## Monday, September 8, 2014

### A Few More Papers

As usual, all these papers are available in the Papers archive.

[Trono 2007] Trono, John A., "An Effective Nonlinear Rewards-Based Ranking System," Journal of Quantitative Analysis in Sports, Volume 3, Issue 2, 2007.

Trono is very concerned about the NCAA football polls and with formulating a rating system that will closely match those polls.  I'm not exactly sure what utility that provides -- surely if I want to know what the polls say I can just look at them?  That issue aside, his description of his ranking system is vague and confusing -- I came away with no good understanding of how it worked or how to implement it.

[Minton 1992] Minton, R. "A mathematical rating system." UMAP Journal 13.4 (1992): 313-334.
This is a teaching module for undergraduate mathematics that illustrates basic linear algebra through application to sports rating.  The ratings systems developed are simple systems of linear equations based upon wins, MOV, etc.  The systems are very simple, but this is a clear and detailed introduction to some basic concepts.

[Redmond 2003] Redmond, Charles. "A natural generalization of the win-loss rating system." Mathematics magazine (2003): 119-126.
Redmond presents a rating system based upon MOV that includes a first-generation strength of schedule factor. It isn't extremely sophisticated, but makes a nice follow-on to [Minton 1992].

[Gleich 2014] Gleich, David. "PageRank Beyond the Web," http://arxiv.org/abs/1407.5107.

This is a thorough and well-written survey of the use of the PageRank algorithm.  Gleich provides clear, non-formal descriptions of the subject but also delves into the mathematical details at a level that will require some knowledge to understand.  There is a section on PageRank applied to sports rankings, and Gleich also shows that the Colley rating is equivalent to a PageRank.  Required reading for anyone interested in applying PageRank-type algorithms.

[Massey 1997] Massey, Kenneth. "Statistical models applied to the rating of sports teams." Bluefield College (1997).
Kenneth Massey's undergraduate thesis is required reading for anyone interesting is sports rating systems.  He covers the least-squares and maximum-likelihood ratings that form the basis of the Massey rating system.