APPENDIX B — Elo Rating System

The Guild Wars Tournament Ladders use the Elo ratings system.

This Elo rating system compares a guild or 1v1 player's (hereby know as competitor) match records against opponents' match records and determines the probability of that competitor winning the matchup. This probability factor determines how many points an Elo rating goes up or down based on the results of each match. When competitors defeat opponents with a higher rating, their Elo rating goes up more than when they defeat opponents with a lower rating (because competitors have a high probability of defeating those with lower ratings). All new competitors start out with a base rating of 1000. The Guild Wars tournament ladder uses the following equation to determine a competitor's win probability in each match:Win Probability = 1
10^((Opposing Elo Rating–Your Elo Rating)/400) + 1


This probability is then used to recalculate each competitor's rating after the match. In the equation below, competitors receive 1 point if they win the match and 0 if they lose. The competitor's new ratings are determined as follows:

Competitor's New Rating = Competitor's Old Rating + (K-Value * (Scoring Points–Competitor's Win Probability))

All competitors are rated beginning with the first rated match in which they play. Further ratings are calculated chronologically from that first match.

The K-Value is the maximum number of points a competitor's rating may go up or down based on the results of a single match within an event that uses the Elo ratings system. The current K ratings ArenaNet uses are as follows:
The K rating for free play matches is 5.
The K rating for Daily Automated Tournaments is 25.
The K rating for Monthly Championships is 50. http://www.guildwars.com/competitive/tournament2008/rules.php