Re: st: Ranking derived from sports scores

[Phil Schumm <pschumm@uchicago.edu>]

On Jan 5, 2011, at 10:48 AM, Jeff Davies wrote:
> I am currently evaluating Stata as a suitable tool for generating  
> numerical rankings for players as a result of head-to-head  
> competition that produces a comparative score (7-4). Most players  
> meet each other in competitive games on a regular basis but there  
> are others who participate only once or rarely. The rankings should  
> be weighted in favor of consistency and more recent performance.
>
> I am not a statistician but have a sound understanding of computer  
> programming and database systems. Any assistance that anyone can  
> offer to point me in the right direction in terms of technique and  
> determining the most suitable tool would be very much appreciated.


A model often used for this type of thing is the Bradley-Terry model:

    http://en.wikipedia.org/wiki/Pairwise_comparison

which is also discussed in most texts on categorical data analysis.   
The model can be fit using certain commands in Stata that perform  
logistic regression, e.g.,

    http://www.ats.ucla.edu/stat/stata/examples/icda/icdast9.htm

(Section 9.6.1).  Agresti's book Categorical Data Analysis has a nice  
introductory discussion of the Bradley-Terry model, and the literature  
is full of applications and various extensions that have been developed.


-- Phil

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