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The Pythagorean Expected Wins Percentage Model was developed by Bill James to estimate a baseball team expected wins percentage over the course of a season. As such, the model can be used to assess how lucky or unfortunate a team was over…
Generative adversarial networks (GANs) usually struggle in learning from highly diverse data, whose underlying manifold is complex. In this work, we revisit the mathematical foundations of GANs, and theoretically reveal that the native…
We ask if there are alternative contest models that minimize error or information loss from misspecification and outperform the Pythagorean model. This article aims to use simulated data to select the optimal expected win percentage model…
As a baseball game progresses, batters appear to perform better the more times they face a particular pitcher. The apparent drop-off in pitcher performance from one time through the order to the next, known as the Time Through the Order…
Baseball is a game of strategic decisions including bullpen usage, pinch-hitting and intentional walks. Managers must adjust their strategies based on the changing state of the game in order to give their team the best chance of winning. In…
We propose a player rating mechanism for Counter-Strike: Global Offensive (CS ), a popular e-sport, by analyzing players' Plus/Minus values. The Plus/Minus value represents the average point difference between a player's team and the…
Graph games provide the foundation for modeling and synthesis of reactive processes. Such games are played over graphs where the vertices are controlled by two adversarial players. We consider graph games where the objective of the first…
Baseball consists of two teams alternating between batting and fielding while competing to score runs through sequential pitching events. Recent advances in tracking technology have enabled all Major League Baseball (MLB) clubs to record…
We present a tractable framework for detecting changes in performance metrics and apply these methods to Major League Baseball (MLB) batting and pitching data from the 2023 and 2024 seasons. We propose a changepoint detection algorithm that…
Can one understand the statistics of wins and losses of baseball teams? Are their consecutive-game winning and losing streaks self-reinforcing or can they be described statistically? We apply the Bradley-Terry model, which incorporates the…
Players are arranged on a regular lattice and coded with a specific strategy for a pre-defined game. Each player sums their payoffs from playing the game with each of their neighbors, and then adopts the strategy of the most successful…
Estimating ballpark effects and team defense in baseball is challenging because batted-ball outcomes are influenced by multiple factors, including contact quality, ballpark environment, defensive performance, and random variation. In this…
We use multivariate change point analysis methods, to identify not only mean shifts but also changes in variance across a wide array of statistical time series. Our primary objective is to empirically discern distinct eras in the evolution…
In the game-theoretic model war of attrition, players are subject to an explicit cost proportional to the duration of contests. We construct a model where the time cost is not explicitly given, but instead depends implicitly on the…
Uncertainty analysis in the form of probabilistic forecasting can significantly improve decision making processes in the smart power grid for better integrating renewable energy sources such as wind. Whereas point forecasting provides a…
In Major League Baseball, strategy and planning are major factors in determining the outcome of a game. Previous studies have aided this by building machine learning models for predicting the winning team of any given game. We extend this…
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 this paper, we aim to develop a simple and scalable reinforcement learning algorithm that uses standard supervised learning methods as subroutines. Our goal is an algorithm that utilizes only simple and convergent maximum likelihood loss…
The comparative analysis of output from multiple models, and against observational data analysis archives, has become a key methodology in reducing uncertainty in climate projections, and in improving forecast skill of medium- and long-term…
Online competitive games have become a mainstream entertainment platform. To create a fair and exciting experience, these games use rating systems to match players with similar skills. While there has been an increasing amount of research…