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On the occasion of the last FIFA World Cup in Brazil, The Economist published a plot depicting how many goals have been scored in all World Cup competitions until present, minute by minute. The plot was followed by a naive and poorly…

Applications · Statistics 2014-08-26 Nicola Mingotti

PageRank is an algorithm introduced in 1998 and used by the Google Internet search engine. It assigns a numerical value to each element of a set of hyperlinked documents (that is, web pages) within the World Wide Web with the purpose of…

Systems and Control · Computer Science 2013-12-09 Hideaki Ishii , Roberto Tempo

The problem of evaluating the performance of soccer players is attracting the interest of many companies and the scientific community, thanks to the availability of massive data capturing all the events generated during a match (e.g.,…

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…

Applications · Statistics 2017-04-04 Shael Brown

The World Wide Web (WWW) is the repository of large number of web pages which can be accessed via Internet by multiple users at the same time and therefore it is Ubiquitous in nature. The search engine is a key application used to search…

Databases · Computer Science 2012-09-25 K. C. Srikantaiah , P. L. Srikanth , V. Tejaswi , K. Shaila , K. R. Venugopal , L. M. Patnaik

PageRank and the Bradley-Terry model are competing approaches to ranking entities such as teams in sports tournaments or journals in citation networks. The Bradley-Terry model is a classical statistical method for ranking based on paired…

Methodology · Statistics 2024-02-13 David Antony Selby

Analyzing football score data with statistical techniques, we investigate how the not purely random, but highly co-operative nature of the game is reflected in averaged properties such as the probability distributions of scored goals for…

Physics and Society · Physics 2009-04-02 Elmar Bittner , Andreas Nussbaumer , Wolfhard Janke , Martin Weigel

In this paper we show a new technique to analyze families of rankings. In particular we focus on sports rankings and, more precisely, on soccer leagues. We consider that two teams compete when they change their relative positions in…

Physics and Society · Physics 2015-06-16 Regino Criado , Esther Garcia , Francisco Pedroche , Miguel Romance

Evaluating a country's sporting success provides insight into its decision-making and infrastructure for developing athletic talent. The Olympic Games serve as a global benchmark, yet conventional medal rankings can be unduly influenced by…

Applications · Statistics 2025-10-17 Cormac MacDermott , Carl J. Scarrott , John Ferguson

The FIFA Men's World Cup Tournament (WCT) is the most important football (soccer) competition, attracting worldwide attention. A popular practice among football fans in Brazil is to organize contests in which each participant informs…

Classification of matches played in the last rounds of sports competitions is a well-established tool for evaluating tournament designs. Both deterministic and probabilistic approaches are available for this purpose. Our paper offers the…

Physics and Society · Physics 2026-05-26 László Csató , András Gyimesi

We present a systematic approach to the prediction of soccer matches. First, we show that the information about chances for goals is by far more informative than about the actual results. Second, we present a multivariate regression…

Data Analysis, Statistics and Probability · Physics 2012-07-20 Andreas Heuer , Oliver Rubner

PageRank, the prestige measure for Web pages used by Google, is the stationary probability of a peculiar random walk on directed graphs, which interpolates between a pure random walk and a process where all nodes have the same probability…

Physics and Society · Physics 2015-06-26 Santo Fortunato , Alessandro Flammini

Over the last few years, there has been a growing interest in the prediction and modelling of competitive sports outcomes, with particular emphasis placed on this area by the Bayesian statistics and machine learning communities. In this…

Applications · Statistics 2024-12-17 Roberto Macrì Demartino , Leonardo Egidi , Nicola Torelli

Although many methods have been designed for ranking universities, there is no suitable system that focuses on the ranking of countries based on the performance of their universities. The overall ranking of the universities in a region can…

Digital Libraries · Computer Science 2020-04-22 Bahram Kalhor , Farzaneh Mehrparvar

Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity…

Multiagent Systems · Computer Science 2021-01-08 Joseph Singleton , Richard Booth

A team of association football players may be envisioned as a directed network with player nodes and weighted pass edges. Such a simplistic representation of an otherwise complex structure yields several benefits, but also permits the…

Social and Information Networks · Computer Science 2021-08-12 Vid Stropnik , Vuk Đuranović , Maruša Oražem

Recovering global rankings from pairwise comparisons has wide applications from time synchronization to sports team ranking. Pairwise comparisons corresponding to matches in a competition can be construed as edges in a directed graph…

Machine Learning · Computer Science 2022-07-20 Yixuan He , Quan Gan , David Wipf , Gesine Reinert , Junchi Yan , Mihai Cucuringu

In this paper we present a novel approach to optimise tactical and strategic decision making in football (soccer). We model the game of football as a multi-stage game which is made up from a Bayesian game to model the pre-match decisions…

Artificial Intelligence · Computer Science 2020-03-24 Ryan Beal , Georgios Chalkiadakis , Timothy J. Norman , Sarvapali D. Ramchurn

Though athletics statistics are abundant, it is a difficult task to quantitatively compare performances from different events of track, field, and road running in a meaningful way. There are several commonly-used methods, but each has its…

Applications · Statistics 2014-08-27 Brian Godsey