Optimal trajectory for the basketball free throw
ABSTRACT Using a theoretical approach, we studied the basketball free throw as a function of angle, speed and spin at release. The ball was constrained to the sagittal plane bisecting the hoop and normal to the backboard, and was permitted to bounce and change spin on both backboard and hoop. Combinations of angle, speed and spin resulting in a successful shot were calculated analytically. Standard deviations for a shooter's angle and speed were used to predict the optimal trajectory for a specific position of release. An optimal trajectory was predicted which had an initial angle and speed of approximately 60 degrees and 7.3 m s(-1) respectively over the domain of spins (-2 to +2 m s(-1) surface speed; -16 to +16 rad s). The effect of air resistance and the sagittal plane constraint on the predicted optimal trajectory were discussed and quantified. The optimal trajectory depended on both the anthropometric characteristics and accuracy of the shooter, but generally a high backspin with an angle and speed combination which sent the ball closer to the far rim of the basket than the near rim was advantageous. We provide recommendations for shooters as a function of the height of ball release.
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- "Firstly, our article is the first to rigorously model what happens when a spinning elastic ball bounces on a series of surfaces that are arbitrarily-tilted at planes AE90 . Secondly, our study is the first to evaluate the effect of the variation in initial launch parameters in said situation, in the spirit of  . "
ABSTRACT: This work is motivated by a staple carnival game. A player throws a ping-pong ball onto a grid of cups with the goal of having the ball land in a cup. Though there are many variations to this game, there is a common underlying characteristic. As the ball bounces on the cup grid, its sequence of bouncing trajectories becomes nonlinear. It is this nonlinearity which makes it impossible for an observer to predict the outcome, and makes the game difficult. The nonlinearity comes from the interaction of the ball’s linear motion, angular motion, and the how it bounces off the cup edges. The insight that led to the development of this model is that the ball bouncing on a cup edge is equivalent to it bouncing on a tilted surface. Thus, to develop a predictive model for this game, we modeled a spinning partially elastic ball as it bounces over a series of arbitrarily-tilted surfaces. We embedded this algorithm in a Monte Carlo simulation model which simulates a player throwing the ball while varying initial launch parameters. Using this model, we were able to track possible trajectories and make probabilistic statements about various outcomes of the game. Furthermore, we used our empirical results to suggest different scenarios for the game, then applied the model to assess and quantify their impacts on difficulty. Visual inspection and brief analysis of an actual game support our model’s credibility.Applied Mathematics and Computation 02/2015; 253:61-71. DOI:10.1016/j.amc.2014.12.061 · 1.60 Impact Factor
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- "The ability to identify key elements that lead to successful shooting has been the focus of previous research. The kinematics of shooting has been investigated for jump shots (Huston and Grau, 2003; Miller and Bartlett, 1993; Miller and Bartlett, 1996), freethrow shooting (Hamilton and Reinschmidt, 1997; Satern and Keller-McNulty, 1992; Tan and Miller, 1981) and three-point shots (Erculj and Supej, 2009). Successful shooting is associated with a straight and high ball release, and forearm position and wrist flexion are critical for consistent straight projection of the ball with backspin (Penrose and Blanksby, 1976; Szymanski, 1967). "
ABSTRACT: Video-based training combined with flotation tank recovery may provide an additional stimulus for improving shooting in basketball. A pre-post controlled trial was conducted to assess the effectiveness of a 3 wk intervention combining video-based training and flotation tank recovery on three-point shooting performance in elite female basketball players. Players were assigned to an experimental (n=10) and control group (n=9). A 3 wk intervention consisted of 2 x 30 min float sessions a week which included 10 min of video-based training footage, followed by a 3 wk retention phase. A total of 100 three-point shots were taken from 5 designated positions on the court at each week to assess three-point shooting performance. There was no clear difference in the mean change in the number of successful three-point shots between the groups (-3%; ±18%, mean; ±90% confidence limits). Video-based training combined with flotation recovery had little effect on three-point shooting performance.International Journal of Performance Analysis in Sport 01/2013; 13(1):1-10. · 0.85 Impact Factor
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- "In this particular case, as concluded by Hamilton and Reinschmidt (1987) and Miller (2002) in their studies in basketball shooting variability, and by Darling and Cooke (1987) and Messier and Kalaska (1999) in their analysis of grasping and reaching movements, we have found an inverse relationship between performance variability, the strength of performance and accuracy in serves. In addition, this variable could provide information about the characteristics present in the task of achieving the player’s desired performance, for strengthening, creating or changing the attractors of performance (Nashner and McCollum, 1985). "
ABSTRACT: The main objective of this study was to analyze the motor variability in the performance of the tennis serve and its relationship to performance outcome. Seventeen male tennis players took part in the research, and they performed 20 serves. Linear and non-linear variability during the hand movement was measured by 3D Motion Tracking. Ball speed was recorded with a sports radar gun and the ball bounces were video recorded to calculate accuracy. The results showed a relationship between the amount of variability and its non-linear structure found in performance of movement and the outcome of the serve. The study also found that movement predictability correlates with performance. An increase in the amount of movement variability could affect the tennis serve performance in a negative way by reducing speed and accuracy of the ball.Journal of Human Kinetics 06/2012; 33:45-53. DOI:10.2478/v10078-012-0043-3 · 0.70 Impact Factor