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How far back are results of matches relevant for Elo purposes? If a player wins a few early matches then they will earn less points for later wins than if they'd lost those early matches. In the end there comes a point at which older results simply don't affect today's rating.

Matches with higher K factor will erase earlier history faster. I think that K factor has a linear effect on change in rating, so for the purpose of this calculation we can just assume constant K.

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  • If you’re going to downvote, fine but please comment to explain, thanks
    – Laska
    Feb 19, 2021 at 22:08

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Let's say a FIDE player is rated 1800, and has k=20. Every month this player plays in one 4-game tournament, in which they play against opponents all rated exactly 2000, and scores exactly 50%. How fast does the rating converge?

After six months, they would be rated 1898. After one year, the player's rating would be 1949. After 18 months,the rating would be 1975, and after two years, it would be 1987. So it seems that the player is getting approximately halfway to their performance rating every six months or so in this scenario.

After 32 months, the player would be rated 1997, and after that the rating no longer moves because a rating difference of 3 has an expected score of 50% according to the table FIDE uses.

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  • That’s a very good way of looking at it. 32 months is 128 games. A single game at k=20 would not cause a change of 200 points. It might be 20 points? How quickly would the impact of that dissipate? In a small pool of players, the guys on 2000 would be dropping as the 1800 rises. I guess that they would meet in the middle more quickly
    – Laska
    Feb 20, 2021 at 0:42
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    Starting 20 points from 2000 at 1980, you're at 1991 after 6 months and at 1997 after a year, using the same assumptions. But I didn't want to pick something like a 20 point difference because then you're only gaining fractional points per game, and it depends a lot on whether the total happens to round up or down at the end of the month. That makes it harder to see the overall pattern.
    – D M
    Feb 20, 2021 at 1:47
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    And I'd say that any ratings difference under 10 points would be meaningless even if ratings were perfectly accurate (which they aren't.) For example, if your rating is 2000 and you play a 2000 player, your rating will go up 0 points with a draw and 10 points if you win. There's nothing in between that can get you to, say, 2005, unless you happen to play some other opponent. So... after six months of what I wrote in my answer, the impact of any one previous game would drop from 20 points to less than that 10 point threshold, and thus be pretty much meaningless.
    – D M
    Feb 20, 2021 at 2:12
  • Remember the other player ratings also get moved down towards the winners rating that is slowly increasing.
    – Ian Ringrose
    Jan 29, 2022 at 12:38
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    @IanRingrose True, but that's a very minor consideration unless you're in a very small and isolated pool. If you go up 200 points and only play against a group containing 20 other people (who also never play outside that group) they'd all go down 10 points on average (assuming they have the same K value as you.)
    – D M
    Jan 31, 2022 at 4:33

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