Primacy and ranking of UEFA soccer teams from biasing organization rules

被引:9
作者
Ausloos, Marcel [1 ,2 ]
Gadomski, Adam [3 ]
Vitanov, Nikolay K. [4 ]
机构
[1] Royal Netherlands Acad Arts & Sci, NL-1096 CJ Amsterdam, Netherlands
[2] GRAPES, B-4031 Liege, Federation Wall, Belgium
[3] Univ Technol & Life Sci, Inst Math & Phys, Dept Phys, PL-85796 Bydgoszcz, Poland
[4] Bulgarian Acad Sci, Inst Mech, BG-1113 Sofia, Bulgaria
关键词
ranking; soccer; primacy index; dissipative structures; self-organization; INHOMOGENEOUS STATIONARY STATES; ZIPF-MANDELBROT; SYSTEMS; LAW; DISTRIBUTIONS; MODEL; CORE; COMPLEXITY; COAUTHORS;
D O I
10.1088/0031-8949/89/10/108002
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A question is raised on whether some implied regularity or structure, as found in the soccer team ranking by the Union of European Football Associations ( UEFA), is due to an implicit game result value or score competition conditions. The analysis is based on considerations of complex systems, i.e. finding whether power or other simple law fits are appropriate to describe some internal dynamics. It is observed that the ranking is specifically organized: a major class comprising a few teams emerges after each season. Other classes, which apparently have regular sizes, occur subsequently. Thus, the notion of the Sheppard primacy index is envisaged to describe the findings. Additional primacy indices are discussed for enhancing the features. These measures can be used to sort out peer classes in more general terms. A very simplified toy model containing components of the UEFA ranking rules suggests that such peer classes are an extrinsic property of the ranking, as obtained in many nonlinear systems under boundary condition constraints.
引用
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页数:12
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共 70 条
  • [1] [Anonymous], 1944, Q Appl Math, DOI [DOI 10.1090/QAM/10666, 10.1090/QAM/10666, DOI 10.1090/QAM/1944-02-02]
  • [2] [Anonymous], 1949, Human behaviour and the principle of least-effort
  • [3] [Anonymous], NONLINEAR DYNAMICS C
  • [4] [Anonymous], 1999, Harnessing complexity: Organizational implications of a scientific frontier
  • [5] Pareto's law for income of individuals and debt of bankrupt companies
    Aoyama, H
    Souma, W
    Nagahara, Y
    Okazaki, MP
    Takayasu, H
    Takayasu, M
    [J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2000, 8 (03) : 293 - 300
  • [6] Complexity and the economy
    Arthur, WB
    [J]. SCIENCE, 1999, 284 (5411) : 107 - 109
  • [7] CONTINUOUSLY FORCED BALLAST RESISTOR MODEL FOR SUPERCONDUCTING HOT SPOTS
    AUSLOOS, M
    [J]. PHYSICA B & C, 1981, 108 (1-3): : 969 - 970
  • [8] A scientometrics law about co-authors and their ranking: the co-author core
    Ausloos, M.
    [J]. SCIENTOMETRICS, 2013, 95 (03) : 895 - 909
  • [9] Ausloos M, 2014, ARXIV14035683
  • [10] Ausloos M., 2014, SCIENTOMETRICS, P1, DOI DOI 10.1007/S11192-014-1302-Y