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From: riddle@emory.UUCP (Larry Riddle)
Newsgroups: sci.math,sci.math.stat
Subject: probability models for tennis scoring systems
Message-ID: <1715@emory.UUCP>
Date: Fri, 10-Oct-86 22:22:18 EDT
Article-I.D.: emory.1715
Posted: Fri Oct 10 22:22:18 1986
Date-Received: Wed, 22-Oct-86 22:50:57 EDT
Organization: Math & Computer Science, Emory University, Atlanta
Lines: 26
Keywords: probability, tennis, markov chains
Xref: mnetor sci.math:43 sci.math.stat:5

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.  My basic assumption was that each player has a fixed
probability of winning a point when that player serves.  I then derived
formulas for computing the probabilities of winning a set under the
four scoring systems.  Of course, if each player has the same
probability of winning a point when serving, then the probability of
winning a set should be 1/2 for each (it makes a difference with the 9
point tiebreaker which player serves first, so there I average the
probabilities obtained for when each player is the first server of the
set).  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.

If anyone is interested in seeing a copy of the paper, just sent me mail
and I will send you one.