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I've recently lost to a 1500 player. My rating is about 1200. Ironically, he got 163 points. How is it possible for a 1500 player to gain more points on a lower-rated player? The system that Lichess uses to calculate rating scores is very confusing. How is it done?

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Without the link to player profiles and the game iteself, it is difficult to say for certain exactly what happened.

For one, Lichess starts new users with a rating of 1500.[1]

Even if your opponent didn't have a 1500 rating, as double-beep points out Lichess uses the Glicko-2 rating system[2] which explicitly tracks the player's rating, a rating deviation, and a rating volatility. The system views a player's rating from a stochastic perspective, as an interval not a single point value.[1]

The system will detect and provide a larger rating change in various circumstances including:

  • "exceptionally strong results after period of stability",[3] or
  • after a period of inactivity (it is less certain if rating is still accurate).

The Glicko-2 creator, Dr. Mark Glickman, provides the mathematical formulas for the system.[3,4]

As an example, consider this classical game on Lichess. At the time of the game, the player with the White pieces had only played 1 rapid game. The system seeded the player (White) with a 1500 rating but annotated it as 1500? to denote the provisional rating.

References:
[1] Chess Rating Systems, Lichess website.
[2] What rating system does Lichess use?, Lichess FAQ page.
[3] Example of the Glicko-2 System, ME Glickman, 30 Nov 2013.
[4] http://www.glicko.net/glicko.html, website by Mark E. Glickman.

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