Related papers: Modeling Baseball Outcomes as Higher-Order Markov …
The baseball game is often seen as many contests that are performed between individuals. The duel between the pitcher and the batter, for example, is considered the engine that drives the sport. The pitchers use a variety of strategies to…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
Card shuffling models have provided simple motivating examples for the mathematical theory of mixing times for Markov chains. As a complement, we introduce a more intricate realistic model of a certain observable real-world scheme for…
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…
In this paper, a new continuous scoring system for soccer is proposed, based on the proportion of time that a team is winning, losing or tied. Several simulations are made applying this technique to complete seasons of different leagues. As…
In this paper, we examine team ball sports to investigate how the likelihood of weaker teams winning against stronger ones, referred to as underdog achievement, is influenced by inherent randomness factors that affect match outcomes in such…
We use a simple machine learning model, logistically-weighted regularized linear least squares regression, in order to predict baseball, basketball, football, and hockey games. We do so using only the thirty-year record of which visiting…
In limited overs cricket, the team batting first posts a target score for the team batting second to achieve in order to win the match. The team batting second is constrained by decreasing resources in terms of number of balls left and…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…
Gerber and Li in \cite{GeLi} formulated, using a Markov chain embedding, a system of equations that describes relations between generating functions of waiting time distributions for occurrences of patterns in a sequence of independent…
Multiplayer Online Battle Arena (MOBA) is one of the most successful game genres. MOBA games such as League of Legends have competitive environments where players race for their rank. In most MOBA games, a player's rank is determined by the…
In J. Schwenk.(2018) ['What is the Correct Way to Seed a Knockout Tournament?' Retrieved from The American Mathematical Monthly], Schwenk identified a surprising weakness in the standard method of seeding a single elimination (or knockout)…
This paper proposes a multiple-membership generalized linear mixed model for ranking college football teams using only their win/loss records. The model results in an intractable, high-dimensional integral due to the random effects…
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…
Prediction and modelling of competitive sports outcomes has received much recent attention, especially from the Bayesian statistics and machine learning communities. In the real world setting of outcome prediction, the seminal \'{E}l\H{o}…
In the literature of Round-Robin scheduling scheme, each job is processed, one after the another after giving a fix quantum. In case of First-come first-served, each process is executed, if the previously arrived processed is completed.…
The dynamics in games involving multiple players, who adaptively learn from their past experience, is not yet well understood. We analyzed a class of stochastic games with Markov strategies in which players choose their actions…
The use of statistical modeling in baseball has received substantial attention recently in both the media and academic community. We focus on a relatively under-explored topic: the use of statistical models for the analysis of fielding…
Statistical analysis is a major aspect of baseball, from player averages to historical benchmarks and records. Much of baseball fanfare is based around players exceeding the norm, some in a single game and others over a long career. Career…
We study a stochastic process that mimics single-game elimination tournaments. In our model, the outcome of each match is stochastic: the weaker player wins with upset probability q<=1/2, and the stronger player wins with probability 1-q.…