Faculty of Information Sciences and Engineering, University of Canberra , Australia.
Physics Department, Faculty of Science, University of Sydney , Australia.
J Sports Sci Med. 2006 Dec 15;5(4):561-6. eCollection 2006.
The objective of this paper is to use data from the highest level in men's tennis to assess whether there is any evidence to reject the hypothesis that the two players in a match have a constant probability of winning each set in the match. The data consists of all 4883 matches of grand slam men's singles over a 10 year period from 1995 to 2004. Each match is categorised by its sequence of win (W) or loss (L) (in set 1, set 2, set 3,...) to the eventual winner. Thus, there are several categories of matches from WWW to LLWWW. The methodology involves fitting several probabilistic models to the frequencies of the above ten categories. One four-set category is observed to occur significantly more often than the other two. Correspondingly, a couple of the five-set categories occur more frequently than the others. This pattern is consistent when the data is split into two five-year subsets. The data provides significant statistical evidence that the probability of winning a set within a match varies from set to set. The data supports the conclusion that, at the highest level of men's singles tennis, the better player (not necessarily the winner) lifts his play in certain situations at least some of the time. Key PointsUsing grand slam men's singles data, the probability of winning a set has been shown to vary from set to set.The data provides statistical evidence that the better player (not necessarily the winner) in some matches is able to lift his play in certain situations. This result gives encouragement to the better player when in difficulties in a match.The authors found no evidence that the weaker player was able to lift his play. The weaker player, when ahead in a match, should be on his guard for his opponent to have a real capacity to lift his game.
本文旨在利用男子网球最高水平的数据，评估在一场比赛中，两名选手每一盘获胜的概率是否存在恒常这一假设是否成立。数据来源于 1995 年至 2004 年 10 年间所有 4883 场大满贯男子单打比赛。每一场比赛都根据最终获胜者的胜负（W 胜或 L 负）（在第一盘、第二盘、第三盘等）进行分类。因此，比赛有从 WWW 到 LLWWW 的多个类别。该方法涉及将几种概率模型拟合到上述十种类别的频率上。有一个四盘的类别被观察到比其他两个类别出现的频率显著更高。相应地，几个五盘的类别比其他类别出现的频率更高。当将数据分为两个五年子集时，这种模式是一致的。数据提供了显著的统计证据，表明在一场比赛中赢得一盘的概率从一盘到另一盘有所不同。数据支持这样的结论，即在男子单打网球的最高水平上，更好的选手（不一定是获胜者）在某些情况下至少在某些时候能够提高自己的比赛水平。要点：使用大满贯男子单打数据，已经证明赢得一盘的概率在每一盘比赛中都有所不同。数据提供了统计证据，表明在某些比赛中，更好的选手（不一定是获胜者）在某些情况下能够提高自己的比赛水平。这一结果在选手处于困境时给予了他们鼓励。作者没有发现较弱的选手能够提高自己比赛水平的证据。较弱的选手在比赛中领先时，应该警惕对手有真正提高比赛水平的能力。
