Baseball players will tell you that a fastball can rise - and elementary physics says it can also, the same way an airplane rises because the teardrop shape of a wing causes air to go over the top faster than below the flatter bottom, 'sucking' it into the air.    Sure, if the baseball is going 200 MPH it can happen.  But they don't.

Likewise, curveballs can break sharply, some say, while others disagree, including us a year ago (see Does A Curveball In Baseball Really Break?).   It's an illusion.  Still a K if you miss them often enough, though, so players are forgiven if they are convinced they got beat by science.

If you recall the names Arthur Shapiro (American University) and Zhong-Lin Lu (University of Southern California) it's because we covered their prize for best illusion at the 2009 Vision Sciences annual meeting  - a demonstration of how an object falling in a straight line can still appear to change direction (try it yourself!)

Naturally, that didn't settle the debate and if you saw Tim Lincecum's ridiculous slider in last week's no-2-hitter against the Braves, you know they aren't wrong for believing in wild motion. A curveball breaks, sure, the ball is spinning at 1500 RPM and a speed of over 75 MPH, it just doesn't break the way the batter thinks it does because part of the magic is the perceptual puzzle of motion and vision.

In a new PLoS ONE study, the group explains the illusion and relates the perceived size of the break to the shifting of the batter's eye between central and peripheral vision.

"If the batter takes his eye off the ball by 10 degrees, the size of the break is about one foot," Lu said.

Interactive Curveball Illusion. A disk descends vertically from the top of the screen to the bottom. If the observer tracks the disk in the periphery (i.e., if the observer looks to the right but attends to the motion of the disk), the disk appears to descend obliquely. The lever allows the observer to adjust the angle of descent. Experiment 1 measured the physical angle of descent at which the observer perceived the disk to descend vertically when viewing the disk in the periphery.

Lu explained that batters tend to switch from central to peripheral vision when the ball is about 20 feet away, or two-thirds of the way to home plate. The eye's peripheral vision lacks the ability to separate the motions of the spinning ball, Lu said. In particular, it gets confused by the combination of the ball's velocity and spin.

The result is a gap between the ball's trajectory and the path as perceived by the batter. The gap is small when the batter switches to peripheral vision, but gets larger as the ball travels the last 20 feet to home plate.

As the ball arrives at the plate, the batter switches back to central vision and sees it in a different spot than expected. That perception of an abrupt change is the "break" in the curveball that frustrates batters.

"Depending on how much and when the batter's eyes shift while tracking the ball, you can actually get a sizable break," Lu said. "The difference between central and peripheral vision is key to understanding the break of the curveball.   A similar illusion explains the "rising fastball".

Experimental results applied to an actual trajectory of a curveball.  A) The parabola fit to the curveball data tabulated in Bahill and Baldwin [34]. B) The line drawn at each point represents the physical velocity of the curveball at every moment of time. C) The deviation of the moment-by-moment perceived velocity of the ball (indicated by the red lines), assuming that the batter's gaze shifts to the expected point of bat/ball contact when the ball is 20 ft away from home plate (i.e., when the ball is 20 ft from home plate, the batter shifts his/her eyes so that the ball is at 10-degree eccentricity; the eccentricity decreases linearly when the ball reaches home plate). D) We used the perceived moment-by-moment velocity of the ball from part C to estimate the perceived trajectory of the ball, which is dependent on the initial eccentricity and when eye shift occurs. Each line indicates when the batter shifts his/her eyes from the ball toward home plate (i.e., the red line indicates that the observer shifts his/her eyes when the ball is 20 ft away; green line, 15 ft; dark blue line, 10 ft; light blue line, 5 ft). The longer the batter is able to maintain foveal fixation on the ball, the less the ball will be perceived to deviate from its parabolic path.  See credit in the citation below.

The obvious remedy for a batter, repeated by parents and coaches everywhere, is to "keep your eye on the ball."

That is easier said than done, according to the authors. As the ball nears home plate, its size in the batter's field of view spills out of the eye's central vision.

"Our central vision is very small," Shapiro said. "It's the size of the tip of your thumb at arm's length. When an object falls outside of that region, strange perceptions can occur."

Lu noted that the spin of the ball tends to draw the eye to the side, making it even harder for the batter to keep the ball in central vision.

"People's eyes have a natural tendency to follow motion," Lu explained.

His advice to hitters: "Don't trust your eyes. Know the limitations of your visual system. This is something that can be trained, probably."

New bats for 2014 can help with this training.

Lu, Shapiro and their co-authors plan to build a physical device to test the curveball illusion. Their study was carried out with volunteers tracking the movement of a disk on a computer monitor.

To the authors' knowledge, the PLoS ONE study represents the first attempt to explain the break in the curveball purely as a visual illusion. Others have tried to explain the break as a result of the hitter overestimating the speed of a pitch.

Responding to comments from baseball fans, Lu agreed that on television, pitches filmed from behind home plate appear to break. He called it a "geometric illusion" based on the fact that for the first part of a pitch, the viewer sees little or no vertical drop.

The ball is falling at the same rate throughout the pitch, Lu said, but because the pitcher tosses the ball at a slight upward angle, the first part of the pitch appears more or less flat.

As a result, the drop of the ball near home plate surprises the eye.

For Shapiro and Lu, who have studied visual perception for many years, the PLoS ONE results go beyond baseball.

"Humans constantly shift objects between central and peripheral vision and may encounter effects like the curveball's break regularly," the authors wrote. "Peripheral vision's inability to separate different visual signals may have f ar-reaching implications in understanding human visual perception and functional vision in daily life."

HOW THE EXPERIMENT WAS CONDUCTED:

The visual stimulus consisted of a descending disk (to represent global motion, or the ball's path through space) with an internal moving grating (representing local motion, or the spin on the ball). When the five observers viewed the disk centrally, they perceived both global and local motion (i.e., observers saw the disk's vertical descent and the internal spinning). When observers viewed the disk peripherally, the internal portion appeared stationary, and the disk appeared to descend at an angle. The angle of perceived descent increased as the observer viewed the stimulus from further in the periphery.

The researchers estimated the magnitude of the illusion by measuring the physical angle of descent that created the perception of vertical descent. The experimenter adjusted the physical angle of descent, and the observer reported whether he/she perceived the disk to fall vertically. For example, the experimenter adjusted the global motion direction of the disk 20 degrees to the right if the observer reported, “No. The disk is moving to the left about 20 degrees.”

The amount of adjustment became smaller as the observer reported that he/she saw the disk falling closer to vertical. The stimulus was on until the observer made a response, in response to which the experimenter changed the physical direction of the descending disk. An observer’s response was measured twice. There were twenty-four different conditions based on every combination of the following: three eccentricities (0, 15 and 30 degrees), two directions for the internal grating (0 and 180 degrees), and four moving speeds (6.7, 10, 13.3 and 20 deg/sec). Each condition was repeated four times.

Observers practiced two trials for each condition before data collection.

Citation: Shapiro A, Lu Z-L, Huang C-B, Knight E, Ennis R (2010) 'Transitions between Central and Peripheral Vision Create Spatial/Temporal Distortions: A Hypothesis Concerning the Perceived Break of the Curveball', PLoS ONE 5(10): e13296. doi:10.1371/journal.pone.0013296