Related papers: Modeling Baseball Outcomes as Higher-Order Markov …
We propose a bottom-up approach to the study of possession and its outcomes for association football, based on probabilistic finite state automata with transition probabilities described by a Markov process. We show how even a very simple…
We develop a Markov model of curling matches, parametrised by the probability of winning an end and the probability distribution of scoring ends. In practical applications, these end-winning probabilities can be estimated econometrically,…
An algorithm based on backward induction is devised in order to compute the optimal sequence of games to be played in Parrondo games. The algorithm can be used to find the optimal sequence for any finite number of turns or in the steady…
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…
Consider QBF, the Quantified Boolean Formula problem, as a combinatorial game ruleset. The problem is rephrased as determining the winner of the game where two opposing players take turns assigning values to boolean variables. In this…
It is well known that any higher order Markov chain can be associated with a first order Markov chain. In this primarily expository article, we present the first fairly comprehensive analysis of the relationship between higher order and…
We present a theoretical analysis of the Elo rating system, a popular method for ranking skills of players in an online setting. In particular, we study Elo under the Bradley--Terry--Luce model and, using techniques from Markov chain…
In the four major North American professional sports (baseball, basketball, football, and hockey), the primary purpose of the regular season is to determine which teams most deserve to advance to the playoffs. Interestingly, while the…
Basketball players' performance measurement is of critical importance for a broad spectrum of decisions related to training and game strategy. Despite this recognized central role, the main part of the studies on this topic focus on…
The limiting probability distribution is one of the key characteristics of a Markov chain since it shows its long-term behavior. In this paper, for a higher order Markov chain, we establish some properties related to its exact limiting…
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…
We propose and study a new model for competitions, specifically sports multi-player leagues where the initial strengths of the teams are independent i.i.d. random variables that evolve during different days of the league according to…
It has been noted that in many professional sports leagues a good predictor of a team's won-loss percentage is Bill James' Pythagorean Formula RSobs^c / (RSobs^c + RAobs^c), where RSobs (resp. RAobs) is the observed average number of runs…
As the technology advances, an ample amount of data is collected in sports with the help of advanced sensors. Sports Analytics is the study of this data to provide a constructive advantage to the team and its players. The game of…
Major League Baseball (MLB) has a storied history of using statistics to better understand and discuss the game of baseball, with an entire discipline of statistics dedicated to the craft, known as sabermetrics. At their core, all…
A common format for sports contests involves pairwise matches between two teams, with the #1 player of team A matched against the #1 player of team B, the #2 player of team A against the #2 player of team B, and so on. This paper addresses…
Understanding the strategic behavior of miners in a blockchain is of great importance for its proper operation. A common model for mining games considers an infinite time horizon, with players optimizing asymptotic average objectives.…
Given a set of sequences comprised of time-ordered events, sequential pattern mining is useful to identify frequent subsequences from different sequences or within the same sequence. However, in sport, these techniques cannot determine the…
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…
In the sports of soccer, hockey and basketball the most commonly used statistics for player performance assessment are divided into two categories: offensive statistics and defensive statistics. However, qualitative assessments of…