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Large language models (LLMs) are increasingly used as automatic evaluators of generative AI outputs, a paradigm often referred to as "LLM-as-a-judge." In practice, LLM judges are imperfect predictions for the underlying truth and can…
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…
Consider the problem of modeling memory effects in discrete-state random walks using higher-order Markov chains. This paper explores cross validation and information criteria as proxies for a model's predictive accuracy. Our objective is to…
Do NFL teams make rational decisions? What factors potentially affect the probability of wining a game in NFL? How can a team come back from a demoralizing interception? In this study we begin by examining the hypothesis of rational…
For some time, point-differential has been thought to be a better predictor for future NBA success than pure win-loss record. Most ranking and team performance predictions rely largely on point-differential, often with some normalizations…
This paper develops metrics from a social network perspective that are directly translatable to the outcome of a basketball game. We extend a state-of-the-art multi-resolution stochastic process approach to modeling basketball by modeling…
Batting average is one of the principle performance measures for an individual baseball player. It is natural to statistically model this as a binomial-variable proportion, with a given (observed) number of qualifying attempts (called…
NBA team managers and owners try to acquire high-performing players. An important consideration in these decisions is how well the new players will perform in combination with their teammates. Our objective is to identify elite five-person…
We develop a machine learning approach to represent and analyze the underlying spatial structure that governs shot selection among professional basketball players in the NBA. Typically, NBA players are discussed and compared in an…
Scoring in a basketball game is a process highly dynamic and non-linear type. The level of NBA teams improve each season. They incorporate to their rosters the best players in the world. These and other mechanisms, make the scoring in the…
We study estimation and inference using data collected by reinforcement learning (RL) algorithms. These algorithms adaptively experiment by interacting with individual units over multiple stages, updating their strategies based on past…
As Basu (1977) writes, "Eliminating nuisance parameters from a model is universally recognized as a major problem of statistics," but after more than 50 years since Basu wrote these words, the two mainstream schools of thought in statistics…
The main objective of this paper is to investigate the extent to which the margin of victory can be predicted solely by the rankings of the opposing teams in NCAA Division I men's basketball games. Several past studies have modeled this…
As a dedicated follower of sports statistics and with the MLB season beginning in late March, I set out to predict how many wins each team would accumulate by the end of the 162 game season. The goal was to build a simulation framework…
The prevailing belief propagated by NBA league observers is that the workload of the NBA season dramatically influences a player's performance$^{1,2,3,4,5}$. We offer an analysis of cross game player fatigue that calls into question the…
Risk assessment tools are widely used around the country to inform decision making within the criminal justice system. Recently, considerable attention has been devoted to the question of whether such tools may suffer from racial bias. In…
Passing during power plays in hockey is a crucial component to move one's team closer to scoring a goal. With the use of women's ice hockey event and tracking data from the elimination round games during the 2022 Winter Olympics, we…
Experience is an important asset in almost any professional activity. In basketball, there is believed to be a positive association between coaching experience and effective use of team timeouts. Here, we analyze both the extent to which a…
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…
Pretrial risk assessment tools are used on over one million U.S. defendants each year, yet their use for predicting rare violent re-offense faces a basic statistical barrier. We derive a universal precision bound -- the Likelihood Ratio…