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How can we monitor, in real time, whether one uncertain prospect has any upside over another? To answer this question, we develop a novel family of sequential, anytime-valid tests for stochastic dominance (SD; also known as stochastic…
Suppose one desires to randomly sample a pair of objects such as socks, hoping to get a matching pair. Even in the simplest situation for sampling, which is sampling with replacement, the innocent phrase "the distribution of the color of a…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We continue our studies of burn-off chip-firing games from [Discrete Math. Theor. Comput. Sci. 15 (2013), no. 1, 121-132; MR3040546] and [Australas. J. Combin. 68 (2017), no. 3, 330-345; MR3656659]. The latter article introduced randomness…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
Studying event time series is a powerful approach for analyzing the dynamics of complex dynamical systems in many fields of science. In this paper, we describe the method of event coincidence analysis to provide a framework for quantifying…
Standard measures of batting performance such as a batting average and an on-base percentage can be decomposed into component rates such as strikeout rates and home run rates. The likelihood of hitting data for a group of players can be…
In sports betting it is easier to predict the winner of a game match than the team that covers the bet. Since, a winner team might not cover a bet. This study focuses on the relation of the variable win to the betting variable cover the…
This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games,…
Scoring rules aggregate individual rankings by assigning some points to each position in each ranking such that the total sum of points provides the overall ranking of the alternatives. They are widely used in sports competitions consisting…
The debate surrounding the hot hand in the NBA has been ongoing for many years. However, many of the previous works on this theme has focused on only the very next sequential shot attempt, often on very select players. This work looks in…
Sports data has become widely available in the recent past. With the improvement of machine learning techniques, there have been attempts to use sports data to analyze not only the outcome of individual games but also to improve insights…
We investigate uniformity properties of strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not \mu-calculus definable. Typically, we can state that a strategy is…
In this article, we study the behavior of a broad family of real sequences derived from randomized one-pile subtraction games. For any subtraction set $S$, we allow any valid number of chips $s\in S$ to be removed at equal probability at…
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…
A tournament on 8 or more vertices may be intrinsically linked as a directed graph. We begin the classification of intrinsically linked tournaments by examining their score sequences. While many distinct tournaments may have the same score…
In this paper, we present a novel sequential team selection model in soccer. Specifically, we model the stochastic process of player injury and unavailability using player-specific information learned from real-world soccer data.…
Technological advances have paved the way for collecting high-resolution network data in basketball, football, and other team-based sports. Such data consist of interactions among players of competing teams indexed by space and time.…
We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform…
Nowadays, it becomes a common practice to capture some data of sports games with devices such as GPS sensors and cameras and then use the data to perform various analyses on sports games, including tactics discovery, similar game retrieval,…