[net.sport] probability models for tennis scoring systems

desj@brahms (David desJardins) (10/23/86)

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

osmigo1@ut-ngp.UUCP (Ron Morgan) (10/30/86)

In article <50@cartan.Berkeley.EDU> desj@brahms (David desJardins) writes:
>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

I'm not sure I agree with this. As anybody who's played seriously (!) knows,
there are a LOT of factors contributing to a victory than points. Tennis is
probably the most psychological game in the world, for example. A championship-
caliber player can be two sets behind and muster up the self-control and drive
to pull up and ahead and go on to win (jeez, I wish I could do that). A
lesser player tends to be psychologically cowed into concession. Uhoh.....I
made a mistake here... actually, I'm disagreeing with the guy who suggested
the system with the *greatest* magnification. At any rate two identical
scoring situations can (among many, many, other things) have drastically 
different results in terms of how the game progresses, thus rendering
statistical, pragmatic analyses somewhat inconclusive.

Ron Morgan

(whackTHUMPwhackTHUMPwhackTHUMP)

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