Related papers: The optimal angle of Release in Shot Put
This paper investigates shape optimization problems in the context of heat transfer, with a focus on the stability and non-optimality of round domains under Robin boundary conditions. Using the flow approach and Steklov eigenvalue…
Football forecasting models traditionally rate teams on past match results, that is based on the number of goals scored. Goals, however, involve a high element of chance and thus past results often do not reflect the performances of the…
We investigate the probability of scoring a point when playing the basketball shooting game called "Horse". We show that under the Traditional Rules, it is optimal to choose very easy shots. We propose alternative rules called Pops Rules,…
A detailed set of experiments are described that capture over a 1000 different instances of the bounce of a golf ball. Video analysis is used to capture velocity and spin immediately prior to and subsequent to each bounce for a wide variety…
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…
A simple algebraic expression is presented to correct men's and women's 100 metre sprint times for ambient wind and altitude effects. The simplified formula is derived from a more complicated equation of motion used to model the athlete's…
The problem of the mechanical evolution of a shock between a cylindrically symmetric bat and a spherical ball is solved in the strict rigid approximation for arbitrary values of the initial conditions. The friction during the impact is…
A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. The projectile motion is described analytically with…
The ill-posed projectile problem of finding the source height from spattered droplets of viscous fluid is a longstanding obstacle to accident reconstruction and crime scene analysis. It is widely known how to infer the impact angle of…
This paper presents an analysis of optimal impact strategies to deflect potentially dangerous asteroids. To compute the increase in the minimum orbit intersection distance of the asteroid due to an impact with a spacecraft, simple…
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…
Sports analytics -- broadly defined as the pursuit of improvement in athletic performance through the analysis of data -- has expanded its footprint both in the professional sports industry and in academia over the past 30 years. In this…
Expected goals (xG) models estimate the probability that a shot results in a goal from its context (e.g., location, pressure), but they operate only on observed shots. We propose xG+, a possession-level framework that first estimates the…
This study applies complexity sciences to analyze the game of Padel. Data from 18 professional matches were collected, and the probability distributions of the total number of shots and the probability distribution of rallies' duration were…
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…
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 present the optimal estimation of an unknown squeezing transformation of the radiation field. The optimal estimation is unbiased and is obtained by properly considering the degeneracy of the squeezing operator. For coherent input states,…
Several performance metrics for quantifying the in-game performances of individual football players have been proposed in recent years. Although the majority of the on-the-ball actions during games constitutes of passes, many of the…
We compare conversion rates of association football (soccer) penalties during regulation or extra time with those during shootouts. Our data consists of roughly 50,000 penalties from the eleven~most recent seasons in European men's football…
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…