On the ranking of a Swiss system chess team tournament
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The paper suggests a family of paired comparison-based scoring procedures for ranking the participants of a Swiss system chess team tournament. We present the challenges of ranking in Swiss system, the features of individual and team competitions as well as the failures of the official rankings based on lexicographical order. The tournament is represented as a ranking problem such that the linearly-solvable row sum (score), generalized row sum, and least squares methods have favourable axiomatic properties. Two chess team European championships are analysed as case studies. Final rankings are compared by their distances and visualized with multidimensional scaling. Differences to the official ranking are revealed by the decomposition of the least squares method. Rankings are evaluated by prediction power, retrodictive performance, and stability. The paper argues for the use of least squares method with a results matrix favouring match points on the basis of its relative insensitivity to the choice between match and board points, retrodictive accuracy, and robustness.
KeywordsPaired comparison Ranking Linear system of equations Swiss system Chess
We are grateful to two anonymous referees for their valuable comments and suggestions. The research was supported by OTKA Grant K 111797 and by the MTA Premium Post Doctorate Research Program. This research was partially supported by Pallas Athene Domus Scientiae Foundation. The views expressed are those of the author’s and do not necessarily reflect the official opinion of Pallas Athene Domus Scientiae Foundation.
- Brozos-Vázquez, M., Campo-Cabana, M. A., Díaz-Ramos, J. C., & González-Díaz, J. (2010). Recursive tie-breaks for chess tournaments. http://eio.usc.es/pub/julio/Desempate/Performance_Recursiva_en.htm.
- Can, B. (2012). Weighted distances between preferences. Technical report RM/12/056, Maastricht University School of Business and Economics, Graduate School of Business and Economics.Google Scholar
- Can, B., & Storcken, T. (2013). A re-characterization of the Kemeny distance. Technical report RM/13/009, Maastricht University School of Business and Economics, Graduate School of Business and Economics.Google Scholar
- Chebotarev, P. (1989). Generalization of the row sum method for incomplete paired comparisons. Automation and Remote Control, 50(8), 1103–1113.Google Scholar
- Csató, L. (2012). A pairwise comparison approach to ranking in chess team championships. In P. Fülöp (Ed.), Tavaszi Szél 2012 Konferenciakötet (pp. 514–519). Budapest: Doktoranduszok Országos Szövetsége.Google Scholar
- Csató, L. (2014). Additive and multiplicative properties of scoring methods for preference aggregation. Corvinus economics working papers 3/2014, Corvinus University of Budapest, Budapest.Google Scholar
- Csató, L. (2016a). Ranking in Swiss system chess team tournaments. http://arxiv.org/abs/1507.05045v3.
- Csató, L. (2016b). An impossibility theorem for paired comparisons. http://arxiv.org/abs/1612.00186.
- ECU. (2012). Tournament rules. http://europechess.net/index.php?option=com_content&view=article&id=9&Itemid=15. ECU stands for European Chess Union.
- ECU. (2013). European team chess championship 2013. Tournament rules. http://etcc2013.com/wp-content/uploads/2013/06/ETCC-2013-tournament-rules-June-06-2013.pdf. ECU stands for European Chess Union.
- FIDE. (2015). Handbook. FIDE stands for Fédération Internationale des Échecs (World Chess Federation). http://www.fide.com/fide/handbook.html.
- Forlano, L. (2011). A new way to rank the players in a Swiss systems tournament. http://www.vegachess.com/Missing_point_score_system.pdf.
- Jeremic, V. M., & Radojicic, Z. (2010). A new approach in the evaluation of team chess championships rankings. Journal of Quantitative Analysis in Sports, 6(3). https://www.degruyter.com/view/j/jqas.2010.6.3 /jqas.2010.6.3.1257/jqas.2010.6.3.1257.xml.
- Kemeny, J. G. (1959). Mathematics without numbers. Daedalus, 88(4), 577–591.Google Scholar
- Kemeny, J. G., & Snell, L. J., (1962). Preference ranking: An axiomatic approach. Mathematical models in the social sciences (pp. 9–23). New York: Ginn.Google Scholar
- Landau, E. (1895). Zur relativen Wertbemessung der Turnierresultate. Deutsches Wochenschach, 11, 366–369.Google Scholar
- Landau, E. (1914). Über Preisverteilung bei Spielturnieren. Zeitschrift für Mathematik und Physik, 63, 192–202.Google Scholar
- Pasteur, R. D. (2010). When perfect isn’t good enough: Retrodictive rankings in college football. In J. A. Gallian (Ed.), Mathematics and Sports, Dolciani Mathematical Expositions 43 (pp. 131–146). Washington, DC: Mathematical Association of America.Google Scholar