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Richard's PBeM Server uses an Internet Chess Server (ICS) based rating system for each of the various game types...

                          ICS Rating system

A player is said to be provisional if he/she has played fewer than 20 games, and established otherwise.  An entirely different system is used for established and provisional players. For the rules determining when a player is inactive, see below.

The rating during the provisional period is the average of a set of values, one for each game played.  The values (of which the rating is an average) depend on whether the opponent is provisional, or is established.  The value against a provisional player is the average of the two ratings (using 1600 if the player has never played) plus 200 times the outcome (which is -1, 0, 1 for loss, draw and win).   The value against an established player is the opponent's rating plus 400 times the outcome.  Some extra points are now added to the rating for the purpose of keeping the average rating of all established active players close to 1720.  In particular, 1/5th of 1720 minus the current average is added to the rating.

To explain the extablished period requires the use of a formula.  Suppose your rating is r1, and the opponent's is r2.  Let w be 1 if you win, .5 if you draw, and 0 if you lose.  After a game, your new rating will be:

                                       1
                   r1 + K (w - (-----------------))
                                      (r2-r1)/400
                                1 + 10

I still need to explain the variable K.  This is the largest change your rating can experience as a result of the game.  The value K=32 is always used for established player versus established player.  (The USCF has a system in which this K-factor diminishes for more highly rated players.)  If you're playing a provisional player, the factor K is scaled by n/20, where n is the number of games your opponent has played.  So, as in the provisional case, if you play an opponent who has never played, your rating can't change.

This formula has the property that if both players are established then the sum of the rating changes is zero.  It turns out that if the rating difference is more than 719 points, then if the strong player wins, there is no change in either rating.

Note that during the provisional period, BEATING a player whose rating is more than 400 points below yours will DECREASE your rating.  This is a consequence of the averaging process.  It's useful too, because it prevents the technique of getting an inflated provisional rating after one game, and then beating 19 weak players to get an established rating that is too high.

A player becomes inactive (in Chess, say) when they refuse a challenge while not playing any other (Chess) games. To become active again you just need to complete a (Chess) game. Your rating is not lost by becoming inactive.

 

apac
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