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Given the issues with rating people who mostly play within a cluster that contains few people who play outside the cluster, I was expecting rating systems to take more notice of results against another player who was well connected to many different clusters of players. Yet they seem not to. What am I missing in my understanding?

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  • I would guess that this hasn't been a main focus because in many scenarios that is unlikely to happen. However, there would be some uses cases of course, so it might be interesting to try and model it.
    – koedem
    Feb 3 at 4:04
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    tl;dr They cope badly
    – Evargalo
    Feb 3 at 7:10
  • @koedem I think the US creates problem for international rating systems by most mid range US players not playing in a international rated match until they have become very experienced players. There is also issues that is clearly easyer to get 2500 in some countries then others. Feb 3 at 11:25

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Your understanding is correct, at least for the Elo system (and systems derived from it). These systems only make adjustments to a player's rating based on results against other players that they've actually played against. They don't make any explicit attempt to extrapolate a player's performance based on how that player's performance compares against other players that their opponents have played (but whom the player under consideration has not played).

You can find a description of the US Chess rating system here, which describes the computations that are done to adjust a player's rating after an event in which they've played.

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  • I was thinking "K" could be higher when playing someone with a low level of connection between the players. Feb 2 at 20:30
  • One could potentially try to atone for a multitude of sins via the K factor. As used in Elo-like systems, though, it's strictly a measure of how volatile a player's rating is, and only information about that player is used to choose K. The general assumption is that the ratings of low-rated players may change quickly, but that that high-rated players probably won't get worse (or much better) quickly. It's further assumed ratings based on a small number of games may change quickly (the rating system doesn't know much about the player yet), while long-established ratings are more stable.
    – patbarron
    Feb 2 at 21:04
  • There is already a system in US when new people who do a lot better then expected get their rating increaed more. Maybe also a bonus when doing a lot better then expected agaist playing who are not well connected to you but are well connected to many other players. Feb 2 at 21:09

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