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      A Simple Non-Markovian Computational Model of the Statistics of Soccer Leagues: Emergence and Scaling effects

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          Abstract

          We propose a novel algorithm that outputs the final standings of a soccer league, based on a simple dynamics that mimics a soccer tournament. In our model, a team is created with a defined potential(ability) which is updated during the tournament according to the results of previous games. The updated potential modifies a teams' future winning/losing probabilities. We show that this evolutionary game is able to reproduce the statistical properties of final standings of actual editions of the Brazilian tournament (Brasileir\~{a}o). However, other leagues such as the Italian and the Spanish tournaments have notoriously non-Gaussian traces and cannot be straightforwardly reproduced by this evolutionary non-Markovian model. A complete understanding of these phenomena deserves much more attention, but we suggest a simple explanation based on data collected in Brazil: Here several teams were crowned champion in previous editions corroborating that the champion typically emerges from random fluctuations that partly preserves the gaussian traces during the tournament. On the other hand, in the Italian and Spanish leagues only a few teams in recent history have won their league tournaments. These leagues are based on more robust and hierarchical structures established even before the beginning of the tournament. For the sake of completeness, we also elaborate a totally Gaussian model (which equalizes the winning, drawing, and losing probabilities) and we show that the scores of the "Brasileir\~{a}o" cannot be reproduced. Such aspects stress that evolutionary aspects are not superfluous in our modeling. Finally, we analyse the distortions of our model in situations where a large number of teams is considered, showing the existence of a transition from a single to a double peaked histogram of the final classification scores. An interesting scaling is presented for different sized tournaments.

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          The Hot (Invisible?) Hand: Can Time Sequence Patterns of Success/Failure in Sports Be Modeled as Repeated Random Independent Trials?

          The long lasting debate initiated by Gilovich, Vallone and Tversky in is revisited: does a “hot hand” phenomenon exist in sports? Hereby we come back to one of the cases analyzed by the original study, but with a much larger data set: all free throws taken during five regular seasons ( ) of the National Basketball Association (NBA). Evidence supporting the existence of the “hot hand” phenomenon is provided. However, while statistical traces of this phenomenon are observed in the data, an open question still remains: are these non random patterns a result of “success breeds success” and “failure breeds failure” mechanisms or simply “better” and “worse” periods? Although free throws data is not adequate to answer this question in a definite way, we speculate based on it, that the latter is the dominant cause behind the appearance of the “hot hand” phenomenon in the data.
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            A Sinister Bias for Calling Fouls in Soccer

            Distinguishing between a fair and unfair tackle in soccer can be difficult. For referees, choosing to call a foul often requires a decision despite some level of ambiguity. We were interested in whether a well documented perceptual-motor bias associated with reading direction influenced foul judgments. Prior studies have shown that readers of left-to-right languages tend to think of prototypical events as unfolding concordantly, from left-to-right in space. It follows that events moving from right-to-left should be perceived as atypical and relatively debased. In an experiment using a go/no-go task and photographs taken from real games, participants made more foul calls for pictures depicting left-moving events compared to pictures depicting right-moving events. These data suggest that two referees watching the same play from distinct vantage points may be differentially predisposed to call a foul.
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              Football fever: goal distributions and non-Gaussian statistics

              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 the home and away teams. As it turns out, especially the tails of the distributions are not well described by the Poissonian or binomial model resulting from the assumption of uncorrelated random events. Instead, a good effective description of the data is provided by less basic distributions such as the negative binomial one or the probability densities of extreme value statistics. To understand this behavior from a microscopical point of view, however, no waiting time problem or extremal process need be invoked. Instead, modifying the Bernoulli random process underlying the Poissonian model to include a simple component of self-affirmation seems to describe the data surprisingly well and allows to understand the observed deviation from Gaussian statistics. The phenomenological distributions used before can be understood as special cases within this framework. We analyzed historical football score data from many leagues in Europe as well as from international tournaments, including data from all past tournaments of the ``FIFA World Cup'' series, and found the proposed models to be applicable rather universally. In particular, here we analyse the results of the German women's premier football league and consider the two separate German men's premier leagues in the East and West during the cold war times and the unified league after 1990 to see how scoring in football and the component of self-affirmation depend on cultural and political circumstances.
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                Author and article information

                Journal
                08 July 2012
                Article
                10.1016/j.cpc.2012.10.030
                1207.1848
                5284944b-2849-4139-8c24-7aca0f07c7e6

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                18 pages, 9 figures
                physics.data-an cond-mat.stat-mech physics.soc-ph

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