Battered Expectations

Do baseballs obey the conventional laws of physics?


A batter accurately tracks the baseball from the pitcher’s mound through the first two-thirds of the ball’s flight. Then the batter’s eyes jump to where he expects the ball will meet his bat (red). If he’s wrong, there is no time to move the bat and hit the ball (blue).

Tom Moore

ON FIELDS OF DREAMS, the duel between the batter and the pitcher at times assumes aspects of humiliation and farce. And never more so than when a batter misses a pitch, swinging so forcefully as to nearly sprain something. The culprit in such cases is usually either a rising fastball or a so-called drop curveball.

From the batter’s perspective, a rising fastball follows a normal trajectory until it is quite close to home plate, at which point it seems to jump several inches, as if lifted by some mysterious force. A drop curveball, on the other hand, appears to drop straight down right in front of the plate, from twelve o’clock to six o’clock—hence its other name, “12-to-6 curveball.” Any well-thrown baseball (except a knuckleball, but that’s another story) does have substantial spin that can bend its trajectory one way or another—depending on how it’s thrown—because the ball’s uneven surface creates more drag, or air friction, on one side of the ball than the other. A ninety-mile-an-hour fastball, for example, should drop nearly three feet owing to gravity, yet it falls less than two feet thanks to backspin-generated lift. It doesn’t rise, though. The perceived pop owes a lot to shattered expectations, as does the drop of a curveball.

I recall watching Kent Tekulve—who played as a Pittsburgh Pirates reliever from 1974 to 1985—use a peculiar underhand, or “submarine delivery,” to make a baseball follow what appeared to be a decidedly non-Newtonian path to the batter. As doubtful as it once seemed to me, however, a thrown baseball obeys all the conventional aerodynamic laws of physics. A. Terry Bahill, a systems engineer at the University of Arizona, and colleagues including David G. Baldwin, a former major-league relief pitcher with an engineering degree and a Ph.D. in genetics, have reams of data to prove it. They can demonstrate that the rising fastball and the drop curve are persuasive tricks, caused by the brain incorrectly processing information to predict the location of the pitched ball.

While playing sports, we almost continuously form mental models of motion in our minds. Outfielders can compute where a fly ball will land just a few moments after it leaves the bat, freeing them to devote their full attention to running to the correct spot on the field. Similarly, you might think a batter could guess where a pitch would be likely to cross home plate.

By equipping players with special glasses that precisely track eye and head movements, Bahill has shown that a batter’s attention is fixed on the ball as it is released, and for the first two-thirds of its flight path his eyes smoothly track the motion of the ball. During this focused tracking, the eyes gather data that the brain busily assembles into a model of where the ball will be when it gets within hitting range, and when that will be.

About the time the batter starts to swing—when the ball is about nineteen feet from home—the batter’s eyes suddenly jump to where he anticipates the bat–ball meeting will take place. Why? Because it’s the only way the eye can move fast enough to keep up with the incoming ball. Now that mental model comes into play. Across that brief gap, the ball’s arc is computed by the brain without further reference to the real world. By the time the batter’s eyes pick up the actual ball again, it’s too late in the swing to reposition the bat.

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