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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…
The Risk Ratio (RR) is the ratio of the outcome among the exposed to risk of the outcome among the unexposed. This is a simple concept, which makes one wonder why it has not gained the same popularity as the odds ratio. Using logistic…
The Bayesian framework is ideally suited for induction problems. The probability of observing $x_t$ at time $t$, given past observations $x_1...x_{t-1}$ can be computed with Bayes' rule if the true distribution $\mu$ of the sequences…
In baseball, every play on the field is quantitatively evaluated and has an effect on individual and team strategies. The weighted on base average (wOBA) is well known as a measure of an batter's hitting contribution. However, this measure…
Existing guarantees in terms of rigorous upper bounds on the generalization error for the original random forest algorithm, one of the most frequently used machine learning methods, are unsatisfying. We discuss and evaluate various…
We have developed a sophisticated statistical model for predicting the hitting performance of Major League baseball players. The Bayesian paradigm provides a principled method for balancing past performance with crucial covariates, such 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…
The National Basketball Association (NBA) imposes a player salary cap. It is therefore useful to develop tools to measure the relative realized return of a player's salary given their on court performance. Very few such studies exist,…
We present an algorithm for learning the intrinsic value of a batted ball in baseball. This work addresses the fundamental problem of separating the value of a batted ball at contact from factors such as the defense, weather, and ballpark…
In 2024, Major League Baseball released new bat tracking data, reporting swing-by-swing bat speed and swing length measured at the point of contact. While exciting, the data present challenges for their interpretation. The timing of the…
Sports analytics -- broadly defined as the pursuit of improvement in athletic performance through the analysis of data -- has expanded its footprint both in the professional sports industry and in academia over the past 30 years. In this…
In most popular sports leagues, like the MLB, NBA, and NFL, none of the commonly used statistics take into account the strengths of the opponents a player faces. One of the main reasons for this is the conventional belief that a player's…
A popular quantitative approach to evaluating player performance in sports involves comparing an observed outcome to the expected outcome ignoring player involvement, which is estimated using statistical or machine learning methods. In…
Prophet inequalities are a central object of study in optimal stopping theory. A gambler is sent values in an online fashion, sampled from an instance of independent distributions, in an adversarial, random or selected order, depending on…
The field of quantitative analytics has transformed the world of sports over the last decade. To date, these analytic approaches are statistical at their core, characterizing what is and what was, while using this information to drive…
We study finite normal-form games in which payoffs are subject to random perturbations and players face uncertainty about how these shocks co-move across actions, an ambiguity that naturally arises when only realized (not counterfactual)…
Probabilistic forecasts in the form of probability distributions over future events have become popular in several fields of statistical science. The dissimilarity between a probability forecast and an outcome is measured by a loss function…
It is shown that at least 50% of the probability mass of a sum of independent Rademacher random variables is within one standard deviation from its mean. This lower bound is sharp, it is much better than for instance the bound that can be…
A long-standing open problem in algorithmic game theory asks whether or not there is a polynomial time algorithm to compute a Nash equilibrium in a random bimatrix game. We study random win-lose games, where the entries of the $n\times n$…
The classic model of computable randomness considers martingales that take real or rational values. Recent work by Bienvenu et al. (2012) and Teutsch (2014) shows that fundamental features of the classic model change when the martingales…