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Influence of Ball Velocity, Attention, and Age on Response Time for a Simulated Catch

OWINGS, TAMMY M.1; LANCIANESE, SARAH L.1; LAMPE, ELISSA M.1; GRABINER, MARK D.1 2

Medicine & Science in Sports & Exercise: August 2003 - Volume 35 - Issue 8 - pp 1397-1405
APPLIED SCIENCES: Biodynamics

OWINGS, T. M., S. L. LANCIANESE, E. M. LAMPE, and M. D. GRABINER. Influence of Ball Velocity, Attention, and Age on Response Time for a Simulated Catch. Med. Sci. Sports Exerc., Vol. 35, No. 8, pp. 1397–1405, 2003.

Purpose: The ability of a baseball infielder to respond to a batted ball may provide the best defense for avoiding injury. This study investigated the response times of young athletes performing a simulated baseball-fielding task to estimate the maximum velocity with which a baseball can leave the bat and allow a player, standing 13.7 m away, to safely respond to the approaching ball.

Methods: Fifty boys and 50 girls between the ages of 8 and 16 yr participated. Baseballs were projected at the subjects who were standing in a standardized position behind a safety net. Two components of response time, reaction time and movement time, were determined using a motion capture system. The influences of baseball velocity (26.8 and 33.5 m·s−1) and level of attention (full attention and attention splitting) on response time for a simulated baseball-fielding task were characterized. Based on the response times for each age group, the maximum exit-velocity from a baseball-bat interaction that would allow a young baseball player sufficient time to safely respond to an approaching baseball was calculated.

Results: The results showed that subjects had sufficient time to respond to exit-velocities from 26.8 m·s−1 (8- to 9-yr-old group) to 33.5 m·s−1 (16-yr-old group). However, the accuracy of the response was negatively affected by baseball velocity.

Conclusions: If the exit-velocities seen during actual competition exceed the calculated maximum exit-velocities for these age groups, then our preliminary data suggest that modifications to the game of baseball that would reduce the actual exit-velocities and serve as an effective means to reduce the potential for serious or catastrophic injury are warranted.

Baseball-related injuries in children range from minor to catastrophic. Minor injuries include contusions, abrasions, and sprains. Serious injuries include fractures and ruptured ligaments and tendons. Catastrophic injuries include death and permanent central nervous system dysfunction. Although catastrophic injuries in youth baseball and softball are rare, they do occur (1,13,15). From 1973–95, there were 88 baseball/softball-related deaths in children 5–14 yr of age (15). Nearly 90% of catastrophic injuries in youth baseball occur by direct contact of a baseball or baseball bat to the head, neck, or chest.

Current efforts to decrease the number of catastrophic injuries have focused on the structural properties of baseballs and baseball bats (6,7,22). Researchers have subsequently suggested the use of reduced impact baseballs that have a mass similar to “standard” baseballs but are made with a softer core. Although many critics argued that the “soft-core” baseball would change the nature of the game of baseball, there has been no evidence of perceivable playing differences among baseballs of different hardness (20). Although soft-core baseballs may reduce the number of catastrophic injuries due to head impact, they may not influence catastrophic injuries due to chest impact (6,7). Another approach to reduce injuries involves the use of safety equipment. Batters and base runners wear batting helmets to protect their heads. Catchers are required to wear helmets, face masks, and chest protectors. Though this equipment provides protection to the batters and catchers, infielders and pitchers generally do not wear protective equipment. To have all infielders and pitchers wear chest protectors seems impractical, especially because it has been shown that a majority of commercially available chest protectors fail to provide consistent reduction to the risk of commotio cordis due to a blunt chest impact (19). Indeed, 28% of commotio cordis victims (within a variety of sports) were wearing some type of protective vest at the time of the impact (11).

The ability of an infielder to respond to a batted baseball may provide the best defense for avoiding injury. Response time, presently defined as the minimum time required by a baseball player to place the gloved hand between an oncoming baseball and her/his body, is an important variable that can distinguish a safely executed catch from a potentially catastrophic injury. The potential for injury increases as the time required for a batted baseball to reach a player (i.e., transit time) approximates and then becomes less than the response time of the player. Because the transit time of a baseball is influenced, in part, by the structural properties of the baseball and the baseball bat, response time may be a physiologically justified consideration in the design of baseballs and baseball bats.

This project investigated the response time of young athletes performing a simulated fielding task. Variables that may influence a participant’s ability to respond to an oncoming baseball include age, expertise with the task, and the velocity of the ball (2,8,23). For example, reaction times tend to be slower in children under 10 yr of age (1), and youth between the ages of 8 and 16 have slower reaction times than adults (8). Furthermore, increasing the velocity at which a ball is projected at a subject has been shown to decrease the reaction time of male college students (23). In that study, reaction time was reduced by 14 ms as the velocity of a projected ball increased from 25 m·s−1 to 55 m·s−1. It is unknown whether children also decrease their reaction time with increased ball velocity, especially at high velocities.

Response times can also be situational. For example, during a baseball game, players may become distracted and, therefore, not be fully attending to the task. Whether such distractions occur from reviewing various fielding scenarios in their mind, reliving their last batting performance, or looking into the stands, it may influence their ability to react to an approaching baseball. Studies have shown an increase in reaction time when attention is divided between two tasks (5,10,18).

The purpose of the current project was to characterize how baseball velocity and level of attention influence the response time of boys and girls. We hypothesized that (a) response times would not be influenced by baseball velocity; (b) slower response times would occur during conditions in which subjects perform an attention-splitting task, compared with conditions in which subjects do not perform an attention-splitting task; (c) response times would be inversely proportional to the age of the subject; and (d) response times would not be influenced by the gender of the subject. The second purpose of the project was to use the response times to determine age-group specific estimates of the maximum exit-velocity (i.e., the velocity with which the baseball leaves the bat) that would allow a player, standing 13.7 m away, to safely respond to an approaching baseball.

1Department of Biomedical Engineering, The Cleveland Clinic Foundation, Cleveland, OH; and

2School of Kinesiology, University of Illinois at Chicago, Chicago, IL

Address for correspondence: Tammy M. Owings, M.S., Department of Biomedical Engineering, ND20, Lerner Research Institute, The Cleveland Clinic Foundation, 9500 Euclid Avenue, Cleveland, OH 44195; E-mail: owings@bme.ri.ccf.org.

Submitted for publication May 2002.

Accepted for publication March 2003.

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METHODS

Subjects.

Fifty boys and 50 girls, who were active in competitive/recreational baseball or softball programs, were recruited. Five age groups (8–9 yr, 10–11 yr, 12–13 yr, 14–15 yr, and 16 yr) were equally represented (Table 1). The study was approved by the Institutional Review Board at The Cleveland Clinic Foundation. All subjects, as well as a parent or legal guardian, provided written informed consent before involvement in the research program. All subjects were compensated for their participation.

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Experimental set-up.

Each subject stood in a standardized fielding position and was asked to simulate a baseball catch when a baseball was projected at them. The subject stood with their feet approximately shoulder-width apart, knees slightly flexed, arms at the side of the body and elbows slightly flexed. Each subject used his or her own baseball glove. A pitching machine (Omni Sports Technologies, Memphis, TN), located 13.7 m away (the standard pitching distance in Little League baseball is 14 m) was employed to project the baseballs toward the subject. Although the direction of the projected baseball varied between trials, the location of the ball impact with the safety net was within a radius of approximately 30 cm that was centered at the subject’s chest. The safety net, which protected the subject from the incoming baseball (StanMar Sports Nets, Fernandina, FL) was placed 2 m in front of the subject and between the subject and the pitching machine.

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Protocol.

A total of 40 trials were performed. Trials were randomly blocked by the velocity of the projected baseball, with 20 trials being performed for each of two velocities, 26.8 m·s−1 and 33.5 m·s−1 (60 and 75 mph, respectively). These velocities represent possible speeds that may be attained by a hard hit line-drive ball. Subjects were given three to four practice trials before each block of velocities. Within each block, the order of administration for the two levels of attention was randomized. Subjects were either instructed to fully concentrate on the incoming baseball or instructed to verbally perform an attention-splitting task while waiting for the baseball to be projected. Examples of the attention-splitting task include counting backward by a specified value, naming familiar objects (e.g., movies, fruits, baseball teams, etc.), and spelling difficult words. The attention-splitting task varied for each trial and was adjusted to account for the age of the subject. Ten trials per level of attention were performed at each velocity.

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Instrumentation.

A six-camera motion capture system (Motion Analysis Corp., Santa Rosa, CA), operating at 180 Hz, recorded the motion of the baseball and of three spherical reflective markers placed on the subject’s baseball glove from which the respective three-dimensional trajectories were computed. The instant at which the baseball was projected was quantified with a piezoresistive accelerometer mounted on the chute of the pitching machine. The signal from the accelerometer was sampled at 1200 Hz and synchronized with the motion capture data.

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Analysis.

Response time was characterized by two components, reaction time and movement time. Reaction time was defined as the elapsed time between the instant of baseball projection and the onset of the baseball glove motion. The instant of baseball projection was determined as the time at which the output signal from the accelerometer exceeded 100 mV. The onset of baseball glove motion was determined as the time at which the computed motion vector in the frontal plane exceeded 5 mm from the initial glove position (Fig. 1). The frontal plane motion vector was calculated as

0EQUATION

where h and v correspond to the horizontal and vertical directions, respectively.

During the analysis, it was necessary to discard the computed reaction time for those trials in which the subject anticipated the approaching baseball and during which the motion of the glove began before the instant of baseball projection. To determine those reaction times to be discarded while maintaining the integrity of the data, a histogram of the computed reaction times for all 4000 trials was plotted and fit with a normal distribution curve. To identify those trials during which subject anticipation played a role, a left-side cutoff value was determined as the point at which the histogram and the normal curve differed by a factor of 2. To maintain the symmetry of the distribution, a right-side cutoff value was located at a distance from the mean equal to that of the left-side cutoff value (Fig. 2).

Movement time, the second component of the response time, was calculated using an estimate of the rate of movement (velocity) of the glove as the subject attempted to make a catch. Glove velocity was calculated from the slope of the motion vector after the onset of glove motion. Glove velocity was determined within a 100-ms window that was centered between the onset of glove motion and the time when glove motion had stopped. Using this average glove velocity, the time required by the subject to move the glove a distance equal to half of their body height was calculated and considered reflective of movement time. Half of the subject’s body height was considered the maximum distance the glove would have to move from the standardized position to prevent the baseball from contacting the subject. This movement time was added to the average reaction time to determine each subject’s trial-specific response time. Using this response time, the maximum exit-velocity with which the baseball could travel 13.7 m and allow the subject to safely respond was determined.

The ability of the subject to appropriately position the glove to catch the projected baseball was determined by extrapolating the baseball trajectory had its motion not been obstructed by the safety net. At the time at which the predicted baseball trajectory intersected the average glove motion, the extrapolated horizontal and vertical trajectory of the baseball was compared with the horizontal and vertical positions of the glove.

Attempts from each trial were classified as a catch, a tip, or a miss. Trials were classified as a catch if the location of the baseball was within the area defined by the glove markers. If the location of the baseball was not within the area defined by the glove markers but was within 5 cm of the outer boundaries defined by the glove markers, then the attempt was considered a tip. For these attempts, the baseball presumably would have been deflected by the glove and would not have made contact with the subject. All other attempts were considered misses. Any trial, regardless of classification, was discarded if the height of the baseball exceeded the height of the subject or if the baseball was located more than 30 cm laterally from the mid-line of the subject. Baseballs that were outside these boundaries would not have contacted the subject, thus rendering a subject’s ability to “catch” these baseballs irrelevant to the context of the study.

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Statistics.

Each subject’s reaction times and glove velocities for each of the four experimental conditions were averaged across trials before performing the statistical analysis. Statistical analysis of the reaction times and glove velocities were performed using 2 × 2 (baseball velocity by level of attention) repeated measures multivariate ANCOVA (MANCOVA) using age as a covariate and gender as a between-subject factor. Significant effects from the MANCOVA were further investigated using Tukey’s honestly significant difference test. Statistics were performed with SPSS 7.0.

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RESULTS

Based on the aforementioned analysis procedure, all reaction times less than 67 ms or greater than 350 ms were eliminated (for final distribution, see Fig. 2). In general, two or three trials per condition were eliminated per subject.

Reaction times were significantly faster during the trials in which the baseball was projected at 33.5 m·s−1 compared with 26.8 m·s−1 (P < 0.001, F = 10.96, df1,98, Fig. 3A, Table 2). On average, compared with the 26.8 m·s−1 trials, reaction times decreased by 16 ms for the 33.5 m·s−1 trials.

Reaction times were significantly faster during the full-attention condition compared with attention-splitting condition (P < 0.001, F = 23.48, df1,98, Fig. 3B, Table 2). On average, compared with the attention-splitting trials, reaction times decreased by 13 ms for the full-attention trials. The baseball velocity by attention interaction was not significant (P = 0.988, F = 0.00, df1,98).

The ANCOVA revealed that the influence of age, the covariate, on reaction time was significant (P < 0.001, b = −8.64, t = 4.181). In general, the oldest subjects had significantly faster reaction times compared with the younger subjects (Fig. 3C, Table 2). Post hoc multiple comparisons revealed that the reaction times of the 8- to 9-yr-olds were significantly slower than the 12–13, 14–15, and 16 yr olds (P = 0.004, 0.033, and 0.005, respectively). Furthermore, the reaction times of the 10–11 yr olds were significantly slower than that of the 12–13 and 16 yr olds (P = 0.012 and 0.015, respectively). The difference between the 10–11 yr olds and the 14–15 yr olds did not achieve significance (P = 0.075).

Although reaction times did not differ significantly between boys and girls (P = 0.105, F = 2.68, df1,97, Fig. 3D, Table 2), the gender by attention interaction was significant (P = 0.003, F = 9.46, df1,98). The gender by baseball velocity and the gender by baseball velocity by attention interaction terms were not significant (P = 0.376, F = 0.79, df1,98 and 0.381, F = 0.77, df1,98, respectively).

The computed glove velocity was significantly faster during the trials in which the baseball was projected at 33.5 m·s−1 compared with 26.8 m·s−1 (P < 0.001, F = 19.16, df1,98, Fig. 4A, Table 3). On average, compared with the 26.8 m·s−1 trials, glove velocities decreased by 0.2 mm·ms−1 for the 33.5 m·s−1 trials.

The computed glove velocity was significantly faster during the full-attention condition compared with attention-splitting condition (P < 0.001, F = 14.43, df1,98, Fig. 4B, Table 3). On average, compared with the attention-splitting trials, glove velocities decreased by 0.2 mm·ms−1 for the full-attention trials. The baseball velocity by attention interaction was not significant (P = 0.531, F =0.93, df1,98).

The ANCOVA revealed that the influence of age, the covariate, on glove velocity was significant (P < 0.001, b = 0.282, t = 6.258, Fig. 4C, Table 3). In general, the oldest subjects had significantly faster glove velocities compared with the younger subjects (Fig. 4C, Table 3). Post hoc multiple comparisons revealed that glove velocities of the 8–9 yr olds, 10–11 yr olds, 12–13 yr olds, and 14–15 yr olds were significantly slower than that of the 16 yr olds (P < 0.001, P = 0.002, 0.004, and 0.021, respectively).

Glove velocities did not differ significantly between boys and girls (P = 0.839, F = 0.04, df1,97, Fig. 4D, Table 3). The gender by baseball velocity, gender by attention, and gender by baseball velocity by attention interactions were not significant (P = 0.337, F = 0.80, df1,98; P = 0.374, F = 0.93, df1,98; and P = 0.444, F = 0.59, df1,98, respectively).

During the trials in which the baseballs were projected at 26.8 m·s−1 and the subjects were fully attentive, the group data indicate that all groups except for the 8- to 9-yr-old boys would have had sufficient time to respond to the projected baseball (Fig. 5). Individually, the response times of 50% of 8–9 yr olds, 75% of 10–11 yr olds, 80% of 12–13 yr olds, 75% of the 14–15 yr olds, and 95% of the 16 yr olds during the full-attention trials were sufficient to respond to calculated baseball exit-velocities of 26.8 m·s−1. The percentages dropped by roughly 15% during the attention-splitting tasks.

During the trials in which the baseballs were projected at 33.5 m·s−1 and the subjects were fully attentive, the group data indicate that only the 14- to 15-yr-old girls and the 16-yr-old boys and girls would have had sufficient time to respond to the projected baseball (Fig. 5). Individually, the response times of 75% of 8–9 yr olds, 90% of 10–11 yr olds, 85% of 12–13 yr olds, 85% of the 14–15 yr olds, and 95% of the 16 yr olds during the full-attention trials were sufficient to respond to calculated baseball exit-velocity of 26.8 m·s−1. These percentages dropped by roughly 10% during the attention-splitting trials.

The ability to appropriately position the glove with respect to the projected baseball, as measured by the percentage of the number of “misses,” was significantly diminished when the baseball was projected at 33.5 m·s−1 compared with 26.8 m·s−1 (P < 0.001, F = 17.60, df1,96, Tables 4 and 5, note: the difference in the degrees of freedom reflects two subjects who were eliminated from the analysis due to missing data). Glove positioning accuracy was also diminished during the attention-splitting condition compared with full-attention condition (P < 0.001, F = 120.12, df1,96,Tables 4 and 5). In addition, there was a significant interaction between gender and attention (P < 0.018, F = 5.76, df1,96). The ANCOVA revealed that, in general, the percentage of misses decreased with age (P < 0.001, b = −5.083, t = −4.265, Tables 4–5). Post hoc multiple comparisons specifically revealed that the number of misses, averaged across conditions, registered by the 8–9 yr olds was significantly larger than that of the 14–15 yr olds and the 16 yr olds (P < 0.031, P = 0.014, respectively).

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DISCUSSION

This project investigated the response times of young athletes performing a simulated baseball-fielding task. Specifically, we sought to characterize how baseball velocity and level of attention influenced response time for young boys and girls and to use the computed response times to estimate the maximum exit-velocity that would allow a young baseball player sufficient time to safely respond to an approaching baseball.

Contrary to our expectations, reaction times and glove velocities were faster when the baseball was projected at 33.5 m·s−1 compared with when the baseball was projected at 26.8 m·s−1. These results agree with those of Williams and MacFarlane (23), who showed that reaction times in male college students decreased as the velocity of an incoming ball increased. At this time, we do not know whether our subjects would have continued to decrease their reaction times if the incoming ball velocity had been increased beyond 33.5 m·s−1, or if they had physiologically reached their minimum reaction time.

In general, the reaction times and glove velocities were diminished by the performance of an attention-splitting task. Although this was an expected finding (5,10,18), it underscores the proverbial phrase “keep your head in the game.” Yet “keeping your head in the game” may involve splitting your attention. With runners at first and third with less than two outs, a shortstop may not only be concentrating on the batter, but also thinking about where to throw the ball if it is hit to his/her left or right, if the ball is hit in the air or on the ground, or even what to do if the runner at first attempts to steal second base. The seemingly small decrease in reaction time during the attention-splitting conditions, 13 ms, translates to a baseball traveling nearly 0.45 m when traveling at 33.5 m·s−1. This increase in reaction time increases the potential for injury and should be taken into consideration when determining safe exit-velocities.

Reaction times and glove velocities did not differ significantly between boys and girls. However, there was an unexpected gender by level of attention interaction for reaction time. For the full-attention trials, boys and girls did not differ. For the attention-splitting trials, girls reacted 20 ms slower than during the full-attention trials, whereas boys showed no change in reaction time between the full-attention and the attention-splitting trials. Von Kluge (21) reported a similar interaction when testing the cognitive process of college students performing the Stroop color-naming task. The results showed a significant interaction between gender and level of anxiety. Manipulating the level of anxiety during the task did not affect the reaction time of men but did affect the reaction time of women. In the context of the current study, this suggests that, relative to baseball, young girls may be affected to a greater, and possibly more dangerous, extent than boys during conditions in which multi-tasking is occurring. From our results, the reason for the absence of a delay in boys’ reaction times during the attention-splitting condition cannot be determined, but it has been suggested that women tend to adopt a more conservative approach to responding than do men (9,17).

As expected, reaction times and glove velocities were faster, in general, for the older subjects. Thus, as evidenced by the results of the calculated maximum baseball exit-velocities, older subjects were able to respond to baseballs having faster exit-velocities. It is fair to assume that older youth would be able to hit the ball harder than younger youth. Thus, comparisons between our computed exit-velocities and the actual exit-velocities that are seen on a baseball field should be compared for each age group individually.

Based on response time, we computed the maximum baseball exit-velocity to which subjects could safely respond. These calculations are based on the subject standing 13.7 m away from the batter, which is the approximate distance a Little League pitcher would be standing from home plate, thus representing the “worst-case” scenario. It must also be noted that no consideration has been given to the body position of the pitcher during and at the completion of the follow-through of the pitch. It should be assumed that a pitcher’s body is positioned differently than the “standard fielding position” that was used in the current study. For the condition in which the baseballs were projected at 26.8 m·s−1, we found that the calculated maximum exit-velocities, on average, ranged from 26.8 m·s−1 for the 8–9 yr olds to over 31.3 m·s−1 for the 16 yr olds. Because of the influence of baseball projection velocity on reaction times and glove velocities, the calculated maximum exit-velocities increased by roughly 2.2 m·s−1 during the 33.5 m·s−1 trials. As previously stated, we do not know if this represents the physiological limit for these subjects. However, by considering the strategies involved in a baseball catch, it seems that at least for the younger subjects, the physiological limit was approached.

Catching a baseball requires a coincidence-timing strategy (12,14). The glove and the baseball must coincide at the same spatial location and at the same instant in time. Baseball players may choose either to (a) place the glove in the desired location and wait for the baseball to arrive or (b) “time” the catch so that the glove and the baseball arrive at the desired location at approximately the same time. If strategy (a) is chosen, then reaction time is unaffected by the velocity of the baseball. If strategy (b) is chosen, the reaction time is proportional to baseball velocities. Similar to the result from Peper et al. (14), our results suggest that strategy (b) was selected by these subjects. During the conditions in which the ball was projected at 33.5 m·s−1 trials, only the 16-yr-old age group had calculated maximum baseball exit-velocities greater than 33.5 m·s−1. This implies that the younger age groups had reached their physiological limit to appropriately “time” the catch.

Although the results suggest that the subjects were physiologically able to respond to a baseball at 26.8 m·s−1, the accuracy of the response was diminished. For example, the data indicate that subjects in the 8- to 9-yr-old group would have missed the baseball over 70% of the time due to inaccurate glove position. Thus, in a time critical situation, these subjects have the ability to move their glove through the requisite distance, but the ability to accurately move their glove to a specific location is negatively affected. This point is highlighted by the comment of a 10-yr-old boy after the experimental session: “The baseball was coming in so fast, I could only turn my head and stick out my glove.” Although a missed baseball would not automatically mean that the player would be hit by the baseball (i.e., players can avoid the baseball in other ways such as ducking or jumping to the side), the possibility of even one of these missed baseballs being able to contact the player is quite alarming.

There are two ways in which the accuracy of glove placement can be improved. One way is to reduce the velocity of glove movement. Clearly, however, because of this velocity-accuracy trade-off, the response time will be increased thus decreasing the maximum exit-velocity to which the subjects can respond. A second way to increase accuracy is by practice. The more times a specific task is performed, the more accurate the response becomes (2), accenting the old saying, “Practice makes perfect.”

This second concept may explain why the girls caught or tipped the baseball fewer times than the boys, even though there was no difference in reaction times or glove velocities. In general, girls participate in organized softball more often than organized baseball. Based on the size of the ball and the velocity with which it is pitched, the exit-velocities of softballs are slower than that of baseballs. Therefore, girls have less practice catching the ball at the faster velocities (3,4,16). For the current study, this translated into the girls missing the baseball 15–25% more often than the boys.

In conclusion, we sought to determine, based on the response times of boys and girls between the ages of 8–16 yr, the maximum baseball exit-velocity that would allow them to safely respond to an approaching baseball. We determined that the subjects had sufficient time to respond to exit-velocities of 26.8 m·s−1 (for the 8- to 9-yr-old group) to 31.3 m·s−1 (for the 16-yr-old group), yet the accuracy of the response was limited. If further investigation can confirm that our calculated maximum baseball exit-velocities are slower than the actual maximum baseball exit-velocities common to a specific level of play, then modifications to the game of baseball, such as the use of soft-core baseballs for certain age groups, would seem prudent. The purpose of this study was not to debate the use of “soft-core” baseballs or to recommend changes to the game of baseball. The results of this study provide a physiological basis for evaluating the safety of the game of baseball. Although catastrophic injuries during baseball are rare, it should be determined whether these types of injuries can be prevented.

This study was supported by a grant from The National Operating Committee on Standards for Athletic Equipment. The opinions expressed herein are those of the authors and do not necessarily reflect the opinions of the Committee.

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Key Word: CHILDREN; BASEBALL; MOVEMENT TIME; REACTION TIME; YOUTH

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A Numerical Model for Risk of Ball-Impact Injury to Baseball Pitchers
NICHOLLS, RL; MILLER, K; ELLIOTT, BC
Medicine & Science in Sports & Exercise, 37(1): 30-38.

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