user15248: 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?

user7147: 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.

15248: <p>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?</p>
 7147: <p>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).</p>
<p>You can find a description of the US Chess rating system <a href="https://new.uschess.org/sites/default/files/media/documents/the-us-chess-rating-system-revised-september-2020.pdf" rel="nofollow noreferrer">here</a>, which describes the computations that are done to adjust a player's rating after an event in which they've played.</p>
