Battered Expectations

Do baseballs obey the conventional laws of physics?

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.

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