Calculation of the number of wins and losses to determine a specific place in sports leagues

• Project/Area Number: 15K00041
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical informatics
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: Ito Satoshi 統計数理研究所, 数理・推論研究系, 教授 (50232442)
• Research Collaborator: SHINANO Yuji
• Project Period (FY): 2015-10-21 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: リーグスポーツ / 総当たり戦 / クリンチナンバー / エリミネーションナンバー / 順位判定基準 / ワイルドカード / 非線形整数計画 / 多層線形計画 / 組合せ最適化 / プロ野球 / バスケットボール / 整数計画

Outline of Final Research Achievements

A general-purpose and efficient calculation framework of clinch and elimination numbers was developed in this research by extending mathematical models based on sets of scenarios. Perspectives were obtained for the possibility of high-speed computation under multiple tiebreaking criteria and for the development of a universal framework by componentization of various criteria including wildcard options.

Academic Significance and Societal Importance of the Research Achievements

本研究は現在の汎用最適化技術がどこまで実用的であるかという観点からの学術的な意義を主として追求するものであるが，元来は社会的な要請に基づいて始めたものであり，研究の過程で得られた直接的もしくは副次的な成果がスポーツ報道などに役立つことがあればよいと考えている．

Research Products

• [Int'l Joint Research] Zuse Institute Berlin(ドイツ)
• [Int'l Joint Research] 国立台湾大学応用数学科学研究所（iAMS）(台湾)
• [Int'l Joint Research] Zuse Institute Berlin(ドイツ)
• [Int'l Joint Research] 國立臺灣大學 應用數學科學研究所 (iAMS)(台湾)
• [Int'l Joint Research] Zuse Institute Berlin(ドイツ)
• [Int'l Joint Research] Zuse Institute Berlin(ドイツ)
• [Journal Article] Computation of clinch and elimination numbers in league sports based on integer programming (2019)
  • Author(s): S. Ito, Y. Shinano and C.-H. Wu
  • Journal Title: Book of Abstracts of the 2019 ISI-ISM-ASISS Joint Conference Volume: -
  • Open Access / Int'l Joint Research
• [Journal Article] Calculation of clinch and elimination numbers for sports leagues with multiple tiebreaking criteria (2019)
  • Author(s): S. Ito and Y. Shinano
  • Journal Title: 最適化：モデリングとアルゴリズム Volume: 31 Pages: 149-195
  • Int'l Joint Research
• [Journal Article] Calculation of clinch and elimination numbers for sports leagues with multiple tiebreaking criteria (2018)
  • Author(s): S. Ito and Y. Shinano
  • Journal Title: ZIB-Report Volume: 18-51
  • Open Access / Int'l Joint Research
• [Journal Article] Nonlinear integer programming formulations for calculating clinch/elimination numbers in league sports (2017)
  • Author(s): S. Ito and Y. Shinano
  • Journal Title: Abstracts of the 2nd ISM-ZIB-IMI MODAL Workshop on Mathematical Optimization and Data Analysis Pages: 1-2
  • Open Access / Int'l Joint Research
• [Presentation] Computation of clinch and elimination numbers in league sports based on integer programming (2019)
  • Author(s): S. Ito, Y. Shinano and C.-H. Wu
  • Organizer: 2019 ISI-ISM-ASISS Joint Conference
  • Int'l Joint Research
• [Presentation] Nonlinear integer programming formulations for calculating clinch/elimination numbers in league sports (2017)
  • Author(s): S. Ito and Y. Shinano
  • Organizer: 2nd ISM-ZIB-IMI MODAL Workshop on Mathematical Optimization and Data Analysis
  • Int'l Joint Research / Invited
• [Presentation] Nonlinear Integer programming formulations for calculating clinch/elimination numbers in league sports (2017)
  • Author(s): S. Ito
  • Organizer: 39th ISM Statistical Machine Learning Seminar
• [Presentation] 非線形整数計画法によるクリンチ／エリミネーションナンバーの計算 (2017)
  • Author(s): 伊藤 聡
  • Organizer: 広島大学組合せ最適化講演会
  • Invited
• [Presentation] B.LEAGUEにおけるクリンチナンバー等の算出 (2017)
  • Author(s): 伊藤 聡
  • Organizer: 統計数理研究所共同研究集会「最適化：モデリングとアルゴリズム」
• [Presentation] 響き合う人とデータ (2015)
  • Author(s): 伊藤 聡
  • Organizer: 数学・数理科学共同利用4研究機関合同市民講演会「万物共通の言葉『数学』」
  • Place of Presentation: 明治大学中野キャンパス
  • Year and Date: 2015-12-12
  • Invited
• [Remarks] Calculation of clinch and elimination numbers ...
  • URL: https://opus4.kobv.de/opus4-zib/frontdoor/index/index/searchtype/series/id/1/start/0/rows/10/facetNumber_institute/all/docId/7059
• [Remarks] Abstracts of the 2nd ISM-ZIB-IMI MODAL Workshop
  • URL: http://optimizationworkshop2017.zib.de/material/abstracts_booklet.pdf
• [Funded Workshop] 4th ISM-ZIB-IMI MODAL Workshop on Mathematical Optimization and Data Analysis (2019)
• [Funded Workshop] 3rd IMI-ISM-ZIB MODAL Workshop on Challenges in Real World Data Analytics and High Performance Optimization (2018)
• [Funded Workshop] 2nd ISM-ZIB-IMI MODAL Workshop on Mathematical Optimization and Data Analysis (2017)