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Published on January 14, 2008

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The Perceptual Illusion of the Rising Fastball :  The Perceptual Illusion of the Rising Fastball Terry Bahill Systems and Industrial Engineering University of Arizona terry@sie.arizona.edu David G. Baldwin Washington Senators et al. SnakeJazz_37@brainpip.com Copyright © 2002-07, Bahill and Baldwin References:  References Terry Bahill and Dave Baldwin, “The rising fastball and other perceptual illusions of batters,” Biomedical Engineering Principles in Sports, George Hung and Jani Pallis (Eds), Kluwer Academic, 2004. Bahill, A.T. and Karnavas, W.J., “The perceptual illusion of baseball’s rising fastball and breaking curveball,” Journal of Experimental Psychology, Human Perception and Performance, 19(1), 3-14, 1993. Watts, R.G. and Bahill, A.T., Keep Your Eye on the Ball: Curve Balls, Knuckleballs and Fallacies of Baseball, W. H. Freeman, 2000, ISBN 0-7167-3717-5. The slides of this presentation are available at http://www.sie.arizona.edu/sysengr/slides/ You will not see all of these slides:  You will not see all of these slides Some are designed for engineers physicians neuroscientists lay people psychologists illusionists The systems engineering process:  The systems engineering process Please note that the SIMILAR process is not a serial process. It is parallel and iterative. State the problem*:  State the problem* Many baseball players have described the rising fastball: the pitch starts normally, but right in front of home plate the ball jumps a half-foot, making it hop over the bat. Such behavior is impossible according to the laws of physics. The problem? Explain this contradiction. The baseball player says1:  The baseball player says1 This perceived rise occurs on fastballs that have exceptional speed, are belt high or higher, and, most often, are on the inside half of the strike zone. Batters say that the pitcher “pumped it up,” or “put a little extra on that one.” The rising fastball is often referred to as “smoke,” “cheese,” or “express.” The baseball player says2:  The baseball player says2 overhand or three-quarter delivery rapid back spin gripped with the index and middle fingers extending across four seams back spin with four seams perpendicular to the trajectory gives the ball maximum lift. The engineer says:  The engineer says Investigate alternatives*:  Investigate alternatives* Alternative definitions of the rising fastball: the ball crosses the plate above the pitcher’s release point crosses the plate going upward falls less than expected due to gravity seems to jump-up, right in front of the plate Launch the system:  Launch the system Run the simulation of the pitch and use it to explain human behavior. 90 and 95 mph fastballs*:  90 and 95 mph fastballs* The baseball player says:  The baseball player says The ball hops, drops, curves, breaks, rises, or tails away. The pitcher throws a curveball, drop curve, flat curve, screwball, slider, backup slider, change up, cutter, sinker, forkball, splitter, fastball, cut fastball, split-fingered fastball, two-seam fastball, or four-seam fastball. This sounds like a lot of variation. The engineer says:  The engineer says The pitch follows a smooth arc determined only by gravity velocity rate of rotation axis of rotation (excepting the knuckleball) We compute the effects of gravity and the aerodynamic forces of lift and drag. What the batter does:  What the batter does during each third of the pitch’s flight observe compute swing Eye tracking strategies:  Eye tracking strategies The optimal learning strategy The optimal hitting strategy Two strategies:  Two strategies The optimal hitting strategy: track the ball with smooth pursuit eye movements and fall behind in the last five feet. The optimal learning strategy: track the ball over the first part of its trajectory with smooth pursuit eye movements, make a fast saccadic eye movement to the predicted point of bat-ball collision, then let the ball catch up to the eye. The batter observes the ball, makes a prediction of where it will hit his bat, sees the actual position of the ball when it hits the bat, and uses this feedback to learn to predict better next time. Perceptual Illusion of the rising fastball*:  Perceptual Illusion of the rising fastball* The perceptual illusion of the rising fastball:  The perceptual illusion of the rising fastball The batter observes the ball for the first third of its flight, using his mental model, he underestimates the pitch-speed and therefore miscomputes the height of the bat-ball collision point, then at the start of his swing, he takes his eye off the ball to look at the predicted bat-ball collision point, when the ball comes back onto his fovea it is higher than he thought it would be. Model the system:  Model the system Make a model for the human brain Validate the model Where and when:  Where and when To hit the ball the batter must predict where and when it will cross the plate. This involves the x, y, and z spatial coordinates and t, the time coordinate. But the batter has no direct visual access to the x, y and z spatial coordinates. What information is available?:  What information is available? The batter’s judgements must be based entirely on retinal image data the angular size of the ball, , the angular distance of the ball's image off the fovea, , and their time derivatives and Predicting when:  Predicting when In his novel The Black Cloud, Sir Fred Hoyle (1957) showed that the time-to-contact () with an object moving along the line-of-sight can be approximated with where  and are respectively the object's angular size and rate of change of angular size. Are there brain systems that can compute when?:  Are there brain systems that can compute when? There is psychophysical evidence that the human uses image size, . Size-tuned neurons have been found in the monkey visual cortex. There is psychophysical evidence that the human visual system uses "looming detectors" that compute changing-size, Specific brain neurons of the monkey are sensitive to changing-size, Using these two pools of neurons the brain could compute Is the baseball’s movement within physiological thresholds? :  Is the baseball’s movement within physiological thresholds? as low as 0.02 deg/sec can be detected. For a 95 mph fastball is 0.66 deg/sec. The smallest value of retinal velocity, that can be detected is 0.02 deg/sec. For a 95 mph pitch reaches 0.02 deg/sec when the ball has traveled about a foot. Therefore, for most of the ball’s flight these variables are within physiological thresholds. Determining where1 :  Determining where1 Humans have no direct measure for the distance of an object* The stereoscopic depth system indicates only relative depth of two objects. The vergence system does not contribute to motion in depth sensations. Humans can discriminate direction of motion in a horizontal plane, but the baseball is moving in the vertical plane. Therefore the batter must estimate the distance to the ball. Determining where2:  Determining where2 For a 95 mph pitch, s = 95 250 msec after the ball’s release, tsr= 250 D = D0 - tsr s = 20.7 ft the vertical velocity, dz/dt = gt = 8 ft/sec producing a retinal velocity = 21 deg/sec However using a 90 mph mental model, = 90 250 msec after the ball’s release underestimating horizontal speed overestimates distance coupled with the actual retinal velocity of 21 deg/sec produces an overestimate of vertical speed = 8.6 ft/sec Therefore the batter would think the ball was falling faster than it really was and would probably swing under the ball. Mental models:  Mental models Humans often use mental models* Model summary:  Model summary The first term is the estimated distance to the ball and the last term is  so the above equation can be rewritten as Neurophysiological model:  Neurophysiological model This model is realistic:  This model is realistic There are pools of neurons in the monkey brain that perform each of its functions. There is psychophysical evidence that humans do use these functions. Movement of the baseball produces stuff that is within physiological thresholds. Model validation:  Model validation Model mimics human behavior Model uses physiologically realistic signals It uses d/dt and  It does not use absolute distance to the ball It does not use second derivatives Model matches experimental data Sensitivity analyses Comparison with other models It can predict something it was not designed for: the breaking curveball Assess performance of the model:  Assess performance of the model Compare model behavior to experimental results Assess performance:  Assess performance How does the model perform when its parameters are changed? a sensitivity analysis. Re-evaluate:  Re-evaluate Simulate something not used in the model’s design The Breaking Curveball A Sidney Harris Cartoon* (from Watts and Bahill, page 31):  A Sidney Harris Cartoon* (from Watts and Bahill, page 31) The breaking curveball :  The breaking curveball If the batter overestimates the pitch speed, then he perceives the ball dropping more than expected in the last few feet. The ball would break so fast it would look "like it rolled off a table." Curveball:  Curveball The two-seam and the four-seam fastballs:  The two-seam and the four-seam fastballs The baseball player says:  The baseball player says The ball is gripped across four seams. Each seam provides high impedance to the airflow around the ball. Back spin with four seams perpendicular to the trajectory gives the ball maximum “lift.” Pitchers believe that this lift accounts for the rise experienced by batters. The engineer says:  The engineer says For puzzling things like this try Physics first then try Physiology finally try Psychology Critical Flicker Fusion Frequency is between 40 and 50 Hz* The fastball:  The fastball The fastball has 20 revolutions per second of back spin. Slide47:  The two seam fastball The 2-seam fastball may flicker:  The 2-seam fastball may flicker The two-seam fastball might flicker between 20 and 40 Hz. If the batter can perceive this flicker, then he could tune his mental model and predict more accurately. Slide49:  The four seam fastball The 4-seam fastball:  The 4-seam fastball The four-seam fastball will present 80 seams per second. There will be no flicker. The batter will have fewer clues about the spin. Hence he will predict less accurately. If he underestimates the pitch speed he might perceive a rising fastball. Right answer, wrong reason:  Right answer, wrong reason So the pitcher is right, the four seam grip induces the batter to perceive more rising fastballs, but his explanation is wrong. Integrate:  Integrate Put it all together in the context of a baseball game. Strategies and heuristics of the batter The baseball player says:  The baseball player says The strategy to be used depends on speed, location and outcome of the previous pitch*, number of outs, runners on base, score, count, and coaches’ signals. With a count of 3 and 0 the batter would expect a fastball,** whereas with a 0 and 1 count the batter might look for a curveball. The engineer says:  The engineer says the speed estimation process could be modeled with a Markov process or a Kalman filter using a weighted average of the last one or two pitches or perhaps just the last 20 seconds and information gathered in the first third of the present pitch Tactics of pitcher versus batter :  Tactics of pitcher versus batter Batter’s tactics:  Batter’s tactics Batter’s objective Hit a line drive Batter’s tactics Build a mental model Look for a specific pitch Pitcher’s tactics:  Pitcher’s tactics Pitcher’s objective Cause the batter to make a vertical error Pitcher’s tactics Confound the batter’s mental model Use the batter’s working memory Put vertical deflection on the ball The pitcher’s tactics:  The pitcher’s tactics The pitcher thinks his tactics work because he does not repeat the kind and location of a pitch However, we think the pitcher’s tactics actually work because he does not repeat the speed of the previous pitch Johnny Sain’s heuristics*:  Johnny Sain’s heuristics* Pitchers should change speed on every pitch work fast The baseball player says1:  The baseball player says1 Throw progressively faster fastballs to go up the ladder Throw progressively slower curveballs to go down the ladder The baseball player says2:  The baseball player says2 Pitchers know that the speed of the pitch is important to its success, but they are unaware that success is dependent upon an perceptual illusion experienced by the batter. Batters, too, do not realize that they are being fooled by their own expectations The engineer says1:  The engineer says1 An illusionist (a magician) would make a good pitcher. The engineer says2:  The engineer says2 Christy Mathewson once said, “Fooling the other fellow was just as valuable as throwing hard – and a darn sight easier on the arm.” Baseball summary1:  Baseball summary1 The rising fastball is a perceptual illusion: the batter tracks the ball in the beginning he underestimates the pitch-speed therefore he underestimates the height of the ball when it crosses the plate he takes his eye off the ball to look at the predicted bat-ball collision point when the ball comes back into view it is higher than he thought it would be. Baseball summary2:  Baseball summary2 The two-seam fastball might flicker between 20 and 40 Hz, which is below the Critical Flicker Fusion Frequency. The four-seam fastball will not flicker, therefore the batter will estimate more poorly. If he underestimates the pitch speed, he may perceive a rising fastball. The pitcher should change speed on every pitch in order to confound the batter’s mental model. Model summary:  Model summary The model was designed to explain the rising fastball, however it also explains something never considered during its development, the breaking curveball. The model is robust with respect to changes in its parameters: it is most sensitive to its inputs. Systems engineering summary:  Systems engineering summary The systems engineering process mapped well to this modeling process for the rising fastball. Seminar materials:  Seminar materials Golf balls Happy balls Convict SE cards How to print:  How to print To print this file, do this one time. View Color/grayscale Grayscale Settings Light grayscale Close grayscale view

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