DCI Ranking : The Gory Details

For those of you who are interested in the mechanics of the DCI ranking,here's an  overview.  As you read this, please keep in mind that the DCI as the final authority on this ranking system, and they can change the rules if it becomes  necesssary.

Based on the theory that a higher ranked ( more skillful ) player is expected to be able to defeat a lower ranked ( less skillful ) player in match play, the DCI uses this formula before   the match to compare the two rankings and determine each player's probability of winning   ( W ) :

W = 1 / ( 10 (( R2 - R1 ) / 400 ) + 1 )

Where R1 is your current ranking, and R2 is your opponent's.  ( The calculation for your opponent would reverse the two - R1 his ranking and R2 yours - and result in the complementary probability. )  After the match is over, the probability is plugged into another formula to calculate each other's new ranking ( Rn ) :

Rn = Rp + ( K * ( S - W ))

Where Rp is the player's old ranking and W is still the probability of winning.  S is that player's score for the match; a win makes S = 1, for a loss S = 0, and a draw sets  S = 1/2.   K depends on the value of Rp.  If the old ranking was between 0 and 1099, K = 32; if it was between 2100 and 2399, then K = 24; otherwise K = 16.

The overall effect of these calculations is that a lower ranked player who defeats a higher ranked player will gain more points ( in rank ) than a high rank who beats a lower rank.