# Rating systems for chess players

• jamalmunshi
In summary, chess rating systems, such as the Elo rating system, use a scoring procedure which assigns a score of 1 for a win, 0 for a loss, and 1/2 for a draw. This simplifies the mathematics of comparing players' performance, but also causes some information to be lost. Attempts to improve the Elo rating system through mathematical methods have been unsuccessful, and the only way to accurately measure chess performance is to use a two-dimensional measure. A proposed method for this has been posted online for feedback.
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

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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

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.

## 1. What is the purpose of a rating system for chess players?

A rating system for chess players is designed to provide a numerical representation of a player's skill level. It allows players to track their progress and compare themselves to other players, as well as determine fair match-ups in tournaments and other competitions.

## 2. How do rating systems for chess players work?

Rating systems for chess players use algorithms to calculate a player's rating based on their performance in previous matches. The specific calculation may vary depending on the system used, but it typically takes into account the rating of the opponent and the outcome of the game.

## 3. What are some common rating systems used for chess players?

Some popular rating systems for chess players include the Elo rating system, the Glicko system, and the US Chess rating system. Each system has its own unique algorithm and is widely used in different parts of the world.

## 4. Can a player's rating change over time?

Yes, a player's rating can change over time as they participate in more matches and their skill level improves or declines. The frequency of rating updates may vary depending on the system used, but most systems update ratings after every match.

## 5. Are rating systems for chess players accurate?

While rating systems for chess players provide a good estimation of a player's skill level, they are not perfect and can be influenced by factors such as the strength of opponents, the type of games played, and the consistency of a player's performance. However, these systems are continuously improving and are generally considered to be a reliable measure of a player's skill in chess.

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