Elo積分於循環賽排名之應用

Abstract

循環賽是一種常見的比賽形式，其優點是所有參賽者之間都會進行一場比賽，因此能夠降低運氣的影響以及容易取得完整的排名。循環賽排名問題是在給定一個循環賽的結果，經過特定的排名方法給出一個最佳或是最能夠被接受的排名。Elo積分為一種對選手的評分方式，利用數值來代表選手間的相對能力，此積分常見於西洋棋比賽，它的特點是會根據比賽雙方的積分差距及比賽結果來更新兩位參賽者的積分。在本論文裡，我們試著將Elo積分應用於循環賽的排名中，解決了一些在原本常用的排名方法容易出現的問題，也根據觀察到的現象提出了猜想並且更深入的探討。

The round-robin tournament is a widely used format. One of its main advantages is that it allows players to compete against each other, reducing the impact of luck and providing a complete ranking for players. The round-robin ranking problem is to determine a ranking that is considered optimal or widely accepted among the players based on the tournament results. The Elo rating system uses numerical values to represent the relative skill level of players, providing a method for evaluating their strengths. This rating system, which is commonly used in chess tournaments, updates the ratings of two players based on differences in their ratings and the outcome of the match. In this thesis, we try to utilize the Elo rating system for ranking round-robin tournaments and resolving some of the challenges posed by the original methods. In addition, we provide conjectures based on our observations and ongoing research.