Examining Speed-Accuracy Tradeoff and Impulse-Variability Theory with Implications for Overarm Throwing: A Literature Review and Study Proposal

Introduction

Multijoint ballistic motor skills (e.g., throwing, striking, kicking) involve the complex coordination and control of multiple joints in a proximal to distal sequence. These skills generally have two outcome measures: one, speed (or power) production; and two, spatial accuracy (Molina et al., 2019). Fitts’ Law (1954) consistently demonstrated an inverse relationship between movement speed and accuracy. However, the simplicity of motor tasks examined led researchers to question the applicability when spatial and temporal constraints are present. Impulse-variability theory (Schmidt et al., 1979) attempted to explain the relationship between muscular forces and their variability across a continuum of force requirements. Further research revealed an inverted-U relationship between force and force variability (Sherwood & Schmidt, 1980; Schmidt & Sherwood, 1982), with force variability peaking between 60-65% of maximal force, then declining at higher force levels. In overarm throwing, only two studies have examined this relationship, with one (Urbin et al., 2012) demonstrating an inverted-U relationship between force and force variability while a second (Molina & Stodden, 2018) showing no relationship. Notably, neither study showed a relationship between speed and accuracy across a range of speed conditions, challenging the generalizability of Fitts’ Law to ballistic motor skills. Because motor competence in a variety of skills is a key influencer in physical activity across the lifespan (Holfelder & Schott, 2014), a synthesis of the research surrounding movement speed, force variability, and accuracy is needed to provide practical guidelines for teachers of these skills.

The purpose of this paper is to review the literature surrounding Fitts’ Law and impulse-variability theory to better understand practical implications for overarm throwing. Also, this paper proposes an experiment to further understand the relationship between force, force variability, and resultant accuracy in baseball pitching.

First, the paper reviews Fitts’ Law and how it provoked further research, leading to impulse-variability theory. Next, the paper looks at modifications made to impulse-variability theory as evidence contested original conclusions. Following that, the paper will evaluate studies that examined the speed-accuracy tradeoff across instructional, effort, and practice conditions, leading to a review of studies that intentionally examined speed, variability, and accuracy across a continuum. The paper will conclude with a study proposal.

Fitts’ Law

In goal-directed motor tasks, the relationship between the speed and accuracy of movement has undergone extensive examination among motor learning researchers. Woodworth (1899) first studied the association between movement speed and its effect on accuracy. In his experiments, subjects used a stylus to rapidly draw a line of a specified distance with and without visual feedback. When visual feedback was present, a movements variable error increased with both amplitude and speed. Woodworth concluded that there were two main phases of control: a pre-programmed initial phase and a control phase. The initial phase was predetermined by the muscular impulse required to execute the movement. The control phase relied on visual feedback to detect and correct errors during the motor task. Woodworth suggested the initial phase explained the inverse relationship between speed and accuracy (Urbin et al., 2011). Decades later, Fitts (1954) conducted experiments examining the relationship between movement speed and accuracy in a variety of simple motor skills. The relationship showed that movement time (MT) had a direct logarithmic relationship between target amplitude (A) and target width (W) such that as amplitude (distance) increased or width decreased, increased movement time could be predictably measured. This work produced the equation: MT = a + b [log2 (2A / W)], where a and b are empirical constants. These findings—hereby referred to as Fitts’ Law—were replicated across a wide range of populations and tasks with little to no evidence that challenged this relationship.

Fitts’ Law reliably predicted movement speed in tasks requiring spatial accuracy. However, many tasks, particularly in sport, require spatial and temporal accuracy to achieve the desired movement outcome. Researchers began testing these skills to determine the generality of Fitts’ Law.

In an early experiment evaluating spatial and temporal accuracy, Schmidt (1969b & 1969c) had subjects project a pointer along a sliding track with the goal of striking a moving target approaching from a perpendicular angle. The pointer was positioned 15, 30, 45, or 60cm from the target, and was loaded or unloaded in separate conditions. Subjects were instructed to project the pointer at either moderate or maximal speeds. In one experiment (Schmidt, 1969b), longer movement times, compared during the moderate and maximal speed conditions, were proportionally associated with greater variable error independent of movement amplitude and the mass of the pointer. The second experiment (Schmidt, 1969c) showed that longer movement times, either through increasing movement amplitude or decreasing movement speed, resulted in greater movement time inconsistency compared to shorter movement times. Both experiments provided evidence that when movement amplitude and movement time are independent variables, the speed-accuracy tradeoff does not follow the relationship outlined in Fitts’ Law (Schmidt et al., 1979).

Impulse-Variability Theory

The Schmidt et al. (1979) findings led these researchers to propose Impulse-Variability Theory which accounts for the relationship among movement amplitude, movement time, the mass to be moved, and the resultant error. The authors specifically looked at rapid movements where feedback cannot account for any corrections in the movement. This distinction resulted from experiments which found that new spatiotemporal movement patterns required at least 120-200ms of reaction time (Schmidt, Zelaznik, & Frank, 1978). So, before a movement is performed, the system must specify: 1) which muscles are to contract; 2) in what order they are to contract; 3) the relative and absolute forces with which they are to contract; and 4) the temporal relations among the contractions (Schmidt et al., 1979). 

The theory centers around the critical nature of the muscular impulse. The muscular impulse is represented by the area under the force-time curve for acceleration. It is the aggregate of accelerative forces acting to propel the limb toward the movement endpoint. Newton’s second law (force x mass = mass x velocity) implies that the velocity of the limb at the end of its acceleration is directly proportional to the muscular impulse (force) given that the limb’s mass is constant (Schmidt et al., 1979). Because the initial muscular impulse is preprogrammed, any errors in the final trajectory of the limb are the consequence of the initial muscular impulse required to produce the movement.

The major implication to impulse-variability theory stipulates that within-subject force variability is proportional to the total movement time. As such, movements requiring greater force or faster speeds displayed proportionally larger variability in the muscular impulse (Schmidt et al., 1979). However, a key limitation to these experiments (Schmidt, 1969b; Schmidt, 1969c; Schmidt et al., 1978) was that a large spectrum of force production was not measured, thus raising the possibility that a linear relationship between force magnitude and force variability may not exist as Schmidt had suggested.

Modifications to Impulse-Variability Theory

To understand force magnitude and force variability across a broader range of force magnitudes, Sherwood and Schmidt (1980) conducted a series of experiments on both static and dynamic contractions of the elbow. In the first experiment, subjects were instructed to attempt a force output target using a lever held in a static position. Forces represented 26 to 58% of maximum force and showed a strong linear relationship between force and force variability. These findings supported earlier conclusions (Schmidt et al., 1979) examining this relationship.

A second experiment was designed to see if this relationship holds for near-maximal isometric contractions. Subjects followed the same procedure from experiment one, except five load conditions were altered to represent between 16-20%, 33-40%, 49-60%, 65-80%, and 79-97% of maximal force output. Results indicated a strong linear trend between force and force variability over the first three load conditions, but peaked, then decreased over the last two load conditions. These findings demonstrated an inverted-U relationship between force and force variability and did not support Schmidt et al. (1979) earlier conclusions.

After these findings, Sherwood and Schmidt (1980) tested this relationship with dynamic contractions. Subjects were instructed to move the lever through 55o of movement in 150 msec under five load conditions: 25%, 45%, 65%, 75%, and 85% of their maximal strength. Analysis showed that within-subject force variability increased linearly at lower levels of force, peaked around 55-60% of maximum force, then decreased as force requirements approached maximum strength. Again, these findings showed an inverted-U relationship between force and force variability. Ultimately, this inverted-U relationship served as a foundation for future experiments where force and force variability were studied.

To examine the relationship between spatial error and force variability, Schmidt and Sherwood (1982, Experiment 2) conducted an experiment in which subjects were tasked to horizontally swing their right arm toward a target. The subjects were seated with their shoulder horizontally abducted to 60o, grasping a D-shaped handle. In this experiment, a movement time of 200msec was held constant across five load conditions (handle only, handle plus 640g, 960g, 1,120g, and 1,640g). The load conditions represented between 41 to 89% of maximum torque. As load increased, variable error and total variability increased linearly in the first two load conditions. Both variable error and total variability peaked at the second load condition (61% of maximum torque) then decreased across the heavier conditions. Interestingly, there were no differences in spatial accuracy across the load conditions. These findings further strengthened the inverted-U relationship between force variability and force and demonstrated no tradeoff between movement speed and accuracy.

Expanding on these findings, Schmidt and Sherwood (1982, Experiment 3) conducted a similar experiment except movement time was varied while mass was held constant. They reasoned that moving a larger mass with the same movement time will yield the same force requirements as moving a constant mass with smaller movement time. In this experiment, subjects were instructed to move their arm toward the target at 70, 100, 130, and 160msec. The time conditions represented between 21% (160msec condition) to 88% (70msec condition) of subjects’ maximum torque. The authors found an inverted-U relationship between movement time and both variable error and variability. Again, there was no relationship between spatial error and the movement time conditions.

One limitation to these studies (Sherwood & Schmidt, 1980; Schmidt & Sherwood, 1982) was the authors did not control for the time to peak force. Newell and Carlton (1985) measured the relationship between peak force and peak force variability in an isometric, elbow flexion task. First, subjects were instructed to pull a handle 20 times over three time-to-peak-force conditions (100, 200, and 300msec). The results showed that peak force increased as time to peak force increased. The authors questioned the findings of previous studies (Sherwood & Schmidt, 1980; Schmidt & Sherwood, 1982) by proposing that the inverted-U relationship observed could be explained by shifting the time to peak force in relation to the percentage of peak force required in a given condition.

Following these findings, Sherwood, Schmidt, and Walter (1988) conducted another experiment controlling for time to peak force across six load conditions. Subjects executed a rapid sequential elbow movement in 160msec in load conditions which ranged from 37% to 89% of maximum torque. Torque variability increased linearly across the first four load conditions then decreased slightly across the fifth and sixth conditions, respectively. Torque variability between the three heaviest load conditions did not reach significance, so an inverted-U relationship was not supported. However, the curvilinear relationship between force and force variability remained even when time was controlled for. The authors suggested that Newell and Carlton’s (1985) findings may only be applicable for isometric movements.

Through further experiments, Schmidt et al.’s (1979) original ideas about impulse-variability were challenged when large spectrums of force output were studied. The empirical evidence displayed an inverted-U (or curvilinear) relationship between force and force variability (Sherwood & Schmidt, 1980; Schmidt & Sherwood, 1982) when controlling for mass, movement time, and movement distance. Notably, none of the studies found significant differences between force, force variability, and spatial accuracy. This calls into question the generalizability of Fitts’ Law, which states that as movement time increases, accuracy will predictably decrease. 

Although much of the research that makes up our understanding of impulse-variability theory has been conducted in controlled, laboratory-based settings using single-joint movements, these findings may have implications for sport. Schmidt and Sherwood (1982) pointed out that in baseball batting there is a commonly held belief that a reduced moment of inertia – either by swinging a lighter bat or choking up on the grip – will result in decreased spatial errors and decreased impact force. However, their experiments indicate that beyond 65% of maximum torque, heavier objects result in greater spatial accuracy and increased impact force. Further research examining the impact of bat mass on spatial accuracy and impact force across a range of bat masses would provide insight on this relationship.

Ballistic, Multijoint Motor Skills

Urbin et al. (2011) outlined three key performance features of ballistic, multijoint movements that are related to impulse-variability theory. First, these skills, such as kicking, striking, and throwing, require effective generation and transfer of energy through the kinetic chain to produce high distal segment and projectile velocities. Second, the aggregate of muscular forces at one joint must be transferred to sequential joints until forces are transferred to the limb or implement. Third, the resultant velocity of the distal segment, implement, or projectile must not decelerate until after release or striking.

Surprisingly, only three studies (Urbin et al., 2012; Chappell et al., 2016; Molina & Stodden, 2018) have examined both impulse-variability theory and a speed-accuracy tradeoff in ballistic skills. That said, others (Van den Tillaar & Ettema, 2003; 2006; Garcia et al., 2013; Van den Tillaar & Ulvik, 2014) have studied the speed-accuracy tradeoff across different instructional conditions. Researchers have also examined spatial error across a variety of effort levels in throwing (Indermill & Husak, 1984; Freeston et al., 2007; Freeston & Rooney, 2014; Urbin et al., 2012), tennis serving (Cauraugh, Gabert, & White; 1990), and kicking (Southard 2014; Chappell et al., 2016), with only one (Freeston & Rooney, 2014) showing evidence of a speed-accuracy tradeoff. Researchers have also studied the effect of speed or accuracy prioritization in the practice of ballistic motor skills in children (Malina, 1969; Englehorn, 1997; Belkin & Eliot, 1987). The following sections will examine those studies in detail.

Speed-Accuracy Tradeoff Across Instructional Conditions

To evaluate the influence of instruction on ball velocity and accuracy, Van den Tillaar & Ettema (2003) recruited nine experienced handball players. The subjects performed seven trials under five instructional conditions: 1) throw the ball as fast as possible in the goal; 2) throw the ball as fast as possible and try to hit the target; 3) hit the target and throw as fast as possible; 4) hit the target and try to throw as fast as possible; and 5) hit the target. When accuracy was prioritized (conditions 4 and 5), throwing velocity was significantly lower. However, the authors observed no effect between velocity and accuracy across all conditions. This fails to support a speed-accuracy tradeoff through task manipulation. Interestingly, the authors omitted analyzing accuracy in condition 1 to ensure the subjects would not prioritize accuracy at all. That omission limits this study’s applicability of analyzing the speed-accuracy tradeoff at the full continuum of force.

Expanding on their findings, Van den Tillaar & Ettema (2006) tested 13 subjects who had no experience participating in an organized sport involving overarm throwing. Testing procedures were identical to their earlier study (Van den Tillaar & Ettema, 2003). The results showed that there was a significant effect for velocity when accuracy was prioritized. Furthermore, no significant effect was observed on accuracy across the instruction conditions. These findings do not support a speed-accuracy tradeoff and extend the applicability to both expert and novice populations.

Garcia et al. (2013) examined the relationship between speed and accuracy in expert and novice handball players across two instructional conditions: 1) throw with the greatest accuracy possible; and 2) throw the ball at more than 90% of their maximum speed and try to be as accurate as possible. In this experiment, ten different targets (40 cm x 40 cm) were placed in a handball goal, and the instructed target goal was randomized for each trial. Both groups threw significantly faster when speed and accuracy were prioritized, and the expert group was more accurate than the novices in both conditions. The expert group showed no difference in accuracy under both conditions, but the novice group displayed significantly greater accuracy under the accuracy condition. These findings support earlier findings (Van den Tillaar & Ettema, 2003) that expert throwers do not sacrifice accuracy even when it is prioritized. However, these results challenge Van den Tillaar & Ettema’s (2006) findings regarding the speed-accuracy tradeoff among novices. 

Research examining the influence of instruction had been limited to overarm throwing until Van den Tillaar & Ulvik (2014) investigated the relationship in experienced soccer players. A 1m x 1m target was placed in the middle of a regulation-sized soccer goal. The subjects kicked balls with their dominant and nondominant feet and were instructed under four conditions: 1) kick the ball as fast as possible straight forwards in the goal; 2) kick the ball as fast as possible and try to hit the center of the target; 3) hit the center of the target and try to kick the ball as fast as possible; 4) hit the center of the target. Results showed that a prioritization on accuracy significantly reduced velocity in both dominant and nondominant feet. In the dominant foot, kicking accuracy significantly improved in the accuracy-priority condition (i.e., condition 4) compared to conditions 2 and 3. These results support Fitts’ Law (1954) regarding speed-accuracy tradeoffs and were not in accordance with similar studies on task prioritization in ballistic motor skills (Van den Tillaar & Ettema, 2003; 2006; Garcia et al., 2013).

The influence of instruction on speed and accuracy shows conflicting findings. In expert overarm throwers, it appears that accuracy is not reduced, only velocity, across a range of instructional conditions (Van den Tillaar & Ettema, 2003; 2006; Garcia et al., 2013). However, Van den Tillaar & Ulvik (2014) found evidence of a speed-accuracy tradeoff in kicking. Perhaps task prioritization is more influential in skills that require a limb to strike an object toward a target rather than projecting an object toward a target. While both involve the spatiotemporal coordination of multiple segments, kicking requires two components of accuracy (foot to ball; ball to target), while throwing only require one component (ball to target).

The instructional conditions where accuracy was the only priority revealed interesting findings regarding preferred throwing and kicking velocity. When accuracy was the only instruction, both experts (85%) and novices (84%) threw at similar percentages of maximal velocity (Van den Tillaar & Ettema, 2003; 2006). In kicking, subjects performed at 73% of maximal ball velocity when accuracy was prioritized. Thus, these studies fail to show the differences in accuracy across a wide range of forces which limits the understanding of a speed-accuracy tradeoff in ballistic motor skills.

Spatial Error Across Limited Effort Levels

Indermill and Husak (1984) had male undergraduate students throw tennis balls at three different percentages of maximal speed (50%, 75%, and 100%). Participants performed 10 throws at each condition standing 12.2m away from an archery target centered 2.2m above the ground. Accuracy was scored via a point system in which hitting the center ring of the target was worth five points, with points decreasing progressively from four to zero across the outer rings. Results showed that participants were significantly more accurate in the 75% condition compared to the 50% and 100% conditions. No difference in accuracy was observed between the 50% and 100% conditions. These findings do not support Fitts’ Law (1954) which proposes an inverse relationship between velocity and accuracy.

Freeston, Ferdinands, & Rooney (2007) examined the relationship between speed and accuracy in 110 male and female elite and sub-elite cricket players. The participants threw 40 balls across four conditions at a cricket target placed 20.1m away and accuracy was scored via a point system. Three conditions required 10 throws at 50%, 75%, and 100% of maximal velocity. The fourth condition required 10 throws at a self-selected velocity. The authors found that accuracy was greater between 75% and 85% of maximal throwing velocity compared to 50% and 100% across all groups. Interestingly, the self-selected velocities for all groups ranged between 75.4% and 83.0% of maximal velocity. These findings are similar to other studies (Van den Tillaar & Ettema, 2003; 2006) where throwers were allowed to choose a velocity level when accuracy was the priority.

Freeston & Rooney (2014) later tested the speed-accuracy tradeoff in 20 male baseball players. Participants were instructed to make 10 throws at 70%, 80%, 90%, and 100% of their maximal velocity. The target was 20.0m away, and the center was 70cm above the ground, the approximate midpoint of the baseball strike zone. Results showed that total error increased significantly as speed increased from 70% to 100% of maximal throwing speed. Thus, a linear relationship was observed between speed and accuracy, supporting Fitts’ Law (1954) and Van den Tillaar & Ulvik’s (2014) findings. Notably, the subjects were described as competing one level below state representation. This may limit the findings to elite level baseball players. 

Southard (2014) studied the speed-accuracy tradeoff in kicking with 20 university students, 10 experienced and 10 inexperienced soccer players. Participants were instructed to kick a soccer ball straight toward a target 5m away at three conditions of maximal velocity (33%, 66%, and 100%). Accuracy was measured as the absolute constant error from a vertical line representing the target. Across both groups and all three velocity conditions, no significant differences were found between accuracy and velocity. These findings fail to support the speed-accuracy tradeoff proposed by Fitts’ (1954) and the findings that were observed when instructional conditions changed (Van den Tillaar & Ulvik, 2014). 

Cauraugh, Gabert, & White (1990) analyzed the relationship between speed, accuracy, and speed variability in tennis serves. 15 highly skilled male and female tennis players participated in the study. They were instructed to serve 10 times toward a target at 50%, 60%, 70%, 80%, and 90% of their maximal serving speed. Across the 70%, 80%, and 90% conditions, no significant differences in spatial error were observed. Furthermore, as service velocities increased from 70% to 90%, total variability and variable error significantly decreased in a linear trend. Notably, serves at the 50% and 60% conditions were not used for analysis, with the authors citing serves at those speeds are rarely performed in competition. This is particularly unfortunate when tying back to impulse-variability theory, as spatial error and variable error across lower levels of force are especially relevant in further understanding ballistic motor skills.

When spatial accuracy was tested across a limited range of maximal velocities, a speed-accuracy tradeoff was not observed (Indermill & Husak, 1984; Freeston et al., 2007; Southard, 2014; Cauraugh, Gabert, & White; 1990), save for one study (Freeston & Rooney, 2014). Interestingly, Freeston & Rooney (2014) was the only study that did not test accuracy at lower levels (<70%) of maximal speed. Two studies (Indermill & Husak, 1984; Freeston et al., 2007) showed that accuracy increased from a 50% condition to a 75% condition, implying that accuracy may be worse at low levels of speed in ballistic motor skills.

Experiments Examining Speed and Accuracy in Ballistic Skills

A surprisingly limited number of studies have examined the practical application of the speed-accuracy tradeoff in promoting the acquisition of ballistic motor skills (Molina, Bott, & Stodden, 2019). Being that ballistic motor skill competence is positively related to overall physical fitness in young adults (Stodden, Langendorfer, & Roberton, 2009), development of these skills may lead to improved fitness over the lifespan. The following studies cover the practice effects of speed and accuracy in ballistic motor skills.

Malina (1969) studied the effect of practice conditions on overarm throwing in 55 high school males. They were randomly divided into five practice condition groups: 1) control, no practice; 2) speed information feedback only; 3) accuracy information feedback only; 4) speed-accuracy information feedback; and 5) no information feedback. Participants received 12 practice sessions over a 4-week period in which they made 20 throws toward a target 9.1 m away, striving for maximal speed and accuracy. Speed information was provided after each trial for groups 2 and 4 in relation to his previous fastest time. Accuracy information was provided through visual feedback for groups 3 and 4 and was withheld by restricting the subjects vision of the target at ball release (groups 2 and 5). After 12 practice sessions, all groups were retested with full feedback on speed and accuracy. The retest revealed that groups 2 and 4 threw at significantly higher velocities compared to groups 1 and 3. However, groups 3 and 4 were significantly more accurate compared to groups 1, 2, and 5. There was no difference in accuracy between groups 3 and 4. Overall, group 4, which received speed and accuracy feedback during all practice sessions, significantly improved in both categories. The speed-feedback group, group 2, regressed in accuracy performance from the initial to post test. The accuracy feedback group, group 3, regressed in throwing speed from the initial to post test. That said, the author noted group 2 demonstrated improvements in accuracy during later practice sessions, suggesting that those subjects may have eventually improved in accuracy had the program continued. This study shows the importance of feedback on developing the two key outcome measures (velocity and accuracy) in throwing performance. Although participants were instructed to throw as fast and as accurate as possible, practice conditions heavily influenced their subsequent adaptations. Notably, throwing form was not measured.

Engelhorn (1997) examined the effect of emphasizing speed or accuracy on the mechanics of fastpitch softball pitching. 26 girls (aged 10-11 years) participated in 12, 90-minute practice sessions over six weeks. Both groups received feedback and instruction on mechanical proficiency. In the speed group, subjects were given velocity feedback and threw to a net without a specified target. Accuracy was also measured for this group, though experimenters did not mention this nor provide feedback. In the accuracy group, subjects were scored on whether they hit a target placed 9.1m away. Velocity was also measured, but that was unknown to the subjects. After six weeks, all participants were retested. During the retest, participants in the speed group threw toward the target and did not receive velocity feedback while participants in the accuracy group threw to a net and received velocity feedback. Results showed that both groups improved in velocity, though the speed group improved significantly more (3.89 mph) than the accuracy group (2.56 mph). There were no significant differences between the groups in accuracy performance. Further, the speed group displayed significantly better technique compared to the accuracy group. The authors determined that emphasizing accuracy when learning softball pitching could be detrimental to technique and long-term performance.

Belkin & Eliot (1997) investigated the speed-accuracy tradeoff in floor hockey shots where either accuracy or velocity were prioritized in practice. 16 children (ages 6 to 11 years) were split into a speed or accuracy group and practiced over three days. The speed group was instructed to shoot the ball as hard as possible toward an unmarked wall, while the accuracy group was instructed to shoot as accurately as possible toward a target 7.6 m away. In a posttest, subjects were instructed to shoot as hard and as accurately as possible. In the posttest, no speed-accuracy tradeoff was observed between either group. However, the speed group shot significantly faster than the accuracy group and the speed group tended to be more accurate the accuracy group, though that did not reach significant levels. Although technique was not assessed, the authors noted that participants in the accuracy group displayed movement patterns similar to a long golf putt, while the speed group displayed a longer back-swing and follow through.

These studies address the practice effects, particularly feedback, of speed or accuracy prioritization on the development of ballistic motor skills. It appears that emphasizing speed (Malina, 1969; Englehorn, 1997; Belkin & Eliot, 1997) or speed and accuracy (Malina, 1969) are more beneficial to development compared to emphasizing accuracy alone. When teaching ballistic motor skills, Molina, Bott, & Stodden (2019) discuss two negative implications that sacrificing speed in hopes of increasing accuracy; one, a reduction in movement speed impedes the development of a movement pattern that promotes effective energy transfer through the kinetic chain; and two, the goal of increasing accuracy may not be achieved as a result of the reduction in limb velocity where both speed and accuracy are important. As such, these findings are especially relevant for practitioners who work with children.

These studies, however, failed to address the effect of accuracy across a variety of maximum velocity percentages. It is unclear what relationship would emerge among children. Studies in adults have shown that accuracy does not decrease when speed is prioritized (Van den Tillaar & Ettema, 2003; 2006; Garcia et al., 2013) and that accuracy does not linearly decline when speed demands are increased (Indermill & Husak, 1984; Freeston et al., 2007; Southard, 2014; Cauraugh, Gabert, & White; 1990; Urbin et al., 2012; Chappell et al., 2016).

Further research in elementary-aged children should address the impact of throwing at a range of maximum velocity on both accuracy and movement form. At lower percentages of throwing velocity, throwing form could diminish to less proficient levels. However, it is likely there is a velocity threshold at which throwing form remains advanced. Quantifying that threshold would have practical implications for teachers and coaches who could design practice environments that elicit throwing speeds above that threshold. Being that there is mounting evidence to refute a speed-accuracy tradeoff in throwing, accuracy prioritization at high velocities should promote advanced form and improved performance.

Speed-Accuracy Tradeoff Examined Through Impulse-Variability Theory

Earlier sections of this review outlined the origins, foundations, and modifications of impulse-variability theory. Later sections examined the literature regarding speed-accuracy tradeoffs in ballistic skills through task prioritization, varying effort levels, and practice conditions. This final section will link impulse-variability theory and speed-accuracy tradeoffs through the few studies that have empirically evaluated this relationship.

Urbin et al. (2012) examined the variability in overarm throwing velocity and spatial output error across a range of maximum velocity percentages. Thirty subjects (8 female, 22 male; 16 skilled, 14 unskilled) first performed maximum velocity throwing testing using a tennis ball. Following the maximal velocity testing, subjects performed ten throwing trials across seven percentages of maximum velocity (40, 50, 60, 70, 80, 90, and 100%). A 1 x 1 cm target was placed 180 cm above ground, and target distance was not specified. Results showed that variability in throwing velocity increased from 40% to 60% of maximum, then decreased at each subsequent interval. Both the skilled and unskilled groups demonstrated this relationship, though the unskilled group displayed significantly less variability overall, except in the 90% and 100% conditions. Analysis of spatial error showed there was no significant linear relationship between the percentage of maximum velocity and spatial error across both groups. The inverted-U relationship observed between the maximum throwing velocity and resultant variability support the work of Sherwood and Schmidt (1980). The lack of a speed-accuracy tradeoff in throwing support multiple studies (Van den Tillaar & Ettema, 2003; 2006; Indermill & Husak, 1984; Freeston et al., 2007; Molina & Stodden, 2017) that have observed a nonlinear relationship between throwing speed and resultant accuracy. That said, this study was the first to demonstrate this relationship across a wide range of maximum velocity percentages.

Chappell et al. (2016) studied the variability in kicking speed and spatial accuracy across a range of maximum velocity percentages. Twenty-eight subjects (aged 18 to 25 years) attended two testing sessions. In the first session, maximum kicking velocity was tested, then subjects were instructed to kick a soccer ball toward a target (1 x 1 cm; 2 m above the ground; 9.14 m away) at six percentages of maximum speed (50, 60, 70, 80, 90, and 100%). The first session was used for task familiarization and data was not used for analysis. In the second session, participants performed 10 blocks of six trials, and within each block there was one trial at each velocity condition. Participants received velocity feedback after each trial. For analysis of spatial error, the authors grouped kicks into five speed bandwidths (≤59%, 60-69%, 70-79%, 80-89%, and ≥ 90%). The results revealed a significant quadratic relationship for mean radial error and subject-centroid radial error. Further, the results showed a significantly higher subject-centroid radial error at kicks ≤59% of maximum speed compared to the 60-69%, 70-79%, and 80-89% bandwidths. These findings do not support a linear relationship between speed and accuracy and do not support other studies involving ballistic skills where no speed-accuracy tradeoff was observed (Urbin et al., 2012; Van den Tillaar & Ettema, 2003; 2006). For speed variability, the results showed a significant inverse linear trend. The 50% and 60% conditions had significantly higher variability compared to the 100% condition. These findings do not support the inverted-U relationship observed by Urbin et al. (2012). They also do not the origins of impulse-variability theory which would expect a positive relationship between force and force variability (Schmidt et al., 1979).

Similar to Urbin et al. (2012), Molina & Stodden (2017) examined the variability in throwing speed and spatial error across a range of maximum speeds. However, this study examined the relationship in children. 45 children (aged 9-11 years) participated in two test sessions. The first session was used to identify maximum throwing speed and to familiarize subjects with the protocols. In the second session, subjects performed five blocks of eight trials across four percentages of maximum speed (45, 65, 85, and 100%). Post hoc, subjects were placed into a skilled (n = 14) or unskilled (n = 31) based on the maximum throwing speed. There was no statistically significant difference for variable error across all speed conditions. However, the unskilled group displayed significantly less variability in the 45, 65, and 100% conditions compared to the skilled group. For spatial accuracy, there were no statistically significant differences in mean radial error, subject-centroid radial error, or bivariate variable error. However, between groups, the skilled group displayed significantly less bivariate variable error compared to the unskilled group. The variable error results do not support the inverted-U relationship observed in overarm throwing with adults (Urbin et al., 2012) nor the inverse linear relationship observed in kicking with adults (Chappell et al., 2016). The spatial accuracy results further contribute to the absence of a speed-accuracy tradeoff in ballistic motor skills (Urbin et al., 2012; Chappell et al., 2016; Southard, 2014; Indermill & Husak, 1984; Van den Tillaar & Ettema, 2003; 2006; Freeston et al., 2007).

These studies examining impulse-variability theory together with speed-accuracy tradeoff yield interesting results. Notably, in a direct contradiction to Fitts’ Law (1954), an inverse relationship between speed and accuracy is not observed. Although the inverted-U relationship between speed and speed variability first observed by Sherwood and Schmidt (1980) was also found by Urbin et al. (2012), other studies found no difference (Molina & Stodden, 2017) or an inverse relationship (Chappell et al., 2016). Further research studying speed and speed variability across a range of maximum speeds is needed to determine if there is relationship. It is possible that the force consistency observed at near-maximal levels in adults (Urbin et al., 2012; Chappell et al., 2016) would have practical implications for those teaching ballistic motor skills.

Conclusion

This paper aimed to address the limitations in the generalizability of Fitts’ Law to ballistic motor skills. Impulse-variability theory first showed that when spatial and temporal constraints are present, an inverse relationship between movement speed and resultant accuracy is not observed. Further research demonstrated an inverted-U relationship between force and force variability in single-joint dynamic and isometric tasks. When examining force and force variability in ballistic, multijoint movements, researchers have not shown a consistent relationship across a range of maximum forces. However, studies of overarm throwing have shown that a speed-accuracy tradeoff does not exist as speed demands change. The lack of support for a speed-accuracy tradeoff has implications for practitioners, as teaching these skills at high levels of force is beneficial for the development of advanced motor patterns. It is imperative that this information proliferates because high levels of motor skill competence promote increased physical activity and well-being across the lifespan. 

Study Proposal

Introduction

From the above review of existing literature, it is clear further research is needed to understand the relationship between speed, speed variability, and a speed-accuracy tradeoff in overarm throwing. The proposed study would be the first to examine the following two questions: one, what is the within-subject relationship between pitching velocity and the spatial error of the baseball; and two, what is the relationship between a prescribed percentage of maximum overhead pitching velocity and the resultant variability in force output.

The first question aims to build on experiments that have addressed the relationship between throwing velocity and spatial error (Urbin et al., 2012; Van den Tillaar & Ettema, 2003; 2006; Indermill & Husak, 1984; Freeston et al., 2007; Freeston & Rooney, 2014; Molina & Stodden, 2017). All these studies, except one (Freeston & Rooney, 2014), have challenged the inverse linear relationship between speed and accuracy demonstrated in Fitts’ Law (1954).  That said, only Urbin et al. (2012) measured the relationship across a wide range (40-100%) of prescribed velocities. Indermill & Husak (1984), Freeston et al. (2007) showed that throwing accuracy was highest at 75% and 80% conditions, respectively, and that accuracy was significantly lower at 50% and 100% of maximum throwing speed. Van den Tillaar & Ettema (2003; 2006) utilized task prioritization through instruction with expert and amateur handball players. They found no significant difference in accuracy across changes in task prioritization. 

The second question would provide further research on the relationship between force and force variability in ballistic motor skills. An inverted-U relationship was first observed by Sherwood & Schmidt (1980) in a dynamic elbow flexion task. Those findings were later supported by Urbin et al. (2012), who showed in overarm throwing, variability in velocity increased from 40 to 60% of maximum velocity, peaked, then decreased from 70 to 100%. However, further work (Chappell et al., 2016) showed an inverse linear relationship between force and force variability in kicking and Molina & Stodden (2017), showed no relationship between force and force variability in overarm throwing in children.

The purpose of this study is to examine the relationship between throwing velocity and spatial error in highly skilled baseball pitchers and to examine the relationship between throwing speed and variable error across a wide range of maximal throwing percentages.

Procedure

Participants in the study will be 5 highly skilled high-school-aged male baseball pitchers. To participate in the study, they will be injury-free for the preceding six months and possess the ability to throw at maximum velocity.

Criterion for skill will be determined based on pitched ball velocity data from Perfect Game, an international baseball scouting service. To be considered highly skilled, the pitcher must be at or above the 75th percentile for maximum throwing velocity for his age according to Perfect Game, an international baseball scouting service.

A target (Pitcher’s Pocket Pro) containing nine equisized catch pockets (25.4 cm wide, 30.5 cm tall) will be placed 18.4m (60’6”) away. The midpoint of the central target will be 70 cm above the ground to represent the midpoint of the strike zone (Figure 1).

 

Figure 1: (n.d.). 9 Hole Pro Pitcher's Pocket Net for Baseball. Retrieved January 3, 2022, from https://www.anytimebaseballsupply.com/products/better-baseball-pitchers-pocket-pro-9-hole. 

Two separate testing sessions will be executed. The first testing session will be used to assess maximum pitching velocity and provide familiarization with the task. If maximum pitching velocity does not meet the threshold, subjects will be excluded.

Participants will engage in a full warm-up consisting of foam rolling, dynamic and static stretching, a surgical tubing routine, and warm-up throwing. Warm-up throwing will conclude when the participant states he is ready to throw at maximum velocity.

On the first testing day, participants will throw 5 pitches at maximal speed, with the average of the top 2 pitches used to calculate velocity conditions. Next, each pitcher will make 5 throws at 7 conditions of effort (40, 50, 60, 70, 80, 90, and 100%). Throwing conditions will be randomized using a random number generator to avoid bias in the data collection. All pitchers will throw from the stretch position. Pitchers will be instructed to aim for the center pocket for each trial. Pitchers will receive velocity feedback after each trial and will be told what speed the given condition calls for.

Participants will be instructed to rest for 10 seconds in between each trial and 30 seconds in between each block to avoid fatigue.

Ball velocities will be recorded using a Stalker Sport 2 Radar Gun. Accuracy will be scored via a point system: 5 points for the center pocket, 3 points for each side pocket, 1 point for the cushion, and 0 points for a miss. All trials will be recorded via iPhone camera to ensure proper accuracy scores.

Data collected during the first testing day will not be used for analysis.

On the second testing day, procedures will be identical to day one, with the exceptions that maximal speed will not be tested and 7 throws at each condition will be performed.

Analysis

Spatial Error

Accuracy will be scored by summing the total points for each participant across each condition. The maximum number of points for each condition is 35, and the minimum is 0. A between-subjects and within-subjects analysis of accuracy across the conditions will be performed using a mixed model regression analysis.

Velocity Variability

Variable error will be calculated for each participant across each condition. A within-subjects repeated-measures ANOVA will be conducted to examine variable error in velocity at each condition.

Hypothesized Results

The author expects to observe no difference in spatial accuracy across all conditions. These results would further support the lack of a speed-accuracy tradeoff in ballistic motor skills (Urbin et al., 2012; Chappell et al., 2016; Molina & Stodden, 2017; Southard, 2014; Indermill & Husak, 1984; Van den Tillaar & Ettema, 2003; 2006; Freeston et al., 2007).

Due to the conflicting research on speed and speed variability across a range of maximum force percentages, it is difficult to hypothesize results. While Urbin et al. (2012) showed an inverted-U relationship, Chappell et al. (2014) showed an inverse linear relationship, and Molina & Stodden (2017) showed no relationship between speed and speed variability. That said, at higher levels of force (80-100%), the author expects to observe an inverse linear relationship between force and force variability. In highly skilled individuals, it is likely that force production will be more consistent as force demands increase. 

Practical Implications

If no difference is measured for spatial accuracy across all velocity conditions, baseball pitchers should not attempt to throw at slower speeds to achieve greater accuracy. A widespread belief in baseball is that when a pitcher is struggling to throw strikes, he should throw at slower speeds to accomplish the task. However, there is little evidence to support a speed-accuracy tradeoff exists. Further, throwing at slower speeds would likely decrease a pitcher’s in-game success, as it provides the batter more time to anticipate the location of an incoming pitch. Thus, in highly skilled pitchers, throwing slower is likely an ineffective strategy.

Although this study involves highly skilled high-school-aged baseball players, there is applicability to practitioners who work with elementary-aged children. An emphasis on accuracy can cause a beginner to constrain the pitching motion and negatively impact the development of more advanced movement patterns (Molina, Bott, & Stodden, 2019). Instruction that emphasizes speed, such as “throw as hard as you can” may provide the proper environment to promote advanced throwing form (Langendorfer & Roberton, 2002). Accuracy prioritization should occur once higher levels of throwing form are achieved. Being that a speed-accuracy tradeoff is not observed, accuracy should be instructed at maximal or near-maximal ball speeds to promote improved performance. Furthermore, accuracy demands should meet the level of the learner; if accuracy demands exceed skill level, throwing form may diminish.

If an inverted-U or inverse linear relationship is observed between speed and speed variability, highly skilled pitchers and their coaches can apply these findings in practice. Due to complex coordination of body segments required in pitching, throwing at higher percentages of maximum speed may lead to less variability in movement and lower output error. However, the injurious nature associated with pitching at high speeds must be accounted for by both pitchers and coaches. 

Limitations

The biggest limitation to this study proposal is the small sample size. Data analyzed likely will not reach significance without a larger population. The relationship between force and force variability is being measured only by ball velocity. Kinetic and kinematic differences across a spectrum of force may reveal significant findings about the torque and angular velocities variations at different output levels. Spatial error is measured using a target-based point system rather than an optical system. Thus, the horizontal and vertical error of the pitches will not be assessed. Freeston and Rooney (2014) found no difference in horizontal error in baseball pitchers across speed conditions compared to a significant difference in vertical error. The study population may limit the generalizability of findings, as elite high-school-aged males are developmentally different than young children and perhaps adults. 

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(n.d.). 9 Hole Pro Pitcher's Pocket Net for Baseball. Retrieved January 3, 2022, from https://www.anytimebaseballsupply.com/products/better-baseball-pitchers-pocket-pro-9-hole.

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