Rating system

Based on the rating system developed by Prof. Árpád Élõ

Absolute rating system, the rating can be used to determine the winning odds of a specific player against another player. The system has been worked out according to statistical and probability theory.
The rating is an integer, the minimum is 0. The starting rate of an unknown player is 0.

Rating difference	Win probability
0	0.50
100	0.64
200	0.76
400	0.91
800	0.99

Ratings are amended each time you finish a game, by adding or subtracting an amount from your previous rating. The amount subtracted or added depends on the outcome of the game and the ratings of the two players involved.

Calculation

The following formula is used:
Rn = Ro + K(W-We)

Rn is the new rating.
Ro the old (pre-event) rating.
K a constant (32 for 0-2099, 24 for 2100-2399, 16 for 2400 and above).
W the score in the event - i.e. for a single match win=1; draw=0.5; lose=0.
We the expected score (Win Expectancy), from the following formula:
We = 1/ (exp10(-dr/400) + 1)
dr equals the difference in ratings.

The sum of the rating changes is zero. It turns out that if the rating difference is more then 719 points, then if the strong player wins, there is no change in either rating.

Provisional ratings (~)

Players who have played less than 20 matches are considered to have "provisional" rating. This is indicated by a ~ sign next to their names. For these players their rating might not reflect their skill as precisely as for a player with "established" rating, therefore playing against a ~ player will have less effect on the other player's rating. The effect will grow gradually as the number of matches rise, and will reach normal level as the number of matches reaches 20.

Rating reduction of idle players

Players who do not play for a while will see their ratings decreased each day after a seven days period. The amount subtracted will depend on the current rating.

The following formula is used:
Rn = ( Ro * Ro ) / 125000
Rn is the new rating.
Ro the old (previous day) rating.

Rating	Amount subtracted
below 353	0-1
354-500	2
501-612	3
613-707	4
708-790	5
791-866	6
867-935	7
936-1000	8

Players with higher rating will see their rating decrease quicker.

Series of games

Playing a series of games against the same opponent within a given time interval will adjust the calculation as follows:
The expected score is calculated for the series of games from the pre-match rating-difference of the two players, and the ratings are amended based on the expected score and the actual score of the series of games.
These are basically the extensions of the above calculation for more games played.
However, as more matches will reflect the skill difference more precisely, the amendment is raised based on the number of games played.

Number of games in a series of games	Maximum rating change
1	16
2	24
3	28
4	30
5	31
infinite	32

In other words the constant K in the above equations is multiplied by a factor of 2-(1/2^(n-1)), where n is the number of games played.

Note that if you play a 3rd player in between playing the same opponent, it will still be treated as a series of games.

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