is the first real evidence showing the effect for baseballs.
• Given that both lift and drag increase with increasing ωb and that they have the opposite effect on distance, it was tentatively concluded that at high enough spin rate there would be no further increase (and perhaps even a decrease) in distance with a further increase in spin.

## Spinning Out of Control

Every now and then, something occurs in a major-league game that just compels me to stop what I’m doing, switch gears, and go into analysis mode. It happened most recently in the top of the fifth inning of NLCS Game Five when Kris Bryant hit a fly ball to straightaway — but slightly on the left-field side of — center field. Center fielder Joc Pederson ran nearly straight backward initially facing toward right field. Then he suddenly and perhaps inexplicably spun around to face left field while still running toward the fence.

At the last minute the ball went just over the reach of his outstretched glove, on the right-field side of center field. The ball bounced on the warning track close to the CF fence, and when the dust had settled, Bryant was on second base with a double. Just to make sure everything is completely clear: Pederson was initially facing the right direction, then he spun around to face the wrong direction, then he spun back at the last second to the original direction, with the ball barely escaping his outstretched reach. Having spun around a complete 360 degrees, he clearly misplayed the ball.