Related papers: A Monte Carlo Approach to Joe DiMaggio and Streaks…
Motivated by the controversy in the chess community, where Hikaru Nakamura, a renowned grandmaster, has posted multiple impressive winning streaks over the years on the online platform chess.com, we derive the probabilities of various types…
The inverse statistics is the distribution of waiting times needed to achieve a predefined level of return obtained from (detrended) historic asset prices \cite{optihori,gainloss}. Such a distribution typically goes through a maximum at a…
In this paper, following the paper ``On the average hitting times of the squares of cycles,'' we provide an explicit formula for the average hitting times of a simple random walk on a directed graph with $N$ vertices, where the graph…
Two new sufficient conditions for generalized cycles (including Hamilton and dominating cycles as special cases) in an arbitrary k-connected graph (k=1,2,...) are derived, which prove the truth of Bondy's (1980) famous conjecture for some…
We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…
Quarterback performance can be difficult to rank, and much effort has been spent in creating new rating systems. However, the input statistics for such ratings are subject to randomness and factors outside the quarterback's control. To…
I published an interview of Leo Breiman in Statistical Science [Olshen (2001)], and also the solution to a problem concerning almost sure convergence of binary tree-structured estimators in regression [Olshen (2007)]. The former summarized…
Consider a gambling game in which we are allowed to repeatedly bet a portion of our bankroll at favorable odds. We investigate the question of how to minimize the expected number of rounds needed to increase our bankroll to a given target…
We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities…
Accurate stellar ages are essential for our understanding of the star formation history of the Milky Way, Galactic chemical evolution, and to constrain exoplanet formation models. Gyrochronology, a relationship between stellar rotation and…
A graph is Hamiltonian if it contains a cycle which passes through every vertex of the graph exactly once. A classical theorem of Dirac from 1952 asserts that every graph on $n$ vertices with minimum degree at least $n/2$ is Hamiltonian. We…
We investigate the properties of the James function, associated with Bill James's so-called "log5 method," which assigns a probability to the result of a game between two teams based on their respective winning percentages. We also…
We investigated the temporal distribution of goals in soccer using event-level data from 3,433 matches across 21 leagues and competitions. Contrary to the prevailing notion of randomness, we found that the probability of a goal being scored…
Linial and Morgenstern conjectured that, among all $n$-vertex tournaments with $d\binom{n}{3}$ cycles of length three, the number of cycles of length four is asymptotically minimized by a random blow-up of a transitive tournament with all…
Random graphs with prescribed degree sequences have been widely used as a model of complex networks. Comparing an observed network to an ensemble of such graphs allows one to detect deviations from randomness in network properties. Here we…
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…
Recent advancements in professional baseball have led to the introduction of the Automated Ball-Strike (ABS) system, or ``robot umpires,'' which utilize machine learning, computer vision, and precise tracking technologies to automate…
The use of the Monte Carlo technique in a reliable and inexpensive way without the need for a standard radioactive source in determining the detector efficiency is becoming widespread every passing day. It is important to model the detector…
Superstars often dominate key tasks because of their exceptional abilities, but this concentration of responsibility may unintentionally limit on-the-job learning opportunities for others. Using panel data from Major League Baseball (MLB),…
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…