Study of Probability Distribution in Paired Comparison  

Oleh:

Imoto, Kazuhiro ; Sano, Natuki ; Suzuki, Tomomichi

Jenis: Article from Proceeding
Dalam koleksi: 12th ANQ Congress in Singapore, 5-8 Agustus 2014, page 1-9.
Topik: Rating; Sports; Poisson distribution; Geometric distribution; Negative binomial distribution
Fulltext: QP2-2.3-P0273.pdf (629.7KB)

Isi artikel

A paired comparison compares two objects and determines superiority or inferiority. This method is applicable not only to comparison of a sample but also to sports. In sports for which two players match, rating system (for example ELO system) is often used for expressing players’ relative strengths, or the determination of ranking. In ELO rating system, a concept called the true strength of the player is considered. However, the strength of a player among match varies. Then, the strength of a player is assumed by a certain probability distribution centering on true strength. The distribution is unknown. By distribution is assumed, it may have influence on the determination of victory or defeat. In this paper, it is the purpose to explore the possibility of various distribution. We newly assume poisson distribution, geometric distribution, and negative binomial distribution. Since it is impossible to analytically devise the expected winning percentage from two persons' rating difference, probability calculation is performed and it asks for the expected winning percentages one by one. As the comparison method, the expected winning percentages in the same percentage of victories difference is computed, and the value is compared. Results of comparison of the distribution, as compared with the distribution of existing data showed differences. For example, Poisson distribution was found that as compared to the other, ability difference is large, the possibility that the stronger win reliably increases

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