政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/141549

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政大典藏 > College of Commerce > Department of Statistics > Theses > Item 140.119/141549

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/141549

Title:	雙打賽事評分系統的研究 A study of rating systems for doubles matches
Authors:	張靜如 Chang, Ching-Ju
Contributors:	翁久幸張靜如 Chang, Ching-Ju
Keywords:	貝氏推論配對比較評分系統 Bayesian inference Paired comparison Rating system
Date:	2022
Issue Date:	2022-09-02 14:46:13 (UTC+8)
Abstract:	此篇論文主要探討在雙打比賽中同時考慮更新球隊和球員實力的機率評分系統。著名的機率評分系統，如 Elo 評分系統和 Glicko 評分系統，都是根基於一對一比賽所設計之評分系統。雙打比賽為二對二的比賽，在雙打比賽中，同一名選手可能在不同時間點與不同選手搭檔組隊。部份研究中，將此情況視為完全不同的隊伍，並直接使用 Elo 系統或 Glicko 系統進行評分。然而，這樣的作法忽略了個別選手的表現結果，是較為保守的處理方法。因此，我們引入文獻中關於多組別、多隊員之評分系統，以實現同時更新球隊和球員技能評分的目的。此外，傳統上 Elo 系統並無考慮實力的變異程度，本論文也將此納入研究。實驗資料為 2007-2014 年的女子沙灘排球資料集和 2010-2017 年的 ATP 雙打比賽資料集。我們發現了兩件事:首先，會更新變異數的模型優於不更新且維持初始變異數的模型。第二，在不同的初始變異數下，隊伍和個人的實力參數同時更新的模型比持保守假設的模型更穩定。 This paper mainly discussed the probabilistic rating system that considers updating both team and player strengths in doubles matches. We investigated the several probabilis- tic rating systems, such as Bradley-Terry Model(1952), Elo Rating System(1978), and Glicko Rating System(1999), and proposed a framework based on them. Among them, the Glicko system, a well-known ranking model for paired comparisons, mentioned a conservative assumption which consider teams that share a player as entirely distinct. However, we found that models based on conservative assumptions compared is unsta- ble with different initial variances.Therefore, we introduced the updating rule in Weng and Lin(2012) to improve the model to realize the purpose that updating both team and player skill rating. The experiments was conducted on the Women’s beach volleyball dataset over the years 2007-2014 and the ATP doubles match dataset over the years 2010-2017. We found two things: Firstly, models with updated variance outperform the models with constant variance. Secondly, under different initial variances, models applying the updating rules is more stable than which based on conservative assump- tions.
Reference:	[1] R. A. Bradley and M. E. Terry, “Rank analysis of incomplete block designs: I. the method of paired comparisons,” Biometrika, vol. 39, no. 3/4, pp. 324–345, 1952. [2] A. E. Elo, The rating of chessplayers, past and present. BT Batsford Limited, 1978. [3] M. E. Glickman, “Parameter estimation in large dynamic paired comparison ex- periments,” Journal of the Royal Statistical Society: Series C (Applied Statistics), vol. 48, no. 3, pp. 377–394, 1999. [4] M. E. Glickman, J. Hennessy, and A. Bent, “A comparison of rating systems for competitive women’s beach volleyball,” Statistica Applicata-Italian Journal of Ap- plied Statistics, no. 2, pp. 233–254, 2018. [5] R. C. Weng and C.-J. Lin, “A Bayesian approximation method for online ranking.” Journal of Machine Learning Research, vol. 12, no. 1, 2011. [6] M. Ingram, “How to extend elo: a Bayesian perspective,” Journal of Quantitative Analysis in Sports, vol. 17, no. 3, pp. 203–219, 2021.
Description:	碩士國立政治大學統計學系 109354021
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0109354021
Data Type:	thesis
DOI:	10.6814/NCCU202201308
Appears in Collections:	[Department of Statistics] Theses

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