Related papers: Bifurcation Adds Flavor to Basketball
The underlying physics of basketball shooting seems to be a straightforward example of the Newtonian mechanics that can easily be traced by numerical methods. However, a human basketball player does not make use of all the possible…
A physical model is developed, which suggests a pathway to determining the optimal release conditions for a basketball free throw. Theoretical framework is supported by Monte Carlo simulations and a series of free throws performed and…
Even though it might have taken some time, the three-point line ultimately changed the way the game is played as evidenced by the increase in the three-point shot attempts over the years. However, during the last few years we have…
This book chapter reviews some of the major principles associated with optimal strategy in basketball. In particular, we consider the principles of allocative efficiency (optimal allocation of shots between offensive options), dynamic…
Ball and hoop system is a well-known model for the education of linear control systems. In this paper, we have a look at this system from another perspective and show that it is also suitable for demonstration of more advanced control…
Accuracy of throwing in games and sports is governed by how errors at projectile release are propagated by flight dynamics. To address the question of what governs the choice of throwing strategy, we use a simple model of throwing with an…
In basketball, every time the offense produces a shot opportunity the player with the ball must decide whether the shot is worth taking. In this paper, I explore the question of when a team should shoot and when they should pass up the shot…
Shot charts in basketball analytics provide an indispensable tool for evaluating players' shooting performance by visually representing the distribution of field goal attempts across different court locations. However, conventional methods…
Modern basketball is all about creating efficient shots, that is, shots with high payoff. This is not necessarily equivalent to creating looks with the highest probability of success. In particular, the two most efficient shots in the NBA -…
Scoring in a basketball game is a process highly dynamic and non-linear type. The level of NBA teams improve each season. They incorporate to their rosters the best players in the world. These and other mechanisms, make the scoring in the…
In this paper, we propose a shot percentage distribution strategy among the players of a basketball team to maximize the score that can be achieved by them. The approach is based on the concepts of game theory related to network flow.
Basketball shooting coaches agree that smoother shooting motions are better, but there is less agreement about what "smooth" means quantitatively or what part of the shooting motion needs to be smooth. Using ball tracking data from the…
As 3-point shooting in the NBA continues to increase, the importance of perimeter defense has never been greater. Perimeter defenders are often evaluated by their ability to tightly contest shots, but how exactly does contesting a jump shot…
Within college basketball, the decision to foul or not with a 3-point lead (the "foul up 3" dilemma) significantly impacts teams. A single fouling decision can directly determine the outcome of a game or even an entire season. Within this…
Optimizing the performance of a basketball offense may be viewed as a network problem, wherein each play represents a "pathway" through which the ball and players may move from origin (the in-bounds pass) to goal (the basket). Effective…
Understanding player shooting profiles is an essential part of basketball analysis: knowing where certain opposing players like to shoot from can help coaches neutralize offensive gameplans from their opponents; understanding where their…
This paper develops a new guidance law for powered descent landing of a rocket-powered vehicle. The proposed law derives the acceleration command for a point mass model of the vehicle by expressing velocity as a dynamical system undergoing…
The coefficient of restitution $\epsilon$ characterizes the energy retained when a ball bounces, and can easily be measured in an ``at home'' experiment. For thin-walled gas-filled balls such as basketballs, we construct a simple two…
The purpose of this paper is to determine whether basketball teams who choose to employ an offensive strategy that involves predominantly shooting three point shots is stable and optimal. We employ a game-theoretical approach using…
We characterize a transition from normal to ballistic diffusion in a bouncing ball dynamics. The system is composed of a particle, or an ensemble of non-interacting particles, experiencing elastic collisions with a heavy and periodically…