"Markov at the bat": a model of cognitive processing in baseball batters

Anecdotal evidence from players and coaches indicates that cognitive processing (e.g., expectations about the upcoming pitch) plays an important role in successful baseball batting, yet this aspect of hitting has not been investigated in detail. The present study provides experimental evidence that prior expectations significantly influence the timing of a baseball swing. A two–state Markov model was used to predict the effects of pitch sequence and pitch count on batting performance. The model is a hitting strategy of switching between expectancy states using a simple set of transition rules. In a simulated batting experiment, the model provided a good fit to the hitting performance of 6 experienced college baseball players, and the estimated model parameters were highly correlated with playing level.     

Acceptable timing error at ball-bat impact for different pitches and its implications for baseball skills

In baseball hitting, batters need high precision timing control to hit the ball with bat’s sweet spot. Knowing the acceptable range of timing error for hitting the ball in the aimed direction for various pitch types is helpful to understand whether the cause of the batter's mis-hit is a spatial or temporal error and highlight the motor skills required by the batter. The purpose of this study was to determine the acceptable timing error in different baseball pitches and the impact characteristics of mis-hits. Twenty-six high school baseball players hit a ball launched from a pitching machine with three types of pitches: fastballs, curveballs, and slowballs. We recorded the three-dimensional behavior of the ball, bat, and human body (pelvis) using an optical motion capture system. We then defined the optimal impact location based on timing accuracy, and determined the acceptable range of timing error by the interactive relationship between the horizontal orientation of the bat’s long axis at the time of ball impact and the horizontal direction of the batted ball. The ±30° width in the horizontal direction of the batted ball was set as the precondition for the tolerance of timing. The acceptable timing error was ±7.9 ms for fastballs, ±10.7 ms for curveballs, and ±10.7 ms for slowballs, and the optimal timing for outside pitches was approximately 10 ms later than that for inside pitches. The timing error was also explained 38.1% by variation in the impact location along the long axis of the bat (R² = 0.381, P < 0.001) and was minimized at a position close to the bat’s sweet spot. These results suggest that the optimal impact location and acceptable range of timing error depend on the pitching course and speed and that timing accuracy is essential to achieve the spatial accuracy required to hit the ball at the bat’s sweet spot.     

A functional modulation for timing a movement: a coordinative structure in baseball hitting

In baseball hitting, a powerful bat-swing needs to be produced by utilizing ground reaction force (GRF) and it should also be temporally coordinated relative to the flight of the pitch. The temporal organization of hitting movements associated with these task requirements was investigated by analyzing GRF during hitting slow and fast pitches. The timing of stepping with a front foot and shifting weight forward was modulated relative to the pitch's speed. The temporal relation between successive motion phases was compensatory and timing variability progressively reduced up to ball-bat contact. These results demonstrated the coordinative structure of the hitting movement for timing the bat-swing relative to the pitch's flight.     

Perception-action coupling and anticipatory performance in baseball batting

The authors examined 10 expert and 10 novice baseball batters' ability to distinguish between a fastball and a change-up in a virtual environment. They used 2 different response modes: (a) an uncoupled response in which the batters verbally predicted the type of pitch and (b) a coupled response in which the batters swung a baseball bat to try and hit the virtual ball. The authors manipulated visual information from the pitcher and ball in 6 visual conditions. The batters were more accurate in predicting the type of pitch when the response was uncoupled. In coupled responses, experts were better able to use the first 100 ms of ball flight independently of the pitcher's kinematics. In addition, the skilled batters' stepping patterns were related to the pitcher's kinematics, whereas their swing time was related to ball speed. Those findings suggest that specific task requirements determine whether a highly coupled perception-action environment improves anticipatory performance. The authors also highlight the need for research on interceptive actions to be conducted in the performer's natural environment.     

The rising fastball: baseball's impossible pitch

Batters in professional baseball are confronted with pitches that appear to curve, dip, wobble, or rise. The rising fastball is a pitch where the ball appears to hop up as much as a third of a meter with a sudden increase in speed. Physics experiments confirm that many reported trajectories are possible, but not the rising fastball. The present paper shows how the apparent rise may be explained as a perceptual illusion due to the hitter underestimating original speed of the pitch.     

Pitch perception

This article is a review of the psychophysical study of pitch perception. The history of the study of pitch has seen a continual competition between spectral and temporal theories of pitch perception. The pitch of complex stimuli is likely based on the temporal regularities in a sound’s waveform, with the strongest pitches occurring for stimuli with low-frequency components. Thus, temporal models, especially those based on autocorrelationlike processes, appear to account for the majority of the data.     

After-effects of using a weighted bat on subsequent swing velocity and batters' perceptions of swing velocity and heaviness

In baseball and softball, warm-up swings with a weighted bat have been believed to increase swing velocity when an ordinary bat is used in the subsequent competitive situation. The purpose of this study was to investigate the after-effects of using a weighted bat on subsequent swing velocity and batters' perceptions of swing velocity and heaviness. Eight men in varsity softball and baseball hit a ball suspended from the ceiling 45 times (3 sets of 15 trials). For each set, the initial 5 trials were done using an ordinary 920-g wooden bat (Control condition), and the following 5 trials by a bat with an 800-g bat ring (Weighted condition), and the final 5 trials again by the ordinary bat (post-Weighted condition). Analysis of variance showed a significant decrease of 3.3% in the measured linear velocity of the bat prior to impact with the ball for the first swing of the post-Weighted condition compared with the Control condition. From the second swing the velocity returned to the level of the Control condition. Subjective judgment of the heaviness and velocity of swings for the Weighted and post-Weighted conditions by each participant showed that the ordinary bat felt lighter and swing speed felt faster for the post-Weighted condition. The advantage of the warm-up with a weighted bat was thus psychological and not biomechanical.     

Hitting is contagious: experience and action induction

In baseball, it is believed that "hitting is contagious," that is, probability of success increases if the previous few batters get a hit. Could this effect be partially explained by action induction--that is, the tendency to perform an action related to one that has just been observed? A simulation was used to investigate the effect of inducing stimuli on batting performance for more-experienced (ME) and less-experienced (LE) baseball players. Three types of inducing stimuli were compared with a no-induction condition: action (a simulated ball traveling from home plate into left, right, or center field), outcome (a ball resting in either left, right, or center field), and verbal (the word "left", "center", or "right"). For both ME and LE players, fewer pitchers were required for a successful hit in the action condition. For ME players, there was a significant relationship between the inducing stimulus direction and hit direction for both the action and outcome prompts. For LE players, the prompt only had a significant effect on batting performance in the action condition, and the magnitude of the effect was significantly smaller than for ME. The effect of the inducing stimulus decreased as the delay (i.e., no. of pitches between prompt and hit) increased, with the effect being eliminated after roughly 4 pitches for ME and 2 pitches for LE. It is proposed that the differences in the magnitude and time course of action induction as a function of experience occurred because ME have more well-developed perceptual-motor representations for directional hitting.     

Maximum key-profile correlation (MKC) as a measure of tonal structure in music

Tonal structure is musical organization on the basis of pitch, in which pitches vary in importance and rate of occurrence according to their relationship to a tonal center. Experiment 1 evaluated the maximum key-profile correlation (MKC), a product of Krumhansl and Schmuckler’s key-finding algorithm (Krumhansl, 1990), as a measure of tonal structure. The MKC is the maximum correlation coefficient between the pitch class distribution in a musical sample and key profiles,which indicate the stability of pitches with respect to particular tonal centers. The MKC values of melodies correlated strongly with listeners’ ratings of tonal structure. To measure the influence of the temporal order of pitches on perceived tonal structure, three measures (fifth span, semitone span, and pitch contour) taken from previous studies of melody perception were also correlated with tonal structure ratings. None of the temporal measures correlated as strongly or as consistently with tonal structure ratings as did the MKC, and nor did combining them with the MKC improve prediction of tonal structure ratings. In Experiment 2, the MKC did not correlate with recognition memory of melodies. However, melodies with very low MKC values were recognized less accurately than melodies with very high MKC values. Although it does not incorporate temporal, rhythmic, or harmonic factors that may influence perceived tonal structure, the MKC can be interpreted as a measure of tonal structure, at least for brief melodies.     

Infants’ perception of musical patterns

This paper examines infants’ ability to perceive various aspects of musical material that are significant in music in general and in Western European music in particular: contour, intervals, exact pitches, diatonic structure, and rhythm. For the most part, infants focus on relational aspects of melodies, synthesizing global representations from local details. They encode the contour of a melody across variations in exact pitches and intervals. They extract information about pitch direction from the smallest musically relevant pitch change in Western music, the semitone. Under certain conditions, infants detect interval changes in the context of transposed sequences, their performance showing enhancement for sequences that conform to Western musical structure. Infants have difficulty retaining exact pitches except for sets of pitches that embody important musical relations. In the temporal domain, they group the elements of auditory sequences on the basis of similarity and they extract the temporal structure of a melody across variations in tempo.     

Visual processing of music notation: a study of event-related potentials

In reading music, the acquisition of pitch information depends mostly on the spatial position of notes, hence more spatial processing, whereas the acquisition of temporal information depends mostly on the visual features of notes and object recognition. This study used both electrophysiological and behavioral methods to compare the processing of pitch and duration in reading single musical notes. It was observed that in the early stage of note reading, identification of pitch could elicit greater N1 and N2 amplitude than identification of duration at the parietal lobe electrodes. In the later stages of note reading, identifying pitch elicited a greater negative slow wave at parietal electrodes than did identifying note duration. The sustained contribution of parietal processes for pitch suggests that the dorsal pathway is essential for pitch processing. However, the duration task did not elicit greater amplitude of any early ERP components than the pitch task at temporal electrodes. Accordingly, a double dissociation, suggesting involvement of the dorsal visual stream, was not observed in spatial pitch processing and ventral visual stream in processing of note durations.     

Temporal grouping in auditory spatial serial memory

Grouping effects in serial recall have been widely studied with verbal stimuli, but hardly ever with spatial stimuli and not at all with auditory spatial stimuli. In Experiment 1, we examined the influence of combined temporal and pitch grouping on recall of the locations from which bursts of white noise were presented. Similar to findings in verbal studies, effects of the grouping manipulation were found in performance accuracy, in the nature of order errors, and in the timing of responses. Experiment 2 was designed to distinguish the role played by pitch grouping from that played by temporal grouping, through independent manipulation of the presence of a shift in pitch and that of a temporal gap. The results showed that the temporal grouping manipulation determined performance and the pitch grouping manipulation did not. Similarities between our findings and those of verbal studies, and implications for the understanding of serial memory are discussed.     

Attending to the execution of a complex sensorimotor skill: expertise differences, choking, and slumps

A simulated baseball batting task was used to compare the relative effects of attending to extraneous information (tone frequency) and attending to skill execution (direction of bat movement) on performance and swing kinematics and to evaluate how these effects differ as a function of expertise. The extraneous dual task degraded batting performance in novices but had no significant effect on experts. The skill-focused dual task increased batting errors and movement variability for experts but had no significant effect on novices. For expert batters, accuracy in the skill-focused dual task was inversely related to the current level of performance. Expert batters were significantly more accurate in the skill-focused dual task when placed under pressure. These findings indicate that the attentional focus varies substantially across and within performers with different levels of expertise.     

Spatial representation of pitch height: the SMARC effect

Through the preferential pairing of response positions to pitch, here we show that the internal representation of pitch height is spatial in nature and affects performance, especially in musically trained participants, when response alternatives are either vertically or horizontally aligned. The finding that our cognitive system maps pitch height onto an internal representation of space, which in turn affects motor performance even when this perceptual attribute is irrelevant to the task, extends previous studies on auditory perception and suggests an interesting analogy between music perception and mathematical cognition. Both the basic elements of mathematical cognition (i.e. numbers) and the basic elements of musical cognition (i.e. pitches), appear to be mapped onto a mental spatial representation in a way that affects motor performance.     

Application of the matching law to pitch selection in professional baseball

This study applied the generalized matching equation (GME) to pitch selection in professional baseball. The GME was fitted to the relation between pitch selection and hitter outcomes for five professional baseball pitchers during the 2014 Major League Baseball season. The GME described pitch selection well. Pitch allocation varied across different game contexts such as inning, count, and number of outs in a manner consistent with the GME. Finally, within games, bias decreased for four of the five pitchers and the sensitivity parameter increased for three of the five pitchers. The results extend the generality of the GME to multialternative natural sporting contexts, and demonstrate the influence of context on behavior in natural environments.     

Brief pitch-priming facilitates infants’ discrimination of pitch-evoking noise: Evidence from event-related potentials

Pitch is derived by the auditory system through complex spectrotemporal processing. Pitch extraction is thought to depend on both spectral cues arising from lower harmonics that are resolved by cochlear filters in the inner ear, and on temporal cues arising from the pattern of action potentials contained in the cochlear output. Adults are capable of extracting pitch in the absence of robust spectral cues, taking advantage of the temporal cues that remain. However, recent behavioral evidence suggests that infants have difficulty discriminating between stimuli with different pitches when resolvable spectral cues are absent. In the current experiments, we used the mismatch negativity (MMN) component of the event related potential derived from electroencephalographic (EEG) recordings to examine a cortical representation of pitch discrimination for iterated rippled noise (IRN) stimuli in 4- and 8-month-old infants. IRN stimuli are pitch-evoking sounds generated by repeatedly adding a segment of white noise to itself at a constant delay. We created IRN stimuli (delays of 5 and 6 ms creating pitch percepts of 200 and 167 Hz) and high-pass filtered them to remove all resolvable spectral pitch cues. In experiment 1, we did not find EEG evidence that infants could detect the change in the pitch of these IRN stimuli. However, in Experiment 2, after a brief period of pitch-priming during which we added a sine wave component to the IRN stimulus at its perceived pitch, infants did show significant MMN in response to pitch changes in the IRN stimuli with sine waves removed. This suggests that (1) infants can use temporal cues to process pitch, although such processing is not mature and (2) that a short amount of pitch-priming experience can alter pitch representations in auditory cortex during infancy.     

Why do temporal generalization gradients change when people make decisions as quickly as possible?

Three experiments investigated temporal generalization performance under conditions in which participants were instructed to make their decisions as quickly as possible (speed), or were allowed to take their time (accuracy). A previous study (Klapproth & Müller, 2008) had shown that under speeded conditions people were more likely to confuse durations shorter than the standard with the standard than in the accuracy conditions, and a possible explanation of this result is that longer stimulus durations are "truncated" (i.e., people make a judgement about them before they have terminated, thereby shortening their effective duration) and that these truncated durations affect the standard used for the task. Experiment 1 investigated performance under speed and accuracy conditions when comparison durations were close to the standard or further away. No performance difference was found as a function of stimulus spacing, even though responses occurred on average before the longest durations had terminated, but this lack of effect was attributed to "task difficulty" effects changing decision thresholds. In Experiment 2, the standard duration was either the longest or the shortest duration in the comparison set, and differences between speed and accuracy groups occurred only when the comparisons were longer than the standard, supporting the "truncation" hypothesis. A third experiment showed that differences between speed and accuracy groups only occurred if some memory of the standard that was valid for more than one trial was used. In general, the results suggest that the generalization gradient shifts in speeded conditions occur because of truncation of longer comparison durations, which influences the effective standard used for the task.     

Brief pitch-priming facilitates infants’ discrimination of pitch-evoking noise: Evidence from event-related potentials

Pitch is derived by the auditory system through complex spectrotemporal processing. Pitch extraction is thought to depend on both spectral cues arising from lower harmonics that are resolved by cochlear filters in the inner ear, and on temporal cues arising from the pattern of action potentials contained in the cochlear output. Adults are capable of extracting pitch in the absence of robust spectral cues, taking advantage of the temporal cues that remain. However, recent behavioral evidence suggests that infants have difficulty discriminating between stimuli with different pitches when resolvable spectral cues are absent. In the current experiments, we used the mismatch negativity (MMN) component of the event related potential derived from electroencephalographic (EEG) recordings to examine a cortical representation of pitch discrimination for iterated rippled noise (IRN) stimuli in 4- and 8-month-old infants. IRN stimuli are pitch-evoking sounds generated by repeatedly adding a segment of white noise to itself at a constant delay. We created IRN stimuli (delays of 5 and 6 ms creating pitch percepts of 200 and 167 Hz) and high-pass filtered them to remove all resolvable spectral pitch cues. In experiment 1, we did not find EEG evidence that infants could detect the change in the pitch of these IRN stimuli. However, in Experiment 2, after a brief period of pitch-priming during which we added a sine wave component to the IRN stimulus at its perceived pitch, infants did show significant MMN in response to pitch changes in the IRN stimuli with sine waves removed. This suggests that (1) infants can use temporal cues to process pitch, although such processing is not mature and (2) that a short amount of pitch-priming experience can alter pitch representations in auditory cortex during infancy.     

先天性音乐障碍的音高空间表征能力研究

利用音高空间表征任务、心理旋转任务和音高辨别任务,探讨先天性音乐障碍者音高空间表征能力、心理旋转加工能力和音高辨别能力。结果发现：先天性音乐障碍组音高空间表征任务标准差、心理旋转任务错误率和音高辨别任务错误率均显著高于控制组。 这些结果表明先天性音乐障碍并非音乐特异性障碍,而是音乐相关性障碍。     

A Chaining-Mastery,Discrimination Training Program to Teach Little Leaguers to Hit a Baseball

One of two little league baseball teams, consisting of boys between the ages of 8 and 12, was taught to hit a baseball using a chaining-mastery program extrapolated from the "Total Golf" (Simek & O'Brien, 1981) program. Following two baseline games and a baseline measurement session, 10 of the 12 boys on the experimental team participated in a chaining-mastery batting program, beginning with slow pitches from close to the batter and progressing to normal speed pitches from the regulation distance. Both game performance and a repeat of the baseline measures following Game 6 showed large increases in the number of hits. The control team showed no such increases. Following Game 6, a program of discrimination training for hitable balls (strikes) was instituted with the experimental team using a mastery approach to produce earlier discriminations of strikes from balls. Number of bases on balls increased for Games 7 through 10 after remaining stable for the first 6 games. For the control team, bases on balls increased during Games 3 through 6, but remained stable for Games 7 through 10. Batting averages revealed similar improvement for the experimental team from a baseline of .250 to .342 for Games 3 through 6, and .369 for Games 7 through 10, and no improvement for the control team (baseline = .281, Games 3 through 6 = .230, Games 7 through 10 = .230). Two members of the experimental team rejected the chaining-discrimination training program in favor of practice in "guided positive fantasy" for batting skills, which was provided by the father of one of the boys. These two boys showed little improvement on the dependent measures. The results suggest that a program of chaining-mastery instruction for batting and discrimination training for pitch selection can be effective in teaching little leaguers to hit.