How Does Scoring Simplify Chess Rating Systems?

[jamalmunshi]

All chess rating systems including the Elo rating system are based on a procedure called "scoring" which assigns a score of 1 for a win, 0 for a loss, and 1/2 for a draw. This procedure reduces the trinomial nature of chess game outcomes to a binomial variable and thereby greatly simplifies the mathematics of comparing the performance of chess players. Of course there is no free lunch in math and so this simplification is achieved at a cost because scoring causes some chess game outcome information to be lost and no amount of mathematical wizardry downstream can recover this information. The extensive effort by many to improve the Elo rating system with mathematical genius is for naught. The only way to improve chess performance measurement is to remain true to the trinomial nature of chess game outcomes which has two degrees of freedom. The way to do that is to use a two-dimensional measure of chess performance. I wrote a paper proposing such a method and posted it online for comments. Here is the link to the download page.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2488369
Your comments appreciated.

 

[Matterwave]

Isn't 1 for win, 1/2 for draw, 0 for loss, still trinomial? After all 1, 1/2, and 0 are 3 different possible values. o.o

 

[jamalmunshi]

The scoring procedure assigns a value of score=1 for a win, score=0 for a loss, and score = 0.5 for a draw. If N chess games are played and the player wins W games, loses L games and D games end in draw, then the player scores (2W+D)/2 and the opponent scores (2L+D)/2. Note that N = W+L+D and that (2W+D)/2 + (2L+D)/2= (2W+D+2L+D)/2 = (2W+2L+2D)/2 = W+L+D = N. The two scores add up to the total number of games played. This means that when the scores are divided by N, the two fractional scores add up to unity. Therefore, when chess game outcomes are converted into scores, chess loses a dimension and is reduced from a trinomial process to a binomial process.