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The DCI
Explanation of rankings/ratings
The DCI tracks the performance of its members through two processes: ratings and rankings. A rating is a numerical description of a person's level of skill at playing Magic. It is based upon the theory that a more skilled player should be able to defeat a less skilled player in match play. The specific probability (We) for each player winning the match is determined by comparing their previous ratings (new players are assigned a base rating of 1600) using the formula:
where We is a player's Win Expectancy, R1 is the player's current rating, and R2 is the opposing player's current rating. This probability is then used to recalculate each player's rating after the match. Players' new ratings are determined using the formula:
where Rn is the new rating, Rp is the previous rating, K is a constant, W is the score in the match (Win=1, Loss=0, Draw=.5), and We is the Win Expectancy. All players are rated beginning with the first match that they play. Further ratings are calculated chronologically from that first match.
The effect of the above formulas is simple. The Win Expectancy establishes the probability for each player winning a given match. This probability, when subtracted from the actual match outcome and multiplied by 32 (the maximum number of points available per match), determines the amount of points added to or subtracted from each player's rating. The end result is that a player receives a greater reward for defeating an higher rated player than he would for defeating a lower rated player, and vice versa.
A ranking is a value representing a player's standing within a specific set of players (e.g. Region, Nation, Worldwide). It is determined by ranking a group of players in order of rating, with the highest rated player being designated as the highest ranking player. This is a relative value as it depends upon which overall set of players is selected. Due to statistical concerns, all players with less than 10 matches in a specific play format are not ranked for that format.
A composite ranking is a value used to compare the abilities of players in multiple play formats. Composite rankings are determined by calculating composite ratings for each player and comparing them. The composite ratings are calculated using a straight (unweighted) average of the ratings for each play format, with a rating of 1600 assigned for those formats in which the player has not yet completed 10 matches.
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