I gave a talk last month at the New York Open Statistical Programming Meetup on ranking systems, specifically applied to the NFL. You can find slides, code, and an IPython notebook which contains most of the information. I encourage you to look at the slides, which I spent a lot of time on. They contain two embedded interactive visualizations. I did get my Super Bowl prediction wrong, though.
There were about 200 attendees, but unfortunately there is no video of the talk. Thanks to everyone who came; it was incredibly fun for me.
The talk was mostly a review/comparison of different methods:
- Pythagorean wins
- Eigenvector methods
- the Bradley-Terry-Luce model
- optimal rankings
The last one warrants more explanation. I had previously reviewed the optimal descriptive ranking problem and my solution. It’s a fascinating application of graph theory to a problem that most people wouldn’t consider to be graph-theoretic. Once the ranking problem is posed as a topological sort of a graph which contains cycles, it’s easy to describe an exact (if non-unique) solution as well as find an algorithm to approximate it. The results are quite stunning: a 10+% increase in the number of correctly described games from the other models.