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    A discrete evolutionary model for chess players' ratings

    Fenner, Trevor and Levene, Mark and Loizou, George (2012) A discrete evolutionary model for chess players' ratings. IEEE Transactions on Computational Intelligence and AI in Games 4 (2), pp. 84-93. ISSN 1943-068X.

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    Abstract

    The Elo system for rating chess players, also used in other games and sports, was adopted by the World Chess Federation over four decades ago. Although not without controversy, it is accepted as generally reliable and provides a method for assessing players' strengths and ranking them in official tournaments. It is generally accepted that the distribution of players' rating data is approximately normal but, to date, no stochastic model of how the distribution might have arisen has been proposed. We propose such an evolutionary stochastic model, which models the arrival of players into the rating pool, the games they play against each other, and how the results of these games affect their ratings, in a similar manner to the Elo system. Using a continuous approximation to the discrete model, we derive the distribution for players' ratings at time t as a normal distribution, where the variance increases in time as a logarithmic function of t. We validate the model using published rating data from 2007-2010, showing that the parameters obtained from the data can be recovered through simulations of the stochastic model. The distribution of players' ratings is only approximately normal and has been shown to have a small negative skew. We show how to modify our evolutionary stochastic model to take this skewness into account, and we validate the modified model using the published official rating data.

    Metadata

    Item Type: Article
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems
    Research Centre: Birkbeck Knowledge Lab
    Depositing User: Administrator
    Date Deposited: 14 May 2013 09:56
    Last Modified: 02 Dec 2016 13:23
    URI: http://eprints.bbk.ac.uk/id/eprint/6749

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