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From: desj@brahms (David desJardins)
Newsgroups: sci.math,sci.math.stat,net.sport
Subject: Re: probability models for tennis scoring systems
Message-ID: <50@cartan.Berkeley.EDU>
Date: Wed, 22-Oct-86 20:14:13 EDT
Article-I.D.: cartan.50
Posted: Wed Oct 22 20:14:13 1986
Date-Received: Thu, 23-Oct-86 18:52:23 EDT
References: <1715@emory.UUCP>
Sender: daemon@cartan.Berkeley.EDU
Reply-To: desj@brahms (David desJardins)
Followup-To: sci.math.stat,net.sport
Organization: Math Dept. UC Berkeley
Lines: 23
Keywords: probability, tennis, markov chains
Xref: mnetor sci.math:48 sci.math.stat:9 net.sport:639

In article <1715@emory.UUCP> riddle@emory.UUCP (Larry Riddle) writes:
>[...]  However, if one player has a small advantage over the other in
>serving efficacy, then this advantage gets magnified when considering
>the entire set.  Which scoring system produces the least magnification?
>Interestingly, the 9 point and the No-Ad systems are "best" in this
>respect.

   This has nothing to do with mathematics, but isn't the system that
produces the *greatest* magnification "best"?  Presumably the objective
is to determine the better player, so it seems desirable to have the
most sensitive possible tool for doing that.

   As for the statistics, I hope that you took into account the length
of the sets resulting from the various scoring systems.  Otherwise, all
you have discovered is that in longer sets the inferior player's chance
of winning is reduced (hardly a revelation!).  The question you probably
want to ask is something like, "Given a certain average number of points
to be played, which scoring system best uses those points to discriminate
between the players?"  Figuring out exactly what question to ask and how
to answer it is actually a fairly interesting problem -- I'm not a
statistician, so I'll leave it to them to discuss if they wish.

   -- David desJardins