On the distribution of winners' scores in a round-robin tournament. Issue 4 (October 2022)

• Record Type: Journal Article
• Authors: Malinovsky, Yaakov
• Is Part Of: Probability in the engineering and informational sciences. Volume 36:Issue 4(2022)
• Page Start: 1098
• Page End: 1102
• Publication Date: 2022-10
• Subjects: Extremes -- Negative correlation; 62G32 -- 05C20; Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S0269964821000267
• Languages: English
• ISSNs: 0269-9648

Abstract

Abstract : In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested in the distribution of the scores associated with ranks of $n$ players after ${{n \choose 2}}$ games, that is, the distribution of the maximal score, second maximum, and so on. The exact distribution for a general $n$ seems impossible to obtain; we obtain a limit distribution.