26 research outputs found
On Elo based prediction models for the FIFA Worldcup 2018
We propose an approach for the analysis and prediction of a football
championship. It is based on Poisson regression models that include the Elo
points of the teams as covariates and incorporates differences of team-specific
effects. These models for the prediction of the FIFA World Cup 2018 are fitted
on all football games on neutral ground of the participating teams since 2010.
Based on the model estimates for single matches Monte-Carlo simulations are
used to estimate probabilities for reaching the different stages in the FIFA
World Cup 2018 for all teams. We propose two score functions for ordinal random
variables that serve together with the rank probability score for the
validation of our models with the results of the FIFA World Cups 2010 and 2014.
All models favor Germany as the new FIFA World Champion. All possible courses
of the tournament and their probabilities are visualized using a single Sankey
diagram.Comment: 22 pages, 7 figure
Capacity of the Range of Random Walks on Free Products of Graphs
In this article we prove existence of the asymptotic capacity of the range of
random walks on free products of graphs. In particular, we will show that the
asymptotic capacity of the range is almost surely constant and strictly
positive.Comment: 14 pages, 2 figure
Nested Zero Inflated Generalized Poisson Regression for FIFA World Cup 2022
This article is devoted to the forecast of the FIFA World Cup 2022 via nested
zero-inflated generalized Poisson regression. Our regression model incorporates
the Elo points of the participating teams, the location of the matches and the
of team-specific skills in attack and defense as covariates. The proposed model
allows predictions in terms of probabilities in order to quantify the chances
for each team to reach a certain stage of the tournament. We use Monte Carlo
simulations for estimating the outcome of each single match of the tournament,
from which we are able to simulate the whole tournament itself. The model is
fitted on all football games of the participating teams since 2016 weighted by
date and importance. Validation with previous tournaments and comparison with
other Poisson models are given.Comment: 22 pages, 14 tables, 4 figures. Update October 30: including now all
historic matches until 30.10.2022 for latest forecast. arXiv admin note:
substantial text overlap with arXiv:2106.05174, arXiv:1806.01930,
arXiv:1905.0362
Range of Random Walks on Free Products
In this article we consider transient nearest neighbour random walks on free
products of graphs. We prove that the asymptotic range of these random walks
exists and is strictly positive. In particular, we show that the range varies
real-analytically in terms of probability measures of constant support.
Moreover, we prove a central limit theorem associated with the range of the
random walk.Comment: 38 page
Rate of Escape of Random Walks on Regular Languages and Free Products by Amalgamation of Finite Groups
We consider random walks on the set of all words over a finite alphabet such
that in each step only the last two letters of the current word may be modified
and only one letter may be adjoined or deleted. We assume that the transition
probabilities depend only on the last two letters of the current word.
Furthermore, we consider also the special case of random walks on free products
by amalgamation of finite groups which arise in a natural way from random walks
on the single factors. The aim of this paper is to compute several equivalent
formulas for the rate of escape with respect to natural length functions for
these random walks using different techniques.Comment: 16 page