I'm a guy who is interested in computer science and algorithms. I've spent a bit of time recently developing my own ranking system based on PageRank.
I'd like to compare it to the Elo system, in particular, the chess Elo ratings of the top 50 chess grandmasters.
I've got 2 datasets. All games played between the top 50 in 2012 and 2013. I've produced my own set of rankings (using a modified PageRank algorithm) based on the 2012 dataset, and I would like to see how well this ranking predicts the results of the 2013 dataset. I would also like to know how well Elo predicts the 2013 dataset, to see which ranking is more accurate.
I do not know how to do this in a meaningful way.
One problem I see is that a chess game between two players, P and Q, can be either a win, loss or draw. How do I use rankings to create some sort of distribution for the expected result of a game between P and Q that also accounts for draws? And even if I have such a distribution (eg P wins = 50%, Q wins 20%, draw = 30%) and I have a game played between P and Q that I want to predict, how do I select from this distribution fairly?
Any thoughts or insights would be helpful. If it helps, my ranking system will assign each player a value between 0-1, eg
- 0.05832816: Karjakin, Sergey
- 0.04895855: Grischuk, Alexander
- 0.04840682: Carlsen, Magnus
- 0.04751164: Ivanchuk, Vassily
- 0.04692380: Nakamura, Hikaru
- 0.04330322: Morozevich, Alexander
- 0.04281909: Aronian, Levon
