Baseball pitchers hurl illusions home.

With major league baseball season fast approaching, you can bet that two types of pitches will drive batters batty. One, dubbed the "rising fastball," rockets toward the hitter, only to jump a few inches to a foot upon reaching home plate, wickedly hopping over the outstretched ,bat. The other, a "breaking curveball," loops toward the batter and at the last moment plunges downward.

Although baseball players have long groused about these pitches, the rising fastball and breakingcurveball do not actuaIly exist, according to a study conducted by two engineers. Instead, the hops and dips are visual !illusions produced when a batter errantly estimates the speed of a pitch and momentarily shifts his gaze as the ball travels to home plate, contend A. Terry Bahiii of the University of Arizona in Tucson and William J. Karnavas of the University of Pittsburgh Medical School.

In experiments directed by Bahill nearly a decade ago, baseball players displayed an inability to track a pitch continuously as it approached them. Measures of! eye movements revealed that often hitters momentarily divert their eyes to where they think the ball will cross home plate.

Michael K. McBeath, a psychologist at Kent (Ohio) State University. proposed in 1990 that a perceptual illusion accounts for the rising fastball. A baseball leaves a pitcher's hand about 6 feet above the ground; it would have to arc down and bounce up to qualify as a rising 'fastball, thus defying gravity. Instead, McBeath argued, if a batter underestimates the initial speed of a fastball, it appears slightly farther away and slightly lower than its actual location. At home plate, the horsehide appears to accelerate upward with a hop.

Bahill and Karnavas devised a mathematical model based on this theory and tested it in a computer simulation. By accounting for the actual speed of a fastball, the batter's underestimation of that speed, and the batter's eye shift to a predicted point ahead of the ball, the model found that the batter perceived the ball as failing faster than it really was and approaching a point lower than its actual height.

The breaking curveball model included the same elements but relied on an overestimation of pitch speed by the batter. In this case,-the batter tracked the ball on a mistakenly elevated trajectory, and the ball reached the plate at a lower point than expected.

Ball players might improve their pitch-speed judgments by consulting a radar gun during batting practice, the scientists suggest in the February JOURNAL OF EXPERIMENTAL PSYCHOLOGY: HUMAN PERCEPTION AND PERFORMANCE.

A competing mathematical model of the same pitches, devised by psychologist Reinoud J. Bootsma of the University of Marseille in France, assumes a batter tracks a ball based on estimates of its size and acceleration. This approach best accounts for studies in which people thrown an unexpectedly small ball mistakenly think it will reach them at a point higher than it actually does, Bootsma argues.