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We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we…

Objectives: Negative splitting (i.e., finishing the race faster) is a tactic commonly employed by elite marathon athletes, even though research supporting the strategy is scarce. The presence of pacers allows the main runner to run behind a…

We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…

We analyze cross-correlation between runs scored over a time interval in cricket matches of different teams using methods of random matrix theory (RMT). We obtain an ensemble of cross-correlation matrices $C$ from runs scored by eight…

This book chapter reviews some of the major principles associated with optimal strategy in basketball. In particular, we consider the principles of allocative efficiency (optimal allocation of shots between offensive options), dynamic…

The Win Ratio has gained significant traction in cardiovascular trials as a novel method for analyzing composite endpoints (Pocock and others, 2012). Compared with conventional approaches based on time to the first event, the Win Ratio…

We present an experimental investigation examining how the complexity of pitching kinematics influences dynamic stall characteristics, including the stall delay and aerodynamic force response. The study examines whether the pitch rate…

The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order…

This paper investigates a robust incentive Stackelberg stochastic differential game problem for a linear-quadratic mean field system, where the model uncertainty appears in the drift term of the leader's state equation. Moreover, both the…

We develop the SEAM (synthetic estimated average matchup) method for describing batter versus pitcher matchups in baseball. We first estimate the distribution of balls put into play by a batter facing a pitcher, called the empirical spray…

In this paper, we present a novel sequential team selection model in soccer. Specifically, we model the stochastic process of player injury and unavailability using player-specific information learned from real-world soccer data.…

Performance measures such as stride length in athletics and the pace of runners can be estimated using different tricks such as measuring the number of steps divided by the running length or helping with markers printed on the track.…

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…

We present a framework for designing scores to summarize performance metrics. Our design has two multi-criteria objectives: (1) improving on scores should improve all performance metrics, and (2) achieving pareto-optimal scores should…

In this paper we present a new theoretical model to find out an optimal weight associated with a soccer player under the presence of a stochastic goal dynamics by using Feynman path integral method, where the action of a player is on…

Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…

In soccer, contextual player performance metrics are invaluable to coaches. For example, the ability to perform under pressure during matches distinguishes the elite from the average. Appropriate pressure metric enables teams to assess…

For professional basketball, finding valuable and suitable players is the key to building a winning team. To deal with such challenges, basketball managers, scouts and coaches are increasingly turning to analytics. Objective evaluation of…

This paper aims to improve existing results about using averaging method for analysis of dynamic systems on time scales. We obtain a more accurate estimate for proximity between solutions of original and averaged systems regarding…

The analysis of income and wealth inequality is often constrained by the lack of reliable data. In this work, we introduce a proxy-based approach in which sports performance data are used to mimic economic distributions. In particular, the…