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From: wjh@wayback.UUCP (Bill Hery)
Newsgroups: sci.math,sci.math.stat
Subject: Re: probability models for tennis scoring systems
Message-ID: <984@wayback.UUCP>
Date: Thu, 23-Oct-86 09:57:40 EDT
Article-I.D.: wayback.984
Posted: Thu Oct 23 09:57:40 1986
Date-Received: Fri, 24-Oct-86 08:21:27 EDT
References: <1715@emory.UUCP>
Organization: AT&T Bell Labs, Whippany, NJ
Lines: 32
Keywords: probability, tennis, markov chains
Xref: watmath sci.math:50 sci.math.stat:10



>  Last fall I posted a request for "real world" applications of stochastic
>  processes that I could use in a course I was going to teach.
>  Many people sent me suggestions, one of which was an example in
>  Kemeny and Snell's book on finite Markov chains in which they consider
>  a game of tennis as a simple random walk (when the score reaches
>  deuce).  Well, the students really liked this example, so this summer,
>  just for fun, I spent some time expanding upon their model and wrote
>  a short paper comparing the four common scoring systems currently in
>  use in tennis - the original rules (win by two games), the 9 point
>  tiebreaker, the 12 point tiebreaker, and the Van Alen No-Ad scoring
>  systme....
>  .................Which scoring system produces the least magnification?
>  Interestingly, the 9 point and the No-Ad systems are "best" in this
>  respect.
>  

I would think that the best is the one that produces the MOST
magnification; i. e., the best way to score tennis is the way in
which when player A is only a little better than player B, then A has
a very high probability of winning.  The best method is thus the best
dicriminator between players.  If I remember correctly, Kemeny and Snell 
also did an analysis for the world series format (win 4 out of 7),
and showed that it was a much worse discriminator than even a single
game of tennis with the regular deuce rules.

Also, please email me a copy of the paper you wrote.  I couldn't
reach you via the paths you posted.

Bill Hery
ihnp4!bonnie!wayback!wjh