A ranking system for Age of Renaissance

The below ranking scheme is shamelessly stolen from the ELO-ranking system that is used by the French Britannia championship, and adapted to Age of Renaissance by me...

Purpose

The idea of the ranking is to have a permanent ranking system.

Computing the Ranking

Once in every 3 months a new ranking list will be computed based on reported games.

For each game in the database, it is assumed that the players 'bet' 5% of their current ELO (Players not yet ranked start at 3000 - it's a good place to start).

Example:

Players:

The total of the 'bets' is 1146

The winner takes 1/2 the points (573), the second takes 2/6 (382), and the third place gets 1/6 (191) of the points. These are added to the player's starting ELO - bet (meaning that four of the players above would actually loose ELO by coming third in this game).

Further, if a player scores better than expected, he will receive a bonus. In the above example player C finishing better than last position would entitle him to a bonus. Player F is expected to win the game, and have no chance of a bonus.

The bonus is calculated as follows:

  1. Calculate the difference between first and last position (total scores)
  2. Divide by number of players
  3. Multiply with the number of places above expected

Player C finishing in third place would receive a bonus based on the following formula:
(winners total score - looser's total score / 6)*(-3-(-6)) = bonus

The final set of parenthesis are a way of saying: finished third, but expected to finish sixth.

If we assume that the final scores were as follows for the players A-F:

The difference between winner and looser is 1614-1184 = 430, which divided by 6 puts the bonus at 72.

Given the final scores above, the resulting ELO rating after this game would be:
created with Emacs
Age of Renaissance <bjoernat@online.no>
Last modified: Thu Feb 10 08:55:48 2000