Related papers: Football Group Draw Probabilities and Corrections
Given a parametric polynomial curve $\gamma:[a,b]\rightarrow \mathbb{R}^n$, how can we sample a random point $\mathfrak{x}\in \mathrm{im}(\gamma)$ in such a way that it is distributed uniformly with respect to the arc-length? Unfortunately,…
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Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a…
When facing a heavily-favored opponent, an underdog must be willing to assume greater-than-average risk. In statistical language, one would say that an underdog must be willing to adopt a strategy whose outcome has a larger-than-average…
How to distribute a set of points uniformly on a spherical surface is a very old problem that still lacks a definite answer. In this work, we introduce a physical measure of uniformity based on the distribution of distances between points,…
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In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to…
We propose a versatile joint regression framework for count responses. The method is implemented in the R add-on package GJRM and allows for modelling linear and non-linear dependence through the use of several copulae. Moreover, the…
We analyse the distributions of the number of goals scored by home teams, away teams, and the total scored in the match, in domestic football games from 169 countries between 1999 and 2001. The probability density functions (PDFs) of goals…
We focus on the problem of finding an optimal strategy for a team of two players that faces an opponent in an imperfect-information zero-sum extensive-form game. Team members are not allowed to communicate during play but can coordinate…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…
Population games model the evolution of strategic interactions among a large number of uniform agents. Due to the agents' uniformity and quantity, their aggregate strategic choices can be approximated by the solutions of a class of ordinary…
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In-game win probability models, which provide a sports team's likelihood of winning at each point in a game based on historical observations, are becoming increasingly popular. In baseball, basketball and American football, they have become…