Guild ladder

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 ladder match is 15.

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 "jump" 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, which is represented as S. 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=15. In the first edition of the ladder, K=30. Later edition of the ladder K=5.), 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.