Optimal release conditions for the free throw in men's basketball

The purpose of this study was to determine the optimum release conditions for the free throw in men's basketball. The study used hundreds of thousands of three-dimensional simulations of basketball trajectories. Five release variables were studied: release height, release speed, launch angle, side angle, and back spin. The free throw shooter was assumed to shoot at 70% and to release the ball 2.134 m (7 ft) above the ground. We found that the shooter should place up to 3 Hz of back spin on the ball, should aim the ball towards the back of the ring, and should launch the ball at 52 degrees to the horizontal. We also found that it is desirable to release the ball as high above the ground as possible, as long as this does not adversely affect the player's launch consistency.     

Dynamics of the basketball shot with application to the free throw

Abstract

A completely general three-dimensional dynamic model is presented for the motion of basketball shots that may contact the rim, the backboard, the bridge between the rim and board, and possibly the board and the bridge simultaneously. Non-linear ordinary differential equations with six degrees of freedom describe the ball angular velocity and ball centre position. The model includes radial ball compliance and damping and contains five sub-models: purely gravitational flight, and ball – rim, ball – bridge, ball – board, and ball – bridge – board contact. Each contact sub-model has both slipping and non-slipping motions. Switching between the sub-models depends on the reaction force at, and velocity of, the contact point. Although the model can be used to study shots from any point on the court, we here use it to study the sets of free throw release angle, velocity, angular velocity, and lateral deviation angle that result in success (capture), as well as underhand free throws and those using an under-inflated ball. Free throw shots with larger backspin, lower inflation pressures, and underhand release conditions are shown to result in larger capture percentages.     

Coordination-variability and kinematics of misses versus swishes of basketball free throws

Abstract

Magnitudes and timings of kinematic variables have often been used to investigate technique. Where large inter-participant differences exist, as in basketball, analysis of intra-participant variability may provide an alternative indicator of good technique. The aim of the present study was to investigate the joint kinematics and coordination-variability between missed and successful (swishes) free throw attempts. Collegiate level basketball players performed 20 free throws, during which ball release parameters and player kinematics were recorded. For each participant, three misses and three swishes were randomly selected and analysed. Margins of error were calculated based on the optimal-minimum-speed principle. Differences in outcome were distinguished by ball release speeds statistically lower than the optimal speed (misses ?0.12 ± 0.10m · s^?1; swishes ?0.02 ± 0.07m · s^?1; P < 0.05). No differences in wrist linear velocity were detected, but as the elbow influences the wrist through velocity-dependent-torques, elbow–wrist angle–angle coordination-variability was quantified using vector-coding and found to increase in misses during the last 0.016s before ball release (P < 0.05). As the margin of error on release parameters is small, the coordination-variability is small, but the increased coordination-variability just before ball release for misses is proposed to arise from players perceiving the technique to be inappropriate and trying to correct the shot. The synergy or coupling relationship between the elbow and wrist angles to generate the appropriate ball speed is proposed as the mechanism determining success of free-throw shots in experienced players.     

Prediction of shot success for basketball free throws: Visual search strategy

Abstract

In ball games, players have to pay close attention to visual information in order to predict the movements of both the opponents and the ball. Previous studies have indicated that players primarily utilise cues concerning the ball and opponents' body motion. The information acquired must be effective for observing players to select the subsequent action. The present study evaluated the effects of changes in the video replay speed on the spatial visual search strategy and ability to predict free throw success. We compared eye movements made while observing a basketball free throw by novices and experienced basketball players. Correct response rates were close to chance (50%) at all video speeds for the novices. The correct response rate of experienced players was significantly above chance (and significantly above that of the novices) at the normal speed, but was not different from chance at both slow and fast speeds. Experienced players gazed more on the lower part of the player's body when viewing a normal speed video than the novices. The players likely detected critical visual information to predict shot success by properly moving their gaze according to the shooter's movements. This pattern did not change when the video speed was decreased, but changed when it was increased. These findings suggest that temporal information is important for predicting action outcomes and that such outcomes are sensitive to video speed.     

The influence of club-head kinematics on early ball flight characteristics in the golf drive

Despite many coaching and biomechanical texts describing how the kinematics of the club-head at impact lead to distance and accuracy of the ball flight, there is limited quantitative evidence supporting these assertions. The purpose of this study was to quantify the relationships between club-head kinematics and subsequent early ball flight characteristics during the golf drive. An opto-reflective system operating at 400 Hz was used to capture the swings of 21 male golfers using their own drivers. The 3D displacement data permitted the calculation of club-head kinematics at impact, as well as subsequent early ball flight characteristics. Using regression analyses, club-head kinematics at impact (velocity, orientation, path, and centeredness) were used to explain the variability in five dependent variables of early ball flight characteristics (resultant velocity, launch angle, side angle, back spin, and side spin). The results of the study indicated that club-head kinematics at impact explained a significant proportion of early ball flight characteristics (adjusted r ² = 0.71–0.82), even when generalized across individual clubs.     

Anticipatory strategies of team-handball goalkeepers

Abstract

This study seeks to discover whether handball goalkeepers employ a general anticipatory strategy when facing long distance throws and the effect of uncertainty on these strategies. Seven goalkeepers and four throwers took part. We used a force platform to analyse the goalkeeper's movements on the basis of reaction forces and two video cameras synchronised at 500 Hz to film the throw using 3D video techniques. The goalkeepers initiated their movement towards the side of the throw 193 ± 67 ms before the release of the ball and when the uncertainty was reduced the time increased to 349 ± 71 ms. The kinematics analysis of their centre of mass indicated that there was an anticipatory strategy of movement with certain modifications when there was greater uncertainty. All the average scores referring to velocity and lateral movement of the goalkeeper's centre of mass are significantly greater than those recorded for the experimental situation with bigger uncertainty. The methodology used has enabled us to tackle the study of anticipation from an analysis of the movement used by goalkeepers to save the ball.     

Kinematic parameters contributing to the production of spin in elite finger spin bowling

ABSTRACT

The aim of this study was to identify the key kinematic parameters which contribute to higher spin rates in elite finger spin bowling. Kinematic data were collected for twenty-three elite male finger spin bowlers with thirty kinematic parameters calculated for each delivery. Stepwise linear regression and Pearson product moment correlations were used to identify kinematic parameters linked to spin rate. Pelvis orientation at front foot contact (r = 0.674, p < 0.001) and ball release (r = 0.676, p < 0.001) were found to be the biggest predictors of spin rate, with both individually predicting 43% of the observed variance in spin rate. Other kinematic parameters correlated with spin rate included: shoulder orientation at ball release (r = 0.462, p = 0.027), and pelvis-shoulder separation angle at front foot contact (r = 0.521, p = 0.011). The bowlers with the highest spin rates adopted a mid-way pelvis orientation angle, a larger pelvis-shoulder separation angle and a shoulder orientation short of side-on at front foot contact. The segments then rotated sequentially, starting with the pelvis and finishing with the pronation of the forearm. This knowledge can be translated to coaches to provide a better understanding of finger spin bowling technique.     

Ritual and free‐throw shooting in basketball

The purpose of this study was to determine the nature and effect of certain highly patterned behaviours utilized prior to free‐throw shooting in basketball. Ten female basketball players comprising the varsity squad of Texas Christian University, Fort Worth, Texas, USA served as subjects for this study. Subjects were filmed with a high‐speed camera and monitored for heart rate during the performance of 10 free throws in each of two conditions: ritual and non‐ritual. For the ritual condition, subjects were given unlimited time and freedom of movement prior to each free‐throw attempt. For the non‐ritual condition, subjects were not restricted by time, but were instructed to shoot the ball without utilizing any movements other than those required to project the ball to the goal. Dependent measures were characteristics of behaviours, physiological changes measured by heart rates, mechanical data (speed, height and angle of release), and number of successful attempts. Condition x trials analyses of variance and low standard deviation concerning characteristics of behaviours indicated that the idiosyncratic behaviours prior to free‐throw shooting were rituals of the auto‐communicative type. Results indicated no significant difference between conditions for free‐throw success. However, partial correlation between dependent measures and successful free‐throw attempts indicated that duration of behaviours was most crucial to free‐throw shooting success.     

Dynamics of the basketball shot with application to the free throw

A completely general three-dimensional dynamic model is presented for the motion of basketball shots that may contact the rim, the backboard, the bridge between the rim and board, and possibly the board and the bridge simultaneously. Non-linear ordinary differential equations with six degrees of freedom describe the ball angular velocity and ball centre position. The model includes radial ball compliance and damping and contains five sub-models: purely gravitational flight, and ball-rim, ball-bridge, ball-board, and ball-bridge-board contact. Each contact sub-model has both slipping and non-slipping motions. Switching between the sub-models depends on the reaction force at, and velocity of, the contact point. Although the model can be used to study shots from any point on the court, we here use it to study the sets of free throw release angle, velocity, angular velocity, and lateral deviation angle that result in success (capture), as well as underhand free throws and those using an under-inflated ball. Free throw shots with larger backspin, lower inflation pressures, and underhand release conditions are shown to result in larger capture percentages.     

Gender comparison in consistency in the basketball free throw by an event-driven approach

This paper compares the free-throw performance of men and women in the National Collegiate Athletic Association (NCAA), taking into account differences in ball size, ball stiffness, and release height. Although some claim that men are more athletic, based on the assumption that athleticism correlates with physical traits, the average free-throw percentages in NCAA Division 1 basketball have been close for decades and across gender. The larger men’s basketball could create a disadvantage for men. On the other hand, the stiffer women’s basketball could create a disadvantage for women. In addition, women typically launch the ball from a lower height above the floor than men do. Therefore, the question of which gender is more consistent was unanswered. To answer this question, we turned to simulations of basketball trajectories. We patched together closed-form trajectory events that terminate at the front rim, back rim, backboard, and a fictitious plane below the ring. This produced what we call speed lines. Using the speed lines and NCAA average free-throw percentages, the consistencies of men- and women-free throws were determined. Examination of the speed lines reveals that they exhibit fractal-like behavior. We analyzed sensitivities with respect to ball size, ball bounce, and release height. We found that the most influential factor in determining free-throw success is the average release height of a gender. Under the stipulated assumptions, this paper found that women are about 3% more consistent than men are.     

The effect of dimple error on the horizontal launch angle and side spin of the golf ball during putting

This study aimed to examine the effect of the impact point on the golf ball on the horizontal launch angle and side spin during putting with a mechanical putting arm and human participants. Putts of 3.2 m were completed with a mechanical putting arm (four putter-ball combinations, total of 160 trials) and human participants (two putter-ball combinations, total of 337 trials). The centre of the dimple pattern (centroid) was located and the following variables were measured: distance and angle of the impact point from the centroid and surface area of the impact zone. Multiple regression analysis was conducted to identify whether impact variables had significant associations with ball roll variables, horizontal launch angle and side spin. Significant associations were identified between impact variables and horizontal launch angle with the mechanical putting arm but this was not replicated with human participants. The variability caused by “dimple error” was minimal with the mechanical putting arm and not evident with human participants. Differences between the mechanical putting arm and human participants may be due to the way impulse is imparted on the ball. Therefore it is concluded that variability of impact point on the golf ball has a minimal effect on putting performance.     

Investigation of toppling ball flight in American football with a mechanical field-goal kicker

A mechanical field-goal kicking machine was used to investigate toppling ball flight in American football place-kicking, eliminating a number of uncontrollable impact variables present with a human kicker. Ball flight trajectories were recorded using a triangulation-based projectile tracking system to account for the football’s 3-dimensional position during flight as well as initial launch conditions. The football flights were described using kinematic equations relating to projectile motion including stagnant air drag and were compared to measured trajectories as well as projectile motion equations that exclude stagnant air drag. Measured football flight range deviations from the non-drag equations of projectile motion corresponded to deficits between 9 and 31%, which is described by a football toppling compound drag coefficient of 0.007 ± 0.003 kg/m. Independent variables including impact location and impact angle orientation resulted in 15 impact conditions. We found that an impact location of 5.5 cm from the bottom of the ball maximized trajectory height and distance. At the 5.5-cm impact location, alterations in impact angle produced minimal change in football trajectory, including launch angle (range = 1.96 deg), launch speed (range = 1.06 m/s), and range (range = 0.94 m).     

Stress and performance: An application of Gray's three‐factor arousal theory to basketball free‐throw shooting

The suitability of Gray's (1975) three‐factor arousal theory as a model of human performance under stress was investigated in a study of basketball free‐throw shooting. Free‐throw attempts, made by members of an NCAA Division I men's varsity team, were videotaped during one full season. On the basis of Gray's theory, we predicted that increased stress (assumed to be present in games as opposed to practices) would be associated with longer pre‐shot preparations and a greater incidence of overthrow shots. The prediction was confirmed by the results. Moreover, we found that free‐throws were more frequently overthrown when attempted during crucial rather than non‐crucial game situations. Further tests of the utility of Gray's theory are suggested.     

A review on the basketball jump shot

The ability to shoot an effective jump shot in the sport of basketball is critical to a player's success. In an attempt to better understand the aspects related to expert performance, researchers have investigated successful free throws and jump shots of various basketball players and identified movement variables that contribute to their success. The purpose of this study was to complete a systematic review of the scientific literature on the basketball free throw and jump shot for the purpose of revealing the critical components of shooting that coaches, teachers, and players should focus on when teaching, learning, practising, and performing a jump shot. The results of this review are presented in three sections: (a) variables that affect ball trajectory, (b) phases of the jump shot, and (c) additional variables that influence shooting.     

Multi-segment trunk models used to investigate the crunch factor in golf and their relationship with selected swing and launch parameters

The use of multi-segment trunk models to investigate the crunch factor in golf may be warranted. The first aim of the study was to investigate the relationship between the trunk and lower trunk for crunch factor-related variables (trunk lateral bending and trunk axial rotation velocity). The second aim was to determine the level of association between crunch factor-related variables with swing (clubhead velocity) and launch (launch angle). Thirty-five high-level amateur male golfers (Mean ± SD: age = 23.8 ± 2.1 years, registered golfing handicap = 5 ± 1.9) without low back pain had kinematic data collected from their golf swing using a 10-camera motion analysis system operating at 500 Hz. Clubhead velocity and launch angle were collected using a validated real-time launch monitor. A positive relationship was found between the trunk and lower trunk for axial rotation velocity (r(35) = .47, P < .01). Cross-correlation analysis revealed a strong coupling relationship for the crunch factor (R² = 0.98) between the trunk and lower trunk. Using generalised linear model analysis, it was evident that faster clubhead velocities and lower launch angles of the golf ball were related to reduced lateral bending of the lower trunk.     

Ball launch conditions for skilled golfers using drivers of different lengths in an indoor testing facility

Abstract

The displacement of the golf ball struck by a driving club is affected by several player characteristics and equipment parameters and their interrelationships. Some modelling and simulation studies have shown a relationship between shaft length and clubhead speed, supported by a few experimental studies. The aim of the present study was to examine the relationship between driver length and ball launch conditions in an indoor test facility using a ball launch monitor. Nine males considered to be skilled golfers participated in the study. Four driving clubs of total length 117, 119, 124, and 132 cm were assembled from commercially available components and were used to strike golf shots while initial ball velocity, backspin rate, and launch angles were measured. Statistical analysis identified a significant difference in initial launch speed due to club length, a significant difference between participants, but no difference between the trials for a given golfer. A positive trend was noted between backspin and launch angle for all four clubs, and significant inverse associations between initial launch speed and backspin rate and launch angle. However, the combined launch conditions associated with increasing length were not considered optimal, with uncontrolled swingweight and moment of inertia effects considered to be limiting factors.     

Influence of shaft length on golf driving performance

The aim of this study was to determine how shaft length affects golf driving performance. A range of drivers with lengths between 1.168 m and 1.270 m, representing lengths close to the 1.219 m limit imposed by R&;A Rules Limited (2008 R&;A Rules Limited. 2008. Rules of golf, St. Andrews: R&;A Rules Limited, The Royal and Ancient Golf Club of St. Andrews.  [Google Scholar]), were assembled and evaluated. Clubhead and ball launch conditions and drive distance and accuracy were determined for seven category 1 golfers (handicaps 0.21 ± 2.41) who performed shots on a purpose-built practice hole. As shaft length increased from 1.168 m to 1.270 m, initial ball velocity increased (+1.8 m/s, P < 0.01). Ball carry (+4.3 m, P = 0.152) also increased, although not significantly so. Furthermore, as shaft length increased, for all club comparisons there was no decrease in accuracy. Ball launch conditions of spin components and launch angle remained unaffected by shaft length. Launch angle increased (0.8°, F = 1.074, P = 0.362) as driver shaft length increased. Our results show that clubhead and ball velocity together with ball carry tended to increase with no loss of accuracy.     

An upper limb kinematic model for the examination of cricket bowling: A case study of Mutiah Muralitharan

We show how biomechanics can be used to accurately assess spin-bowling techniques (offspin, legspin and topspin) in cricket, under controlled conditions, when the player is suspected of throwing. A 50 Hz six-camera Vicon Motion Analysis system was used to record the movements of markers strategically placed on the upper limb during each of the above bowling actions. A kinematic model of the upper limb, created using Vicon BodyBuilder® software, enabled the movements of the upper arm and forearm to be described during each delivery. Selected physical characteristics of the upper limb were also measured. The present 'no ball' law in cricket with reference to throwing states that 'the arm should not be straightened in the part of the delivery that immediately precedes ball release'. The bowler, Mutiah Muralitharan, was shown to maintain a relatively constant elbow angle in the 0.06 s before ball release. Furthermore, this angle changed little from the time that the upper arm was angled vertically downward until ball release during the three spin-bowling actions.     

Does maximising ball speed in cricket fast bowling necessitate higher ground reaction forces?

This study aimed to investigate whether high peak ground reaction forces and high average loading rates are necessary to bowl fast. Kinematic and kinetic bowling data were collected for 20 elite male fast bowlers. A moderate non-significant correlation was found between ball speed and peak vertical ground reaction force with faster bowlers tending to have lower peak vertical ground reaction force (r = ?0.364, P = 0.114). Faster ball speeds were correlated with both lower average vertical and lower average horizontal loading rates (r = ?0.452, P = 0.046 and r = ?0.484, P = 0.031, respectively). A larger horizontal (braking) impulse was associated with a faster ball speed (r = 0.574, P = 0.008) and a larger plant angle of the front leg (measured from the vertical) at front foot contact was associated with a larger horizontal impulse (r = 0.706, P = 0.001). These findings suggest that there does not necessarily need to be a trade-off between maximum ball release speed and the forces exerted on fast bowlers (peak ground reaction forces and average loading rates). Furthermore, it appears that one of the key determinants of ball speed is the horizontal impulse generated at the ground over the period from front foot contact until ball release.     

Kinematic analyses of seated throwing activities with and without an assistive pole

In Paralympic seated throwing events, the athlete can throw with and without an assistive pole. This study aimed to identify and compare performance-related kinematic variables associated with both seated throwing techniques. Twenty-nine non-disabled males (21.9 ± 2.6 years) performed 12 maximal throws using a 1-kg ball in two conditions (no-pole and pole). Automatic 3D-kinematic tracking (150 Hz) and temporal data were acquired. There was no significant difference between ball speeds at the point of release between conditions (no-pole = 12.8 ± 1.6 m/s vs. pole = 12.9 ± 1.5 m/s). There were four kinematic variables that were strongly correlated with ball speed when throwing with or without an assistive pole. These variables were elbow flexion at the start phase (pole r = .39 and no-pole r = .41), maximum shoulder external rotation angular velocity during the arm cocking phase (pole r = .42), maximum shoulder internal rotation angular velocity during the arm acceleration phase (pole r = .47), and should internal rotation angular velocity at the instant of ball release (pole r = .40). The pole clearly influenced the throwing technique with all four strongly correlated variables identified in this condition, compared to only one during the no-pole condition. When using the pole, participants produced significantly higher shoulder internal rotation angular velocities during the arm acceleration phase (pole = 367 ± 183°/s vs. no-pole = 275 ± 178°/s, p < .05) and at the instant of ball release (pole = 355 ± 115°/s vs. no-pole = 264 ± 120°/s, p < .05), compared to throwing without the pole. These findings have implications for the development of evidence-based classification systems in Paralympic seated throwing, and facilitate research that investigates the impact of impairment on seated throwing performance.