Related papers: The hardest-hit home run?
This paper considers the flight dynamics of the ball in the sport of pickleball. Various simplifications are introduced according to the features of the game. These simplifications and some approximations enable straightforward coding to…
In this article, we discuss some classical problems in combinatorics which can be solved by exploiting analogues between graph theory and the theory of manifolds. One well-known example is the McMullen conjecture, which was settled twenty…
In 1934 L. R\'edei published his famous theorem that the number of Hamiltonian paths in a tournament is odd. In fact it is a corollary of a stronger theorem in his paper. Stronger theorems were also obtained in the early 1970s by G.A. Dirac…
Consider the commonly known puzzle, given $k$ glass balls, find an optimal algorithm to determine the lowest floor of a building of $n$ floors from which a thrown glass ball will break. This puzzle was originally posed in its original form…
Runs Batted IN (RBI) records the number of runs a hitter directly drives in during their plate appearances and reflects a batter's ability to convert opportunities into scoring. Because producing runs determines game outcomes, RBI has long…
We address the value of a baserunner at first base waiting to see if a ball in play falls in for a hit, before running. When a ball is hit in the air, the baserunner will usually wait, to gather additional information as to whether a ball…
Magnitude is a measure of size defined for certain classes of metric spaces; it arose from ideas in category theory. In particular, magnitude is defined for compact subsets of Euclidean space and, in arXiv:1507.02502, Barcel\'o and Carbery…
We consider the periodic Manhattan lattice with alternating orientations going north-south and east-west. Place obstructions on vertices independently with probability $0<p<1$. A particle is moving on the edges with unit speed following the…
Major League Baseball (MLB) has a storied history of using statistics to better understand and discuss the game of baseball, with an entire discipline of statistics dedicated to the craft, known as sabermetrics. At their core, all…
Fitts' law has been widely employed as a research method for analyzing tasks within the domain of Human-Computer Interaction (HCI). However, its application to non-computer tasks has remained limited. This study aims to extend the…
Moore introduced a method for graduate mathematics instruction that consisted primarily of individual student work on challenging proofs (Jones, 1977). Cohen (1982) described an adaptation with less explicit competition suitable for…
Magic: the Gathering is a popular and famously complicated card game about magical combat. Recently, several authors including Chatterjee and Ibsen-Jensen (2016) and Churchill, Biderman, and Herrick (2019) have investigated the…
The Taxman game has proven to be hard to solve optimally, so efforts have been made to find heuristic strategies that do well in practice. We present results on the NP-hardness of a variant of the game via an equivalence to a particular…
In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance…
A classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. An analytic approach is mainly used for the…
Disavowed by one its fathers, ill defined, never empirically tested, the Wheeler-DeWitt equation has nevertheless had a powerful influence on fundamental physics. A well deserved one.
Even professional baseball players occasionally find it difficult to gracefully approach seemingly routine pop-ups. This paper describes a set of towering pop-ups with trajectories that exhibit cusps and loops near the apex. For a normal…
We study a general family of problems that form a common generalization of classic hitting (also referred to as covering or transversal) and packing problems. An instance of X-HitPack asks: Can removing k (deletable) vertices of a graph G…
Streaks of success have always fascinated people and a lot of research has been conducted to identify whether the "hot hand" effect is real. While sports have provided an appropriate platform for studying this phenomenon, the majority of…
Predicting the outcome of sports events is a hard task. We quantify this difficulty with a coefficient that measures the distance between the observed final results of sports leagues and idealized perfectly balanced competitions in terms of…