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##

Statistical Relative Strength (RS)

To further analyze performance and learning within the Tron system, we employ
a paired-comparisons maximum likelihood model.

Paired comparisons models are statistical methods that estimate the relative
strengths or preferences of a group of participants. The ``Elo ratings''
for Chess, conceived by A. Elo [34] are one example of such method.
Chess poses some problems akin to ours, as one would like to ask, say, ``was
Capablanca better than Fisher?'' Even if the two players did play each other,
one might not have been at the peak of his abilities at the time. All the information
from opponents they played in common, and how well they performed, should be
put together. We have followed the maximum likelihood approach described by
Joe [73], applied by the author to the Chess problem among others.

Elo's model -- used today for many other games, including the so-called ``game
ladders'' -- assigns a low ranking to a novice, who can slowly climb up as
she wins games against other ranked players. Maximum likelihood statistics such
as Joe's are better suited to our problem because they compute the most feasible
ranking for all players, without presuming that young ones are bad.

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** Up:** Results
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*Pablo Funes*

*2001-05-08*