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## Standard rating formula

This algorithm is to be used for players with who have not had either all wins or all losses in every previous rated game.

Define the Standard winning expectancy,'' , between a player rated and his/her -th opponent rated to be

The value of , which used to take on the values 32, 24 or 16, depending only on a player's pre-event rating, is now defined as

where is the effective number of games, and is the number of games the player completed in the event. The following are example values of for particular values of and .

 Value of Full-K Half-K 6 4 80 50 6 6 66.67 44.44 6 10 50 36.36 20 4 33.33 18.18 20 6 30.77 17.39 20 10 26.67 16 50 4 14.81 7.69 50 6 14.29 7.54 50 10 13.33 7.27

If , or if the player competes against any opponent more than twice, the standard'' rating formula that results in is given by

where the player scores a total of points (1 for each win, 0 for each loss, and 0.5 for each draw), and where the total winning expectancy .

If both and the player competes against no player more than twice, then the standard'' rating formula that results in is given by

where (3-round events are treated as 4-round events when computing this extra term). The quantity

is, in effect, a bonus amount for a player who performs unusually better than expected. Note that the value 10'' in the above formula will change to 16'' in January 2003.

The resulting value of is the rating produced by the standard'' rating algorithm.

Next: Rating floors Up: Details of the Rating Previous: Special rating formula
Mark Glickman
2004-09-22