火箭目前已经20连胜位列西部第二，也许只有星期一的湖人才有可能阻止他们。连胜在一个成熟的联赛中是很有意思的现象，长期以来人们就知道连胜或者连败都不是偶然的，这两个过程都具有”自激励”特征：当一个队已经连胜N场，这个连胜会激励他们去取得第N+1场胜利，也就是说下一场获胜的概率增加了。根据这个理论，如果火箭下一场赢山猫取得21连胜，那么他们在星期一对湖人的比赛中获胜的概率将会大大高于两队平时对阵的胜负统计。

关于连胜，有什么特别的数学么？

物理学家一贯关心任何有意思的事件。波士顿大学物理系的 Sidney Redner (http://physics.bu.edu/~redner/) 最近连续做了关于美国棒球联赛中连胜和排名的数学分析，下一场报告将于3月31日在Santa Fe研究所举行。以下是报告摘要：

Seminar Abstract

Monday, March 31, 2008 • 12:15 PM • Medium Conference Room, SFI

Sidney Redner Boston University

Understanding Baseball Team Standings and Streaks
Can one understand the statistics of wins and losses of baseball teams, and also their winning and losing streaks? Streaks are particularly appealing because popular discussion often suggests that long consecutive-game winning and losing streaks are self-reinforcing. We apply the Bradley-Terry model of competition, which incorporates the heterogeneity of team strengths in a simple way, to quantify the average win/loss record of any team as a function of its rank in major-league baseball over the past century. We also show that the distribution of winning and losing streaks decays exponentially with streak length at a rate that is determined by the spread in team strengths. More importantly, we present evidence that long winning and losing streaks have a purely statistical origin. The data further shows that the past half-century of baseball has been more competitive than the preceding half-century.

美国棒球联盟赛程非常密集（每个队要打162场常规赛），比赛比NBA（每队打82场）要多很多，因此提供了更多的数据。这篇摘要说，连胜的概率指数分布：如果 f(N) 是连胜或者连败 N 场的概率，那么 f(N)~N^γ. 其中的γ<0由各球队实力分布决定。这是一个很有意思的结果，因为如果比赛胜负按照实力来随机决定，N连胜的概率应该差不多正比于 p^N，其中p是这个球队取胜一场的平均概率。显然当N足够大，从N连胜到N+1连胜，这个self-reinforcing 模型预言的可能性比随机模型要高得多。 另一个结果，"More importantly, we present evidence that long winning and losing streaks have a purely statistical origin." 我没听报告不知道什么意思。这个研究同时显示，过去50年棒球联赛的竞争性比上更一个50年要激烈。 仅仅通过分析比赛数据，而不用专门看任何一场具体的比赛，就能分析出来这么多东西。这个研究很像 《Freakonomics》这本书里提到的只从比赛胜负统计分析出日本相扑比赛中的造假行为很类似。