I am looking for hints on how to estimate ratings for competitors
in an ongoing pairwise competition using R... my particular area of
interest being the game of Go, but the idea of identifying ratings
(on a continuous scale) rather than relative rankings seems easily
generalized to other competitions so I thought someone might be
studying something related already.
I presume the rating of a competitor would be best modeled as a random
variate on the rating scale, and an encounter between two
competitors would be represented by a binary result. Logistic regression
seems promising, but I am at a loss how to represent the model since
the pairings are arbitrary and not necessarily repeated often.
I have read about some approaches to estimating ratings for Go,
but they seem to involve optimization using assumed distributions
rather than model fitting which characterizes analysis in R.
Does any of this sound familiar? Suggestions for reading, anyone?
--
---------------------------------------------------------------------------
Jeff Newmiller The ..... ..... Go Live...
DCN:<jdnewmil at dcn.davis.ca.us> Basics: ##.#. ##.#. Live
Go...
Live: OO#.. Dead: OO#.. Playing
Research Engineer (Solar/Batteries O.O#. #.O#. with
/Software/Embedded Controllers) .OO#. .OO#. rocks...1k
Have you considered Bradley-Terry models? RSiteSearch("bradley",
"functions") just returned 31 hits for me.
Hope this helps.
Spencer Graves
Jeff Newmiller wrote:> I am looking for hints on how to estimate ratings for competitors
> in an ongoing pairwise competition using R... my particular area of
> interest being the game of Go, but the idea of identifying ratings
> (on a continuous scale) rather than relative rankings seems easily
> generalized to other competitions so I thought someone might be
> studying something related already.
>
> I presume the rating of a competitor would be best modeled as a random
> variate on the rating scale, and an encounter between two
> competitors would be represented by a binary result. Logistic regression
> seems promising, but I am at a loss how to represent the model since
> the pairings are arbitrary and not necessarily repeated often.
>
> I have read about some approaches to estimating ratings for Go,
> but they seem to involve optimization using assumed distributions
> rather than model fitting which characterizes analysis in R.
>
> Does any of this sound familiar? Suggestions for reading, anyone?
>
>
There is a substantial literature on 'statistics in sports' and pairwise comparisons are of obvious interest. Here is a starting point: http://www.amstat.org/sections/sis/ You might browse the newsletters posted there. You might enjoy: Bridging Different Eras in Sports by Scott M. Berry, Patrick D. Larkey, C. Shane Reese; Journal of the American Statistical Association, Vol. 94, 1999 or Baseball's All-Time Best Hitters: How Statistics Can Level the Playing Field by Michael J. Schell http://press.princeton.edu/titles/6550.html On Tue, 26 Dec 2006, Jeff Newmiller wrote:> I am looking for hints on how to estimate ratings for competitors > in an ongoing pairwise competition using R... my particular area of > interest being the game of Go, but the idea of identifying ratings > (on a continuous scale) rather than relative rankings seems easily > generalized to other competitions so I thought someone might be > studying something related already. > > I presume the rating of a competitor would be best modeled as a random > variate on the rating scale, and an encounter between two > competitors would be represented by a binary result. Logistic regression > seems promising, but I am at a loss how to represent the model since > the pairings are arbitrary and not necessarily repeated often. > > I have read about some approaches to estimating ratings for Go, > but they seem to involve optimization using assumed distributions > rather than model fitting which characterizes analysis in R. > > Does any of this sound familiar? Suggestions for reading, anyone? > > -- > --------------------------------------------------------------------------- > Jeff Newmiller The ..... ..... Go Live... > DCN:<jdnewmil at dcn.davis.ca.us> Basics: ##.#. ##.#. Live Go... > Live: OO#.. Dead: OO#.. Playing > Research Engineer (Solar/Batteries O.O#. #.O#. with > /Software/Embedded Controllers) .OO#. .OO#. rocks...1k > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >Charles C. Berry (858) 534-2098 Dept of Family/Preventive Medicine E mailto:cberry at tajo.ucsd.edu UC San Diego http://biostat.ucsd.edu/~cberry/ La Jolla, San Diego 92093-0717
I would start with elimination-by-aspects models: ?eba I would read the Tversky 1972 paper (cited on the help page for the eba() function), which is brilliant. Jeff Newmiller wrote:> I am looking for hints on how to estimate ratings for competitors > in an ongoing pairwise competition using R... my particular area of > interest being the game of Go, but the idea of identifying ratings > (on a continuous scale) rather than relative rankings seems easily > generalized to other competitions so I thought someone might be > studying something related already. > > I presume the rating of a competitor would be best modeled as a random > variate on the rating scale, and an encounter between two > competitors would be represented by a binary result. Logistic > regression > seems promising, but I am at a loss how to represent the model since > the pairings are arbitrary and not necessarily repeated often._____________________________ Professor Michael Kubovy University of Virginia Department of Psychology USPS: P.O.Box 400400 Charlottesville, VA 22904-4400 Parcels: Room 102 Gilmer Hall McCormick Road Charlottesville, VA 22903 Office: B011 +1-434-982-4729 Lab: B019 +1-434-982-4751 Fax: +1-434-982-4766 WWW: http://www.people.virginia.edu/~mk9y/
One approach that is already coded in R is the Bradley-Terry model
(found in the BradleyTerry package of all places).
This could be a good place to start if you want something quick, others
have given you references if you want more detail and/or control.
--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at intermountainmail.org
(801) 408-8111
-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Jeff Newmiller
Sent: Tuesday, December 26, 2006 10:54 AM
To: r-help at stat.math.ethz.ch
Subject: [R] Rating competitors
I am looking for hints on how to estimate ratings for competitors in an
ongoing pairwise competition using R... my particular area of interest
being the game of Go, but the idea of identifying ratings (on a
continuous scale) rather than relative rankings seems easily generalized
to other competitions so I thought someone might be studying something
related already.
I presume the rating of a competitor would be best modeled as a random
variate on the rating scale, and an encounter between two competitors
would be represented by a binary result. Logistic regression seems
promising, but I am at a loss how to represent the model since the
pairings are arbitrary and not necessarily repeated often.
I have read about some approaches to estimating ratings for Go, but they
seem to involve optimization using assumed distributions rather than
model fitting which characterizes analysis in R.
Does any of this sound familiar? Suggestions for reading, anyone?
--
------------------------------------------------------------------------
---
Jeff Newmiller The ..... ..... Go
Live...
DCN:<jdnewmil at dcn.davis.ca.us> Basics: ##.#. ##.#. Live
Go...
Live: OO#.. Dead: OO#..
Playing
Research Engineer (Solar/Batteries O.O#. #.O#. with
/Software/Embedded Controllers) .OO#. .OO#.
rocks...1k
______________________________________________
R-help at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.