Optimization of the Tournament Format for the Nationwide High School Kyudo Competition in Japan

Presented in Mathsport International 2025 (https://math.uni.lu/midas/events/mathsports2025/)

Abstract: This study proposes an optimized format for a nationwide high school Kyudo tournament in Japan, addressing the challenges in balancing fairness, educational value, and practical constraints. Kyudo’s binary scoring system makes skill assessment difficult with limited attempts. Using historical data, we estimated the participants’ skill distributions and conducted simulations to evaluate tournament formats. The proposed format increases the number of preliminary attempts from four to six and removes the semifinals, reducing the variability in total attempts while maintaining comparable ranking accuracy. This ensures fairness, sufficient opportunities for skill demonstration, and alignment with Kyudo’s traditional and educational values, offering a robust framework for student-focused competition.

Transcript

1. Optimization of the Tournament Format for the Nationwide High School Kyudo Competition in Japan Kazu Hashimoto, *Eiji Konaka (Meijo University, JAPAN)
2. Kyudo(弓道) Mathsport International 2025 @ Luxembourg Pierre-Yves Beaudouin / Wikimedia Commons, CC 表示-継承 4.0, https://commons.wikimedia.org/w/index.php?curid=35657342による Do you know about “kyudo” (Japanese archery)?
3. Popularity among High School Students • Sport originated in Japan • Few quantitative research • How popular? • 7th popular sport among All Japan High School Athlete Federation • 65,000 students are registered Mathsport International 2025 @ Luxembourg Its tournament format is worth researching.
4. Research summary Background, Objective, and Result • Kyudo • High-school competition • Proposal: Improved format • Increase students’ opportunity • Improve skill estimation accuracy Mathematical elements • Estimate probability distribution of students’ skill • Propose a performance index for tournament format • Numerical experiment Mathsport International 2025 @ Luxembourg
5. Contents • Background • Objective • Data • Method • Estimation of skill distribution • Performance index • Results and discussions Mathsport International 2025 @ Luxembourg [PhotoAC]
6. Contents • Background • Objective • Data • Method • Estimation of skill distribution • Performance index • Results and discussions Mathsport International 2025 @ Luxembourg [PhotoAC]
7. Background: Kyudo and target sports • Research subject: Kyudo • Traditional Japanese Archery • Target sports • Equipment: bow/gun • Target: static/moving • Criteria: distance/binary • Discipline: Single/Combined Mathsport International 2025 @ Luxembourg Sport Target Scoring Criteria Kyudo Static Binary Archery Static Distance Rifle Static Distance Clay shooting Moving Binary Laser run (in Modern Pentathlon) Static Binary Shooting (in Biathlon) Static Binary Kyudo is different from other target sports
8. Background: Kyudo and target sports • Research subject: Kyudo • Kyudo is different from other (single) target sports • Binary scoring criteria • Binary=Hit or not • Pros: simple equipment and tournament operations • Cons: Estimating players' skills is difficult. Sport Target Scoring Criteria Kyudo Static Binary Archery Static Distance Rifle Static Distance Clay shooting Moving Binary Laser run (in Modern Pentathlon) Static Binary Shooting (in Biathlon) Static Binary Mathsport International 2025 @ Luxembourg
9. Sportification of kyudo :Competition for high-school students • Sportification in modern era • All Japan High School Kyudo Tournament • Regulation • Minimum num. of shots: (only) 4 • Preliminary -> Semifinals -> Finals Mathsport International 2025 @ Luxembourg 令和６年度 全国高校弓道選抜 個人予選 (YouTube)
10. Sportification of kyudo :Competition for high-school students • Regulation • Minimum num. of shots: (only) 4 • Preliminary -> Semifinals -> Finals • Issues • Skill measurement accuracy • The format increases the chance of upsets. • Opportunities for students • Total cost Mathsport International 2025 @ Luxembourg 令和６年度 全国高校弓道選抜 個人予選 (YouTube)
11. Research summary Background, Objective, and Result • Kyudo • High-school competition • Proposal: Improved format • Increase students’ opportunity • Improve skill estimation accuracy Mathematical elements • Estimate probability distribution of students’ skill • Propose a performance index for tournament format • Numerical experiment Mathsport International 2025 @ Luxembourg
12. Contents • Background • Objective • Data • Method • Estimation of skill distribution • Performance index • Results and discussions Mathsport International 2025 @ Luxembourg [PhotoAC]
13. Data and regulations • 5 tournaments / 982 student (492 men, 490 women) / 3928 shots • Regulation • Preliminary: 3 out of 4→Semifinal • Semifinal: 3 out of 4→Final • Final: Izume (shootout) • Notation: “3/4-3/4-Izume” Mathsport International 2025 @ Luxembourg
14. Contents • Background • Objective • Data • Method • Estimation of skill distribution • Performance index • Results and discussions Mathsport International 2025 @ Luxembourg [PhotoAC]
15. • Skill parameter 𝑟𝑖 →Beta distribution • 𝑟𝑖 ∈ 0,1 , unimodal • 𝑟𝑖 ~𝑓 𝑥 𝛼, 𝛽 = 𝐶𝑥𝛼−1 1 − 𝑥 𝛽−1 • Mean Τ 𝛼 𝛼 + 𝛽 =Sample mean • Select 𝛼 • →Sampling 𝑟1 , 𝑟2 , ⋯ from 𝑓 • →Simulate 4 shots • →Calculate distance between samples Mathsport International 2025 @ Luxembourg Estimation of skill distribution
16. Estimation of skill distribution • Skill parameter 𝑟𝑖 →Beta distribution • 𝑟𝑖 ∈ 0,1 , unimodal • 𝑟𝑖 ~𝑓 𝑥 𝛼, 𝛽 = 𝐶𝑥𝛼−1 1 − 𝑥 𝛽−1 • Mean Τ 𝛼 𝛼 + 𝛽 =Sample mean • Select 𝛼 • →Sampling 𝑟1 , 𝑟2 , ⋯ from 𝑓 • →Simulate 4 shots • →Calculate distance between samples Mathsport International 2025 @ Luxembourg
17. Mathsport International 2025 @ Luxembourg Select parameters Sampling Simulation Calc. distance
18. Performance index for tournament format • Minimum shots • Opportunities for students • Official:4→Increase! • Total shots • Alternative index of running cost • Skill estimation accuracy • Formulation • 𝑖: rank in skill parameter • Rank(𝑖): rank in tournament • Skilled students end up in lower ranks are penalized heavily. Mathsport International 2025 @ Luxembourg 𝐽𝑟𝑎𝑛𝑘 = σ𝑖=1 𝑁 log2 𝑖 − log2 Rank 𝑖 2
19. Contents • Background • Objective • Data • Method • Estimation of skill distribution • Performance index • Results and discussions Mathsport International 2025 @ Luxembourg [PhotoAC]
20. Estimation result of skill distribution Mathsport International 2025 @ Luxembourg Estimated Beta distribution Men: ( 𝛼, 𝛽 = (5.16, 3.71))
21. Performance indices :Total shots and Skill estimation performance Min. Cost* J** 3/4-3/4- Izume (Official) 4 M M 5/6-Izume 6 M G 6/8-Izume 8 H G Izume 1 L P Mathsport International 2025 @ Luxembourg * High/Medium/Low **Good/Moderate/Poor
22. Performance indices :Total shots and Skill estimation performance Min. Cost* J** 3/4-3/4- Izume (Official) 4 M M 5/6-Izume 6 M G 6/8-Izume 8 H G Izume 1 L P Mathsport International 2025 @ Luxembourg Two rounds/6 shots Cost→ Opportunity⤴ Skill estimation⤴
23. Performance indices :Total shots and Skill estimation performance Min. Cost* J** 3/4-3/4- Izume (Official) 4 M M 5/6-Izume 6 M G 6/8-Izume 8 H G Izume 1 L P Mathsport International 2025 @ Luxembourg Two rounds/6 shots Cost→ Opportunity⤴ Skill estimation⤴ Our final proposal 5/6-Izume
24. Research summary Background, Objective, and Result • Kyudo • High-school competition • Proposal: Improved format • Minimum num. of trials⤴ • Total num. of trials→ • Estimation accuracy⤴ Mathematical elements • Estimate probability distribution of students’ skill • Propose a performance index for tournament format • Numerical experiment Mathsport International 2025 @ Luxembourg
25. Thank you! Eiji Konaka (konakalab) Meijo University, JAPAN konakalab@X (a.k.a. Twitter)
27. Kyudo and Archery Mathsport International 2025 @ Luxembourg Score; 0-10 Kyudo Archery 28[m] Distance 70[m] 36[cm] Target size 122[cm] No Supporting device Yes Binary Scoring criteria Distance (0-10) Stripes are irrelevant to the score. Low res.
28. Mathsport International 2025 @ Luxembourg Cost J 3/4-3/4- Izume (Official) M M 5/6- Izume M G 6/8- Izume H G Izume L P Best Our final proposal 5/6-Izume
29. Data and regulations • 5 tournaments / 982 student (492 men, 490 women) / 3928 shots • Regulation • Preliminary: 3 out of 4→Semifinal • Semifinal: 3 out of 4→Final • Final: Izume (shootout) • Notation: “3/4-3/4-Izume” Mathsport International 2025 @ Luxembourg
30. Data and regulations • 5 tournaments / 982 student (492 men, 490 women) / 3928 shots • Regulation • Preliminary: 3 out of 4→Semifinal • Semifinal: 3 out of 4→Final • Final: Izume (shootout) • Notation: “3/4-3/4-Izume” Mathsport International 2025 @ Luxembourg