The Elo player-rating system compares players' match records against their opponents' match records and determines the probability of the player winning the matchup. This probability factor determines how many points players' ratings go up or down based on the results of each match. When a player defeats an opponent with a higher rating, the player's rating goes up more than if he or she defeated a player with a lower rating (since players should defeat opponents who have lower ratings). All new players start out with a base rating of 1600.
The following equation is used to determine a player's win probability in each match:
This probability is then used to recalculate each player's rating after the match. The following equation is used for that purpose:
Where "Scoring Points" is 1 for a match win, 0.5 for a match draw, or 0 for a match loss.
All players are rated at the beginning with the first match they play. Further ratings are calculated chronologically from that first match.
Ratings are provided in four cathegories, each of them refer to a particular format. During a tournament, only the corresponding rating will be modified.
Each tournament has a base value to recalculate player's ratings during the tournament. This value is called K-Value, and is used in the equation to control the amount of points a player's rating will go up or down. The default K-Value for Magic: The Gathering tournaments is 16.
Events with higher K-Values allow players to earn more rating points when they do well within these events. For example, a player who earns 30 rating points in a tournament with a K-Value of 16 would earn 60 rating points in a tournament with a K-Value of 32.
