The Ranking System of the Online Game
The Gauss Curve
As many of you often ask about the ranking system used in our online games, here is a detailed description, including the formulae for the mathematically inclined reader. Read on, and you will know it all!
There are many ranking systems in sports (tennis, football,...) and in games (chess, bridge, backgammon, etc.). All these systems have their limits, and are often the subject of heated debate inside the federations. So you need to be aware that there is no perfect system.
The reason is that the goal of a ranking system is to sort the players by their "proficiency". This is a very subjective notion, that varies in time depending on the player progress or fatigue, and on the amount of chance of the game. Even with chess, the best ranked players do not systematically beat the lesser ranked players.
Let's consider two player games (duels). There can be three possible outcomes of a game: player A wins, player B wins, or stalemate. Any system must cope only with these three possibilities (even though some try to include the fact that the victory was more or less easy, but this is not our case here).
Let's suppose that each player plays at a constant level of proficiency (this is wrong of course, but it can be considered valid during a limited time). The trick is to "converge" the player toward the place he belongs to by having him play several games.
Everybody agrees that there are few good players, few bad ones, and many average players. This is a classic "bell curve" distribution (called a Gauss curve). A good ranking system will have to show such a distribution.