Baseball Physics: Deception and Battered Expectations
New York Yankees' Babe Ruth clouts a towering home run in this undated photo.
Credit: AP Photo

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.

To accurately predict where and when the eye will reacquire the horsehide target, the brain needs position information. As the ball travels toward the batter, its image on the retina gets bigger, and we are very good at translating that change in size into a time of arrival for the ball. For a fastball taking about two-fifths of a second to travel to the plate, the average person can predict its time of flight to within twenty-five thousandths of a second. Although impressively close, that spread in timing would result in a spray of foul balls and misses; there is only a window of plus or minus nine-thousandths of a second for fair balls. Bahill has shown the pros do considerably better at this timing task, estimating the time of arrival to within plus or minus five-thousandths of a second.

It's an oddity of the way our visual system works that batters can accurately model the "when" of the ball's arrival by directly observing it, but the "where" is another matter. That variable depends on knowing things that are hard to estimate visually: the ball's distance from the batter, and the rate and direction of its spin. To put these parameters into a mental model, the batter relies on cues such as the pattern of the moving ball's gray-and-red blur (different angles of spin look different); the posture of the pitcher, especially his arm and hand; the point at which the pitcher releases the ball; and expectations of ball speed derived from previous pitches. Herein lies the secret to that hoppin' fastball.

If the pitcher can fool the batter about the speed of the pitch, even just a little bit, the effect is a startling difference between where the batter expects the ball and where it actually appears. For example, a few ninety-mile-an-hour fastballs set up the batter to expect more of the same heaters. If the next pitch is 5.5 percent faster, at ninety-five miles per hour, the ball will appear at its point of impact with the bat three inches above where the slower pitch would have. A batter using a mental model to follow the ball perceives that as a sudden leap upwards as the ball comes back into his region of focus.

That perceptual jump can also explain the phenomenon of the diving curve. While a curve ball certainly does curve, there is a particular pitch that appears to the batter to behave quite badly. Players often say "that one rolled off a table" to describe a ball that drops, or "breaks hard," just before the plate. Bahill and his colleagues report that in this case, the pitcher has fooled the batter into thinking the ball is moving faster than it is, leading to a perceptual drop when the ball appears below where the batter expects it.

Faced with such deceit, maybe batters would be better off just closing their eyes. Then again, if they keep them open, they can learn the specific tricks a pitcher employs to throw off their clear perception of the ball's flight. That could explain why some hurlers have great success early in their careers, but then lose their mystique as batters catch on to them.

Adam Summers teaches bioengineering at the University of California at Irvine, home of the Anteaters, participants in the 2007 NCAA College World Series.