title: Analysis of Soccer Players' Positional Variability During the 2012 UEFA European Championship: A Case Study.
abstract: The purpose of this study was to analyse players' positional variability during the 2012 UEFA European Championship by applying principal component analysis (PCA) to data gathered from heat maps posted on the UEFA website. We analysed the teams that reached the finals and semi-finals of the competition. The players' 2D coordinates from each match were obtained by applying an image-processing algorithm to the heat maps. With all the players' 2D coordinates for each match, we applied PCA to identify the directions of greatest variability. Then, two orthogonal segments were centred on each player's mean position for all matches. The segments' directions were driven by the eigenvectors of the PCA, and the length of each segment was defined as one standard deviation around the mean. Finally, an ellipse was circumscribed around both segments. To represent player variability, segment lengths and elliptical areas were analysed. The results demonstrate that Portugal exhibited the lowest variability, followed by Germany, Spain and Italy. Additionally, a graphical representation of every player's ellipse provided insight into the teams' organisational features throughout the competition. The presented study provides important information regarding soccer teams' tactical strategy in high-level championships that allows coaches to better control team organisation on the pitch.
authors.affiliation: Laboratory of Applied Biomechanics, Sport Sciences Department, State University of Londrina, Londrina, Brazil.
authors.forename: Felipe Arruda
authors.initials: FA
authors.lastname: Moura
authors.affiliation: Laboratory of Instrumentation for Biomechanics, College of Physical Education, University of Campinas, Campinas, Brazil.
authors.forename: Juliana Exel
authors.initials: JE
authors.lastname: Santana
authors.affiliation: Laboratory of Instrumentation for Biomechanics, College of Physical Education, University of Campinas, Campinas, Brazil.
authors.forename: Nathália Arnosti
authors.initials: NA
authors.lastname: Vieira
authors.affiliation: Biomechanics and Motor Control Laboratory, School of Physical Education and Sport of Ribeirão Preto, University of São Paulo, Ribeirão Preto, Brazil.
authors.forename: Paulo Roberto Pereira
authors.initials: PR
authors.lastname: Santiago
authors.affiliation: Laboratory of Instrumentation for Biomechanics, College of Physical Education, University of Campinas, Campinas, Brazil.
authors.forename: Sergio Augusto
authors.initials: SA
authors.lastname: Cunha
keywords: heat map; match analysis; principal component analysis; tactics