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Over the last few decades, the player recruitment process in professional football has evolved into a multi-billion industry and has thus become of vital importance. To gain insights into the general level of their candidate reinforcements,…
We consider a computing system where a master processor assigns tasks for execution to worker processors through the Internet. We model the workers decision of whether to comply (compute the task) or not (return a bogus result to save the…
The paper illustrates an application of the Resampling approach [2] for the estimation of the aircraft circulation plan reliability. Resampling is an intensive computer statistical method, which can be used effectively in the case of small…
Can one understand the statistics of wins and losses of baseball teams? Are their consecutive-game winning and losing streaks self-reinforcing or can they be described statistically? We apply the Bradley-Terry model, which incorporates the…
In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the online rating algorithms which estimate the skills after each new…
This work introduces a unified framework for analyzing games in greater depth. In the existing literature, players' strategies are typically assigned scalar values, and equilibrium concepts are used to identify compatible choices. However,…
Analysis of invasive sports such as soccer is challenging because the game situation changes continuously in time and space, and multiple agents individually recognize the game situation and make decisions. Previous studies using deep…
We give recurrences, generating functions and explicit exact expressions for the enumeration of fundamental quantities involving runs in binary strings. We first focus on enumerations concerning runs of ones, and we then analyse the same…
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…
Scientifically evaluating soccer players represents a challenging Machine Learning problem. Unfortunately, most existing answers have very opaque algorithm training procedures; relevant data are scarcely accessible and almost impossible to…
Humans are routinely asked to evaluate the performance of other individuals, separating success from failure and affecting outcomes from science to education and sports. Yet, in many contexts, the metrics driving the human evaluation…
Several performance metrics for quantifying the in-game performances of individual football players have been proposed in recent years. Although the majority of the on-the-ball actions during games constitutes of passes, many of the…
A same-score streak in sports is a sequence of games where the scores are equivalent in all games. The motivating problem arose from college basketball, however due to the difficulty in collecting data, streaks in Major League Baseball…
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
Betting games provide a natural setting to capture how information yields strategic advantage. The Kelly criterion for betting, long a cornerstone of portfolio theory and information theory, admits an interpretation in the limit of…
Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a…
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…
Evaluating and comparing the academic performance of a journal, a researcher or a single paper has long remained a critical, necessary but also controversial issue. Most of existing metrics invalidate comparison across different fields of…
Citation count is a quantifiable measure to indicate the number of times an article is cited by other articles. It is believed that if an article is cited often then it must be an important or influential article; however, there is no…
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…