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.

中文翻译：

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论循环赛中胜者分数的分布

在经典的国际象棋循环赛中，每个$n$玩家与其他$n-1$玩家每人赢、平或输一局。获胜者奖励 1 分，平局奖励 1/2 点，失败奖励 0 分。我们感兴趣的是在${{n \choose 2}}$游戏之后与$n$玩家等级相关的分数分布，即最大分数、第二最大值等的分布。一般$n$的确切分布似乎无法获得；我们得到一个极限分布。