INTRODUCTION
We base our ratings on the Chess Express Ratings Inc. method ( aka "CXR"). This rating system was developed by its president, Russell Mollot, in the early 1980's, and has been adopted by chess clubs and scholastic chess organizations across North America.
The CXR system has been thoroughly tested over many years, thousands of players, and tens of thousands of games.
BASIC PREMISE
The idea behind CXR ratings is that you gain points for good performance and lose points for bad performance.
BASIC DEFINITIONS
Rated Player: A player who has an established CXR rating.
Provisionally-rated Player: A player who has a tentative rating based on an estimated initial rating and the results of less than 5 games against Rated Players.
RATING FORMULAS
There are three basic situations when two players meet over-the-board (certain adjustments are made for scholastic ratings, which are discussed later in this document). These 3 situations are:
I. Both players are RATED
II. Neither player is RATED (both are PROVISIONALLY-RATED)
III. One player is RATED and the other is PROVISIONALLY-RATED
For situations I and II, the following formula is used:
Formula 1: Rnew = Rold + (S x 21) + (Ropponent - Rold) / 25
where:
Rnew = the new rating for either player
Rold = his or her old (pre-game) rating
S = his or her SCORE for the game;
This is +1 for a WIN,
0 for a DRAW,
-1 for a LOSS
Ropponent = the pre-game rating of the opponent
EXAMPLE 1:
A player whose rating is 1500 defeats an opponent who is rated 1650.
Rnew = 1500 + (+1 x 21) + (1650 - 1500) / 25;
= 1500 + ( + 21 ) + 150 / 25
= 1500 + 21 + 6 = 1527
EXAMPLE 2:
A player who is provisionally-rated 1600 draws an opponent who is provisionally-rated 1400.
Rnew = 1600 + (0 x 21) + (1400 - 1600) / 25;
= 1600 + 0 + - 200 / 25
= 1600 - 8 = 1592;
EXAMPLE 3:
A player rated 1714 loses to an opponent rated 2007.
Rnew = 1714 + ( - 1 x 21) + (2007 - 1714) / 25;
= 1714 + ( - 21 ) + ( 293 ) / 25
= 1714 + - 21 + 12
= 1714 - 9 = 1705
NOTE: When the difference in the ratings of the two players is very large ( e.g. 500 points or more) the formula needs the following three overriding RULES -- otherwise, for example, a 2100-rated player could LOSE 3 points for defeating a 1500-rated opponent!
OVERRIDING RULES:
(for games where Formula 1 is used)
RULE R1: THE WINNING PLAYER ALWAYS MUST GAIN AT LEAST 2 POINTS.
RULE R2: THE LOSING PLAYER ALWAYS MUST LOSE AT LEAST 2 POINTS.
RULE R3: NEITHER PLAYER MAY GAIN OR LOSE MORE THAN 41 POINTS.
In normal tournaments and matches, the rating difference between opponents will rarely exceed 400 points.
For situation III, where one player is rated and the other is only provisionally-rated, Formula 2 is used for the rated player, and Formula 3 for the provisionally-rated player.
Formula 2: Rnew = Rold + (S x 6) + (Ropponent - Rold) / 100
This has the effect of giving the game less weight than normal because the rating of the opponent has less statistical significance, since it is based on few games.
Formula 3: Rnew = (4 / 5) x Rold + (1 / 5) x Ropponent + (S x 80)
This has the effect of heavily weighting both the result of the game and the strength of the rated opponent, thus making a coarse adjustment to the provisional rating. After the fifth such match-up (that is, after 5 games versus rated opponents) the rating is no longer regarded as provisional but, rather, as an established rating.
EXAMPLE 4:
A player whose provisional rating is 1325 defeats an opponent who is rated 1650.
Rnew = (4 / 5) x 1325 + (1 / 5) x 1650 + (+1 x 80)
Rnew = 1060 + 330 + 80
= 1470
For his rated opponent, Formula 2 is employed.
Rnew = 1650 + ( - 1 x 6) + (1325 - 1650) / 100
= 1650 - 6 + ( - 325 ) / 100
= 1650 - 6 - 3
= 1641
If you wish to read about more the CXR system and additional edge case scenarious, please check out their page.