Modeling and visualizing competitiveness in soccer leagues

Abstract This paper adopts concepts of systems’ theory and multidimensional scaling to study the competitiveness in soccer leagues of four countries. A season for a given league is read as a dynamical system with states that are measured at discrete time samples corresponding to the rounds. The system state is inferred from the accumulated points won and lost by each team. These data are interpreted as active and reactive power and are processed in the complex plane. The league competitiveness is visualized through 2-dim maps of items that represent the relative positioning of the teams over the season. The results are compared with those obtained with two classic competitiveness measures.

[1]  Elena Deza,et al.  Encyclopedia of Distances , 2014 .

[2]  Francisco Pedroche,et al.  A new method for comparing rankings through complex networks: Model and analysis of competitiveness of major European soccer leagues , 2013, Chaos.

[3]  José António Tenreiro Machado,et al.  Multidimensional Scaling Visualization Using Parametric Entropy , 2015, Int. J. Bifurc. Chaos.

[4]  José António Tenreiro Machado,et al.  Entropy Analysis of Soccer Dynamics , 2019, Entropy.

[5]  Charu C. Aggarwal,et al.  On the Surprising Behavior of Distance Metrics in High Dimensional Spaces , 2001, ICDT.

[6]  Jarryd Luke Wallace,et al.  Evolution of World Cup soccer final games 1966-2010: game structure, speed and play patterns. , 2014, Journal of science and medicine in sport.

[7]  António M. Lopes,et al.  Multidimensional scaling analysis of soccer dynamics , 2017 .

[8]  Kelly Goossens,et al.  Competitive Balance in European Football - Comparison by Adapting Measures: National Measure of Seasonal Imbalance and Top 3 , 2006 .

[9]  António M. Lopes,et al.  Multidimensional scaling locus of memristor and fractional order elements , 2020, Journal of advanced research.

[10]  Loek Groot,et al.  Economics, Uncertainty and European Football: Trends in Competitive Balance , 2008 .

[11]  Bruno Travassos,et al.  Application of entropy measures to analysis of performance in team sports , 2016 .

[12]  Christoph Breuer,et al.  Top Clubs’ Performance and the Competitive Situation in European Domestic Football Competitions , 2010 .

[13]  António M. Lopes,et al.  Artistic painting: A fractional calculus perspective , 2019, Applied Mathematical Modelling.

[14]  S. Emmonds,et al.  Hidden dynamics of soccer leagues: The predictive ‘power’ of partial standings , 2019, PloS one.

[15]  Richard K. Beatson,et al.  Surface interpolation with radial basis functions for medical imaging , 1997, IEEE Transactions on Medical Imaging.

[16]  Keith Davids,et al.  Decision making in social neurobiological systems modeled as transitions in dynamic pattern formation , 2014, Adapt. Behav..

[17]  Hugo Folgado,et al.  Competing with Lower Level Opponents Decreases Intra-Team Movement Synchronization and Time-Motion Demands during Pre-Season Soccer Matches , 2014, PloS one.

[18]  Fabio Giuliano Caetano,et al.  Analysis of Match Dynamics of Different Soccer Competition Levels Based on the Player Dyads , 2019, Journal of human kinetics.

[19]  I. Brocas,et al.  Do the “Three-Point Victory” and “Golden Goal” Rules Make Soccer More Exciting? , 2002 .

[20]  Eric Dunning,et al.  Sport Matters: Sociological Studies of Sport, Violence and Civilisation , 1999 .

[21]  José António Tenreiro Machado,et al.  Fractional Dynamics in Soccer Leagues , 2020, Symmetry.

[22]  Nasir Saeed,et al.  A Survey on Multidimensional Scaling , 2018, ACM Comput. Surv..

[23]  Keith Davids,et al.  The Role of Hypernetworks as a Multilevel Methodology for Modelling and Understanding Dynamics of Team Sports Performance , 2019, Sports Medicine.

[24]  J. T. Tenreiro Machado,et al.  A fractional perspective to the modelling of Lisbon’s public transportation network , 2018, Transportation.

[25]  Dan Vilenchik,et al.  The Adaptive Behavior of a Soccer Team: An Entropy-Based Analysis , 2018, Entropy.

[26]  Sung-Hyuk Cha.  Comprehensive Survey on Distance/Similarity Measures between Probability Density Functions , 2007 .

[27]  John W. Sammon,et al.  A Nonlinear Mapping for Data Structure Analysis , 1969, IEEE Transactions on Computers.

[28]  Emmanuel Paradis.  Multidimensional Scaling With Very Large Datasets , 2018 .

[29]  José António Tenreiro Machado,et al.  Multidimensional Scaling Visualization Using Parametric Similarity Indices , 2015, Entropy.

[30]  T. Downarowicz.  Entropy in Dynamical Systems , 2011 .

[31]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

[32]  Stephen Dobson,et al.  The Economics of Football , 2001 .

[33]  W. Opstal,et al.  Competitive balance between national leagues in European football after the Bosman Case , 2010 .

[34]  J. Sampaio,et al.  Exploring the determinants of success in different clusters of ball possession sequences in soccer , 2020, Research in sports medicine.

[35]  Keith Davids,et al.  The micro-macro link in understanding sport tactical behaviours: Integrating information and action at different levels of system analysis in sport , 2015 .

[36]  José António Tenreiro Machado,et al.  Dynamical Stability and Predictability of Football Players: The Study of One Match , 2014, Entropy.