Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter August 1, 2019

Combinatorial models of cross-country dual meets: what is a big victory?

  • Kurt S. Riedel EMAIL logo

Abstract

Combinatorial/probabilistic models for cross-country dual-meets are proposed. The first model assumes that all runners are equally likely to finish in any possible order. The second model assumes that each team is selected from a large identically distributed population of potential runners and with each potential runner’s ranking determined by the initial draw from the combined population.

MSC 2010: 68R05; 97K20; 97K80; 97M40; 05A15

Acknowledgement

We thank the anonymmous referee for pointing out the Wilcoxon rank-sum statistic as well as many other references.

References

Boudreau, J. W. and S. Sanders. 2015. “Choosing “Flawed” Aggregation Rules: The Benefit of Social Choice Violations in a League that Values Competitive Balance.” Economics Letters 137:106–108.10.1016/j.econlet.2015.10.001Search in Google Scholar

Boudreau, J., J. Ehrlich, S. Sanders, and A. Winn. 2014. “Social Choice Violations in Rank Sum Scoring: A Formalization of Conditions and Corrective Probability Computations.” Mathematical Social Sciences 71:20–29.10.1016/j.mathsocsci.2014.03.004Search in Google Scholar

Boudreau, J., J. Ehrlich, M. F. Raza, and S. Sanders. 2018. “The Likelihood of Social Choice Violations in Rank Sum Scoring: Algorithms and Evidence from NCAA Cross Country Running.” Public Choice 174:219–238.10.1007/s11127-017-0494-0Search in Google Scholar

Conover, William J. 1980. Practical Nonparametric Statistics, (2nd Edition), pp. 252–256, John Wiley and Sons. https://onlinepubs.trb.org/onlinepubs/nchrp/cd-22/manual/v2chapter6.pdf.Search in Google Scholar

Hammond, T. H. 2007. “Rank Injustice?: How the Scoring Method for Cross-Country Running Competitions Violates Major Social Choice Principles.” Public Choice 133:359–375.10.1007/s11127-007-9193-6Search in Google Scholar

Huntington, E. V. 1938. “A Paradox in the Scoring of Competing Teams.” Science 88(2282): 287–288.10.1126/science.88.2282.287Search in Google Scholar PubMed

Lehman, E. L. 2006. Nonparametrics: Statistical Methods Based on Ranks. New York: Springer.Search in Google Scholar

Mann, H. B. and D. R. Whitney. 1947. “On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other.” Annals of Mathematical Statistics 18(1): 50–60.10.1214/aoms/1177730491Search in Google Scholar

Mixon Jr, F. G. and E. W. King. 2012. “Social Choice Theory in 10,000 Meters: Examining Independence and Transitivity in the NCAA Cross-Country Championships.” The American Economist 57:32–41.10.1177/056943451205700103Search in Google Scholar

National Federation of State High School Associations. 2016–17. Participation Survey Results, http://www.nfhs.org/ParticipationStatistics.Search in Google Scholar

Szedlik, S. 2010. “May the Best Team Win, Determining the Winner of a Cross-Country Race.” In Mathematics and Sports, edited by Joseph A. Gallian, Ch. 24. Mathematical Association of America, pp. 295–315.10.5948/UPO9781614442004.025Search in Google Scholar

Wilcoxon, F. 1945. “Individual Comparisons by Ranking Methods.” Biometrics Bulletin 1:80–83.10.1007/978-1-4612-4380-9_16Search in Google Scholar

Published Online: 2019-08-01
Published in Print: 2019-10-25

©2019 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 25.2.2024 from https://www.degruyter.com/document/doi/10.1515/jqas-2019-0025/html
Scroll to top button