Ranking paired contestants
作者:
Edwin L. Crow,
期刊:
Communications in Statistics - Simulation and Computation
(Taylor Available online 1990)
卷期:
Volume 19,
issue 3
页码: 749-769
ISSN:0361-0918
年代: 1990
DOI:10.1080/03610919008812886
出版商: Marcel Dekker, Inc.
关键词: David's score;football;likeli-hood ratio;net difference in ranks;net number of in-consistencies;paired comparisons;Slater's criterion;tennis
数据来源: Taylor
摘要:
The ranking of paired contestants (players) after a series of contests is difficult when every player does not play every other player. In the 1975 JASA Mark Thompson presented a maximum likelihood solution based on the assumption that the probability of any one player defeating any other is a function only of the difference in their ranks. Here the linear approximation to that likelihood is shown to lead to a nonparametric measure of the efficacy of the ranking, called the net difference in ranks (NDR) , which is the sum of the differences in ranks of the paired players in the observed contests that agree with the ranking minus the sum of the differences in ranks in the observed contests that disagree with the ranking (upsets) . The subject is part of a large literature that has been consolidated by H.A. David in The Method of Paired Comparisons (1963, 1988). The method was introduced by the psychophysicist Fechner in 1860 and has been widely applied to sensory testing,
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