Chess rating systems
You have accounts on several chess servers, and your ratings don't match from a server to another. Why is that?
This is a very legitimate and frequently asked question, which also has a simple answer:
It's because chess federations and servers use different rating systems.
There are 3 main systems:
Elo
The Elo rating system is relatively ancient and mathematically simple. It is still in use by many sports and federations, including FIDE.
The Elo system does not recommend any initial rating.
Glicko 1
The Glicko rating system has a better prediction accuracy than Elo, but is more complex mathematically. It is a popular choice for new games and sports.
The Glicko system paper specifies that ratings start at 1500.
Glicko 2
An improvement over Glicko 1, adding the concepts of volatility, for even greater accuracy.
Ratings still start at 1500.
Which federation/server uses which system
By chronological order of creation:
FIDE
The International Chess Federation uses the Elo system. Back in 1971, it was the only choice.
New players get a rating equal to the performance in their first rated game results.
FICS
The Free Internet Chess Server uses the Glicko 1 System.
New players get a rating equal to the performance in their first rated game results.
ICC
The Internet Chess Club uses the Elo System.
New players get an initial rating of 1400 or 1600 depending on the pool.
Chess.com
Chess.com uses the Glicko 1 system.
New players used to get an initial rating of 1200. Nowadays, new players get to choose their initial rating themselves.
Lichess.org
Lichess.org uses the Glicko 2 system.
New players get an initial rating of 1500 , as recommended by the Glicko definition.
Comparing ratings between federations or servers
As tempting as it sounds, it is not easy.
Directly comparing the numbers is not possible, because they use different rating systems and also differ in the way they implement them.
More complex comparisons have to account for the different pool of players of each federation or server.
FAQ
Are Lichess ratings inflated?
Lichess ratings start at 1500, as is recommended by the Glicko system definition. The median player rating of Lichess is close to 1500, and there is no significant deviation of this value over time.
The Lichess ratings can often be higher than ratings from other systems that start at 1200, such as FIDE or chess.com. This only shows that ratings from different systems cannot be compared.
Are players from server X stronger/weaker, because their ratings are higher/lower?
No. Ratings can't be compared from a server to another. They only serve to compare the skill of players within the same rating pool.
Which rating system is best?
The purpose of rating systems is to predict the outcome of games, in order to make balanced pairings. Therefore, they can be objectively better or worse, according to their ability to make such predictions. Glicko 1 makes better predictions than Elo, and Glicko 2 makes better predictions than Glicko 1 (source).
Why don't they all use the same rating system?
Because the first rating system historically used, Elo, is pretty bad. Glicko 1, then Glicko 2, make considerable improvements, and offer greater accuracy. Even if everyone would use the same rating system, ratings would still not be comparable across different pools of players, so there's no need for chess servers to pay the cost of legacy forever, and they moved on to superior systems.
We hope it clears it up
If you notice a mistake or an omission in this document, please let us know.