Dynamics of tournaments: the soccer case

Ribeiro, Haroldo V.; Mendes, R. S.; Malacarne, L. C.; Picoli, S.; Santoro, P. A.

doi:10.1140/epjb/e2010-00115-5

Cited by 25 publications

(21 citation statements)

References 26 publications

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“…This approach has been successfully applied to a variety of fields, from physics and astronomy [6] to genetics [7] and economy [8]. Moreover, this framework has been a trend towards investigating and modeling interdisciplinary fields, such as religion [9], elections [10], vehicular traffic [11], tournaments [12], and many others. These few examples and social phenomena in general [13] illustrate as physicists have gone far from their traditional domain of investigations.…”

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confidence: 99%

Universal patterns in sound amplitudes of songs and music genres

et al. 2011

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We report a statistical analysis over more than eight thousand songs. Specifically, we investigate the probability distribution of the normalized sound amplitudes. Our findings seems to suggest a universal form of distribution which presents a good agreement with a one-parameter stretched Gaussian. We also argue that this parameter can give information on music complexity, and consequently it goes towards classifying songs as well as music genres. Additionally, we present statistical evidences that correlation aspects of the songs are directly related with the non-Gaussian nature of their sound amplitude distributions. In recent years, studies of complex systems have become widespread among the scientific community, specially in the statistical physics one [1][2][3][4][5]. Many of these investigations deal with data records ordered in time or space (i.e., time series), trying to extract some features, patterns or laws that may be present in the systems studied. This approach has been successfully applied to a variety of fields, from physics and astronomy [6] Music is a well known worldwide social phenomenon linked to the human cognitive habits, modes of consciousness as well as historical developments [14]. In the direction of music's social role, some authors investigated collective listening habits. For instance, Lambiotte and Ausloos [15] analyzed data from people music library finding audience groups with the size distribution following a power law. They also investigated correlations among these music groups, reporting non-trivial relations [16]. In another work, Silva et al.[17] studied the network structure of the song writers and the singers of Brazilian popular music (mpb). There is also an interest in the behavior of music sales [18] as well as in the success of musicians [19][20][21].Despite these cultural aspects, songs form a highly organized system presenting very complex structures and long-range correlations. All these features have attracted the attention of statistical physicists. In a seminal paper, Voss and Clarke [22] analyzed the power spectrum of radio stations and observed a 1/f noise like pattern. They also showed that the correlation can extend to longer or shorter time scales, depending on the music genre. Hsü and Hsü[23] investigated the changes of acoustic frequency in Bach's and Mozart's compositions, finding self-similarity and fractals structures. In contrast, they report no resemblance to fractal geometry [24] for modern music. Fractal structures have also been reported in the study of sequences of music notes [25], where Su and Wu [26] suggest that the multifractal spectrum can be used to distinguish different styles of music. In this brief literature review, we see that special attention was paid to the fractal structures of music, correlations and power spectrum analysis. However, much less attention has been paid to the understanding of the amplitude distribution. This last point has been noted by Diodati and Piazza[34]. In their work, they investigated the distribution of t...

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confidence: 99%

Universal patterns in sound amplitudes of songs and music genres

et al. 2011

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“…It has been indicated that measures, called V r and W r , independent of the empirical law functional form, lead to subsequent numerical results pointing to some inner structure of the team rank-value distribution, according to the present set of UEFA rules. It can be guessed, without more mathematical work than is necessary, that the inner structure is likely tied to the pool, in the first rounds, followed by the "direct elimination" tournament-like process [40] in UEFA competition, and the "increase in value" of the team when progressing further in the competitions through an accelerating effect. with a set of nonlinear constraints (similar to boundary conditions) inducing an unstable organization, similar to what is found in intermittent processes, when forced cycles drive an interplay between (two or several) feedback mechanisms and leading to visible physically characterized zones [59].…”

Section: Discussionmentioning

confidence: 99%

Primacy and ranking of UEFA soccer teams from biasing organization rules

2014

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A question is raised on whether some implied regularity or structure, as found in soccer team ranking by the Union of European Football Associations (UEFA), is due to implicit game result value or score competition conditions. The analysis is based on considerations about complex systems, i.e. searching 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 made of a few teams emerges after each game season. Other classes which apparently have regular sizes subsequently occur. Thus, the notion of 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 ingredients 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.

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“…Each element P i→j of P gives the ball-passing probability from the node i to the node j. The transition matrix is also normalized as N j=1 P i→j = 1 (7) for each i. Note that the transition matrix is not necessarily symmetric.…”

Section: Markov-chain Modelmentioning

confidence: 99%

“…From the viewpoint of physics, studies with respect to football games are considered to be classified into the following two types: mechanical and statistical. In the latter case, goal distribution [2,3,4,5] and outcome prediction of football games [6,7,8,9] have been studied for example. A football game can be considered as a dynamical system in which game players interact with each other via one ball.…”

Section: Introductionmentioning

confidence: 99%