[blind-chess] Elo Rating Overview
- From: "R Dinger" <rrdinger@xxxxxxxxxx>
- To: "chess" <blind-chess@xxxxxxxxxxxxx>
- Date: Sun, 30 May 2010 14:17:12 -0700
The Elo Rating System
The Elo rating system is a method for calculating the relative skill levels of
chess players. The method is named after its creator Arpad Elo a Hungarian
born American physics professor. Arpad Elo was a master-level chess player and
an active participant in the United States Chess Federation (USCF) from its
founding in 1939. The USCF adopted the Elo system in 1960 and FIDE in 1970.
The purpose of the Elo rating system is to provide an unbiased measure of your
chess skill; it is not an arbitrary reward system for winning games. Your
point score in a tournament is the reward based system.
Because your true chess skill level varies from day to daydepending on fatigue,
mood health and so on, the Elo method estimates your rating using a statistical
model based on past performance. Doctor Elo originally assumed performance
variations would follow a normal distribution, but experience in the USCF
resulted in changing to the logistical distribution. These mathematical
details are probably of little interest to most of you, but if you are
interested there is an article on Wikipedia explaining in more detail:
http://en.wikipedia.org/wiki/Elo_rating_system
Say we have two players both rated at 1500 and we call them A and B. The basic
idea is that if these two players play 100 games receiving one point for a win
and one half for a draw, after the 100 games their scores should be nearly
equal at 50 points each. The nearly equal score could be obtained by 100
draws; 25 wins for A, 25 wins for B and 50 draws; or any number of similar
combinations of wins, losses and draws. Since that would be expected, their
ratings are correct and do not need adjusting. This, by the way, is why nearly
equal players playing a draw does not change ratings.
But say player A wins 60 of the 100 points available. Then player A should
have a small rating adjustment upwards because his actual performance is
slightly better than player b. If player A wins 90 of the 100 points, then the
adjustment should be much greater because player A is playing much better than
player B.
So how is this adjustment calculated? First, each of the players in a specific
game has a win expectancy (E) based solely on the ratings of the two players.
The win expectancy is the decimal form of the probability of winning. The sum
of the two win expectancies totals 1, so our two 1500 rated players would have
win expectancies E = 0.5.
If player A is rated at 1600 and player B at 1500 (a 100 point rating
difference), player A has a win expectancy E = 0.64 and player B has E = 0.36.
A200 point difference results in win expectancies of 0.76 and 0.24 respectively.
Your rating is adjusted after each game based on your game score (S) and your
win expectancy (E). Your rating change is calculated by the formula:
Change = K * (S - E)
Where K is the so called K factor and is 32.0 for us normal beings and 16.0 for
master level players.
Since ratings are used to group players into various divisions of non-ladder
tournaments, it is important that ratings be as acurate as possible. That is
why I try to start new blind-chess players at their true rating rather than an
arbitrary value. So if new players have a rating somewhere else I will try to
convert to an approximation of our system.
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