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Proposed Statistical Model for Scoring and Ranking Sport Tournaments: Racquetball, Squash, and Badminton

المصدر: مجلة جامعة جيهان أربيل للعلوم الإنسانية والاجتماعية
الناشر: جامعة جيهان أربيل
المؤلف الرئيسي: Jameel, Abbood M. (Author)
المجلد/العدد: مج3, ع1
محكمة: نعم
الدولة: العراق
التاريخ الميلادي: 2019
الشهر: يونيو
الصفحات: 15 - 19
ISSN: 2709-8648
رقم MD: 1430701
نوع المحتوى: بحوث ومقالات
اللغة: الإنجليزية
قواعد المعلومات: EduSearch, HumanIndex
مواضيع:
البطولات الرياضية | المقارنات الزوجية | الفرق الرياضية
كلمات المؤلف المفتاحية:
Paired Comparisons | Ranking | Rating on a Scale | Scoring | Sport Tournaments Unbalanced Incomplete Design
رابط المحتوى:

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المستخلص: A class of modification is proposed for calculating a score for each player/team in unbalanced, incomplete paired-comparison sports tournaments. Many papers dealing with balanced incomplete paired-comparison sports tournaments with at most one comparison per pair have appeared since 1950. However, little has been written about unbalanced situations in which the player/the team (object) (j) plays unequal number of games against the player/the team (m) in a tournament, and the results of all games can be summarized in a Win-Lose matrix Y={Yjm}, where Yjm=1, 0, 1/2, respectively, according to the player or the team (j) wins, losses or draws against the player or the team (m). Published papers by Ramanujacharyulu (1964), Cowden (1975), and David (1988) have concentrated on the problem of converting the results of unbalanced incomplete paired-comparison tournaments into rank with little consideration of the main relative ability on each player or team. We suggest (modification) other way of quantifying the outcomes of the games/tournaments, in particular, ratings on a scale, 0–5, 1–10, ect. It is important to consider not only the vector Vj(d) or the vectors Sj, in scoring and ranking the k teams in such tournaments but also the vector Zj, where Zj=Sj+SjRj, to take into account the ratio of the relative ability of each team (Rj). The proposed modification helps to introduce these methods for use in comparisons/games (tournaments), where the player/team are quantified on a special scale, for example, 0–5 and 1–10. We conclude the following: The scores stabilized to three decimal places at iteration two in Cowden’s method Vj(d) Table III. The scores stabilized to three decimal places at iteration two in David’s method Sj, and its modification Zj. The proposed modification (Zj) has the advantage of removing ties from David’s method (Sj), and hence, it is the best method.
ISSN: 2709-8648

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