Guild ladder
From Guild Wars Wiki
The Guild ladder is the marker to which all competitive PvP guilds aspire. The topmost 1,000 guilds are listed according to their ranking, which is derived through a win/loss record that is weighted, with every GvG match, to take into consideration the strength and ranking of the opposing guild.
The Guild ladder is a way of measuring how skilled a guild is, by comparing each guild that plays through the Elo rating system that was designed for chess matches. To be ranked on the guild ladder, a guild must have played at least one rated Guild vs. Guild match. To be shown on the Guild ladder on ArenaNet's site, your team must be ranked in the top 1000 guilds.
[edit] Elo rating system
The Guild Wars Guild ladder ranks guilds based on a system created for ranking Chess masters by a Hungarian Physics professor named Árpád Élő. Rather than simply rewarding players a certain number of points per win, this system also lowers ranking for a loss, and adjusts rating change based on the rankings of the players or teams involved.
The system is weighted based on a particular K value (see below for details), so a higher K value will result in larger rating changes than a smaller value. According to the current K-value, the maximum rating that can be won/lost in any particular match is 4; in the previous version of the ladder (prior to January 1st, 2007), the maximum was 29.
[edit] The Math
This equation finds the expected score of the team, which translates into the probability of that team winning the game. For example, if a team has an expected score of 0.6, it means that that team has, based on the ranking, a 60% chance of winning.
Note that this equation takes the current ratings of both teams into account. Because of this, the system assumes that rating is a proper measure of skill, which may not always be the case, as some highly skilled teams will not play as many matches, which means that teams that "grind" the ladder, or play a huge number of games without worrying about losses, will often pass up the more skilled guilds.
This equation takes the expected score from the first formula, and compares it to the actual score. In Guild Wars, a win counts for one point, and a loss counts for zero points. This result is weighted by the K value (for the current Guild Ladder, that value is K=5. In the first edition of the ladder, K=30), and then added to the rating of the guild in question.
These formulas are applied so that the winning guild is Team A, and the losing guild is Team B.
After finding the rating change in equation two, that value is added to the winning guild's rating, and subtracted from the losing guild's rating.
