# How to get started with rating and ranking based on pairwise competition data?

I'm interesting in learning about how to rate and rank individuals in a group who only interact/compete in a pairwise fashion (i.e., systems like the ELO rating system for chess).

• Are there are any go-to methods or more accurate and advanced methods out there?
• Are there any R packages that make implementation easy?
• Are there methods that can use auxiliary information as well as the outcome of a match/game?
• Are there methods that can better use the information of winning margin as opposed to dichotomous win/lose?
• What should I be looking for in the literature?

## 4 Answers

Regarding "how to do it in R", the prefmod package http://cran.r-project.org/web/packages/prefmod/index.html is meant for preference analysis with paired comparisons, rankings and ratings. It fits Bradley-Terry models and pattern models with object and subject covariates. See my answer here How to fit Bradley–Terry–Luce model in R, without complicated formula? for a short intro, or this paper http://www.jstatsoft.org/v48/i10 for more info.

• Also, it is slightly tedious, but not terribly difficult to fit BT and related models "manually" in $R$. – cardinal Jun 23 '12 at 17:33

I just finished a pretty good book on that subject. It discusses ELO as well as many other ranking methods like Massey, Colley, and Keener's. Most of the methods in the book use sports matches as the example and use both win/loss and margin of victory as inputs.

• A review of this book by @Xi'an. – user10525 Jun 23 '12 at 17:35

Since asking this question, I've found I've had lots of success with the PlayerRatings package for R. It makes creating ELO/Glicko and the authors own method of performance ratings very easy.

This book does not work with margins but provides the theory of rank teams based on paired comparisons. The Method of Paired Comparison by Herbert A. David http://www.amazon.com/Method-Paired-Comparisons-Statistical-Monograph/dp/0852640137/ref=sr_1_1?s=books&ie=UTF8&qid=1340424897&sr=1-1&keywords=The+method+of+paired+comparisons

Regarding victory margins I beleive some of the computer methods used for the BCS combine paired comparison methods such as the Bradley-Terry model with victory margins.

• Cheers I'll look in to them. – dcl Jun 23 '12 at 5:09
• @dcl If you are interested on Bradley-Terry models, two useful R packages are BradleyTerry and BradleyTerry2 created by David Firth. – user10525 Jun 23 '12 at 10:15
• I wanted to add that the use of victory margins in rankings is controversial because it can be more a factor of strategy than a true measure of skill. Some coaches will not let their teams roll up the score after gettinga comfortable lead while others may deliberately roll it up to help with their rankings. This was very common in college football. – Michael R. Chernick Jun 23 '12 at 14:17
• The David text is a very good classical one to look at. The BCS has not allowed margin of victory to be incorporated in the computer rankings for several years now. – cardinal Jun 23 '12 at 14:23
• It would be interesting to see how these methods that don't involve winning margin compare to the more modern systems designed for chess and other games, ie Glicko, chessmetrics and trueskill. – dcl Jun 24 '12 at 2:11