Related papers: The hardest-hit home run?
American football is an increasingly popular sport, with a growing audience in many countries in the world. The most watched American football league in the world is the United States' National Football League (NFL), where every offensive…
Here, we present the quantum version of a very famous statistical decision problem, whose classical version is counter-intuitive to many. The Monty Hall game can be phrased as a two person game between Alice and Bob. In their pioneering…
Can an infinite-strength magnetic beacon always ``catch'' an iron ball, when the beacon is a point required to be remain nonstrictly outside a polygon, and the ball is a point always moving instantaneously and maximally toward the beacon…
Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by…
The halting problem is considered to be an essential part of the theoretical background to computing. That halting is not in general computable has supposedly been proved in many text books and taught on many computer science courses, in…
In this paper we introduce a new methodology to determine an optimal coefficient for a positive finite measure of batting average, strike rate, and bowling average of a player in order to get an optimal score of a team under dynamic…
The Monty Hall problem is notorious for its deceptive simplicity. Although today it is widely used as a provocative thought experiment to introduce Bayesian thinking to students of probability, in the not so distant past it was rejected by…
In most popular sports leagues, like the MLB, NBA, and NFL, none of the commonly used statistics take into account the strengths of the opponents a player faces. One of the main reasons for this is the conventional belief that a player's…
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…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
The game of Knockout is a classic playground game played with two basketballs. This paper uses a Markov process to analyze each player's probability of winning the game given their starting position in line and shooting percentages,…
The hitting set problem asks for a collection of sets over a universe $U$ to find a minimum subset of $U$ that intersects each of the given sets. It is NP-hard and equivalent to the problem set cover. We give a branch-and-bound algorithm to…
The score sequence of a tournament is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The problem of counting score sequences of a tournament with $n$ vertices is more than 100 years old (MacMahon 1920). In…
We present an extensive statistical analysis of the results of all sports competitions in five major sports leagues in England and the United States. We characterize the parity among teams by the variance in the winning fraction from…
Given a domain or, more generally, a Riemannian manifold with boundary, a billiard is the motion of a particle when the field of force is absent. Trajectories of such a motion are geodesics inside the domain; and the particle reflects from…
When facing a heavily-favored opponent, an underdog must be willing to assume greater-than-average risk. In statistical language, one would say that an underdog must be willing to adopt a strategy whose outcome has a larger-than-average…
Exploiting the symmetry of the regular icosahedron, Peter Doyle and Curt McMullen constructed a solution to the quintic equation. Their algorithm relied on the dynamics of a certain icosahedral equivariant map for which the icosahedron's…
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. The quadratic law for the resistance force is used. An analytic approach applies for the…
Our objective is to find the five best college sports coaches of past century for three different sports. We decided to look at men's basketball, football, and baseball. We wanted to use an approach that could definitively determine team…
The Pythagorean formula is one of the most popular ways to measure the true ability of a team. It is very easy to use, estimating a team's winning percentage from the runs they score and allow. This data is readily available on standings…