相关论文: The physics of an optimal basketball free throw
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…
We report an emergence of bifurcation in basketball, a single-particle system governed by Newtonian mechanics. When shooting the basketball, the obvious control parameters are the launch speed and the launch angle. We propose to use the…
We investigate the hot hand phenomenon using data on 110,513 free throws taken in the National Basketball Association (NBA). As free throws occur at unevenly spaced time points within a game, we consider a state-space model formulated in…
We determine the optimal angle of release in shot put. The simplest model - mostly used in textbooks - gives a value of $45^\circ$, while measurements of top athletes cluster around $37 - 38^\circ$. Including simply the height of the…
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…
We investigated the release angle that maximises the distance attained in a long soccer throw-in. One male soccer player performed maximum-effort throws using release angles of between 10 and 60 degrees, and the throws were analysed using…
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…
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…
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.
We analyze the impact of two equal billiard balls in three ideal situations: when the balls freely slide on the plane of the billiard, when they roll without sliding and when one of them freely slides and the other rolls. In all the cases…
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…
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…
With the NBA's adoption of in-game limb tracking in 2023, Sony's Hawk-Eye system now captures high-resolution, 3D poses of players and the ball 60 times per second. Linking these data to key events opens a new era in NBA analytics. Here, we…
This paper develops metrics from a social network perspective that are directly translatable to the outcome of a basketball game. We extend a state-of-the-art multi-resolution stochastic process approach to modeling basketball by modeling…
Consider the problem of modeling memory effects in discrete-state random walks using higher-order Markov chains. This paper explores cross validation and information criteria as proxies for a model's predictive accuracy. Our objective is to…
This paper aims to revisit and expand upon previous work on the "hot hand" phenomenon in basketball, specifically in the NBA. Using larger, modern data sets, we test streakiness of shooting patterns and the presence of hot hand behavior in…
Many have dedicated their time trying to determine the ideal conditions for a cylinder to have equal probabilities of falling with one of its faces facing upwards or on its side. However, to this day, there is no concrete analysis of what…
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…
Optimum projection angles for achieving maximum horizontal range in throwing and jumping events are considerably less than 45 degrees. This unexpected result arise because an athlete can generate a greater projection velocity at low…
The problem of determining the angle at which a point mass launched from ground level with a given speed is a standard exercise in mechanics. Similar, yet conceptually and calculationally more difficult problems have been suggested to…