1. NCCU Academic Hub
  2. 學術產出
  3. 商學院
  4. 學位論文
  5. Item

學術產出-學位論文

文章檢視/開啟

書目匯出

Google ScholarTM

政大圖書館

引文資訊

TAIR相關學術產出

題名 雙打賽事評分系統的研究
A study of rating systems for doubles matches
作者 張靜如
Chang, Ching-Ju
貢獻者 翁久幸
張靜如
Chang, Ching-Ju
關鍵詞 貝氏推論
配對比較
評分系統
Bayesian inference
Paired comparison
Rating system
日期 2022
上傳時間 2-九月-2022 14:46:13 (UTC+8)
摘要 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.
參考文獻 [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.
描述 碩士
國立政治大學
統計學系
109354021
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0109354021
資料類型 thesis
dc.contributor.advisor 翁久幸zh_TW
dc.contributor.author (作者) 張靜如zh_TW
dc.contributor.author (作者) Chang, Ching-Juen_US
dc.creator (作者) 張靜如zh_TW
dc.creator (作者) Chang, Ching-Juen_US
dc.date (日期) 2022en_US
dc.date.accessioned 2-九月-2022 14:46:13 (UTC+8)-
dc.date.available 2-九月-2022 14:46:13 (UTC+8)-
dc.date.issued (上傳時間) 2-九月-2022 14:46:13 (UTC+8)-
dc.identifier (其他 識別碼) G0109354021en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/141549-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 109354021zh_TW
dc.description.abstract (摘要) 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。zh_TW
dc.description.abstract (摘要) 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.en_US
dc.description.tableofcontents 1 緒論 7
2 文獻回顧 8
2.1 BRADLEY-TERRY模型 8
2.2 ELO評分系統 9
2.3 GLICKO評分系統 10
2.4 多隊別多隊員比賽 11
2.5 FIVB得分系統 12
3 研究方法 14
3.1 方法一 14
3.2 方法二 16
4 資料介紹 20
4.1 FIVB女子沙灘排球巡迴賽 20
4.2 ATP男子網球雙打比賽 23
5 實驗結果 25
5.1 參數設定 25
5.2 模型預測結果 25
5.2.1 評判標準 25
5.2.2 FIVB女子沙灘排球巡迴賽 26
5.2.3 ATP男子網球雙打比賽 30
5.2.4 小結 31
5.3 前15名的隊伍 32
6 結論 35
References 36		zh_TW
dc.format.extent 1321177 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0109354021en_US
dc.subject (關鍵詞) 貝氏推論zh_TW
dc.subject (關鍵詞) 配對比較zh_TW
dc.subject (關鍵詞) 評分系統zh_TW
dc.subject (關鍵詞) Bayesian inferenceen_US
dc.subject (關鍵詞) Paired comparisonen_US
dc.subject (關鍵詞) Rating systemen_US
dc.title (題名) 雙打賽事評分系統的研究zh_TW
dc.title (題名) A study of rating systems for doubles matchesen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [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.		zh_TW
dc.identifier.doi (DOI) 10.6814/NCCU202201308en_US