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We introduce a three-step framework to determine at which pitches Major League batters should swing. Unlike traditional plate discipline metrics, which implicitly assume that all batters should always swing at (resp. take) pitches inside…
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…
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…
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 consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…
For decades, National Football League (NFL) coaches' observed fourth down decisions have been largely inconsistent with prescriptions based on statistical models. In this paper, we develop a framework to explain this discrepancy using an…
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…
In this paper, we consider zero-sum repeated games in which the maximizer is restricted to strategies requiring no more than a limited amount of randomness. Particularly, we analyze the maxmin payoff of the maximizer in two models: the…
Numerous statistics have been proposed for the measure of offensive ability in major league baseball. While some of these measures may offer moderate predictive power in certain situations, it is unclear which simple offensive metrics are…
This paper investigates the application of game-theoretic principles combined with advanced Kalman filtering techniques to enhance maritime target tracking systems. Specifically, the paper presents a two-player, imperfect information,…
We address the value of a baserunner at first base waiting to see if a ball in play falls in for a hit, before running. When a ball is hit in the air, the baserunner will usually wait, to gather additional information as to whether a ball…
We consider two-player iterated survival games in which players may switch from a more cooperative behavior to a less cooperative one at some step of the game. Payoffs are survival probabilities and lone individuals have to finish the game…
Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative…
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…
This manuscript uses machine learning techniques to exploit baseball pitchers' decision making, so-called "Baseball IQ," by modeling the at-bat information, pitch selection and counts, as a Markov Decision Process (MDP). Each state of the…
Game theory serves as a powerful tool for distributed optimization in multi-agent systems in different applications. In this paper we consider multi-agent systems that can be modeled by means of potential games whose potential function…
From 2020 to 2023, Major League Baseball changed rules affecting team composition, player positioning, and game time. Understanding the effects of these rules is crucial for leagues, teams, players, and other relevant parties to assess…
We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose…
The success of a football team depends on various individual skills and performances of the selected players as well as how cohesively they perform. We propose a two-stage process for selecting optimal playing eleven of a football team from…
Originating in evolutionary game theory, the class of "zero-determinant" strategies enables a player to unilaterally enforce linear payoff relationships in simple repeated games. An upshot of this kind of payoff constraint is that it can…