ELO rating • page 1/6 • General Chess Discussion • lichess.org

What is the limit of ELO rating?

There is no limit.
If you win 99% of your games against an opponent, then you get a rating 677 higher.
If he wins 99% of his games against an opponent then you get a rating 677 higher.
Carlsen has 2839 now.
If an engine beats Carlsen 99 to 1 then it gets at 2839 + 677 = 3516.
If an improved engine beats that engine 99 to 1 then it gets 3516 + 677 = 4193.

There is no limit. If you win 99% of your games against an opponent, then you get a rating 677 higher. If he wins 99% of his games against an opponent then you get a rating 677 higher. Carlsen has 2839 now. If an engine beats Carlsen 99 to 1 then it gets at 2839 + 677 = 3516. If an improved engine beats that engine 99 to 1 then it gets 3516 + 677 = 4193.

lecw

#3

I'd be surprised if they invented a 4000 Elo bot that Stockfish / a 3500 bot was not able to draw against at least 10% of the time though

mkubecek

#4

@tpr said in #2:

There is no limit.
There is lower limit, 1400 for FIDE.

If you win 99% of your games against an opponent, then you get a rating 677 higher.
Because of the "400 point rule", if you were, hypothetically, playing against the same set of opponents and scoring 99% consistently, your rating would not stabilize and would keep growing without bounds. Whatever the rating gap would be, you would get +0.08K for each win and -0.92K for each loss, i.e. statistically 7*K (70 with K=10) rating points per 100 games.

@tpr said in #2: > There is no limit. There is lower limit, 1400 for FIDE. > If you win 99% of your games against an opponent, then you get a rating 677 higher. Because of the "400 point rule", if you were, hypothetically, playing against the same set of opponents and scoring 99% consistently, your rating would not stabilize and would keep growing without bounds. Whatever the rating gap would be, you would get +0.08*K for each win and -0.92*K for each loss, i.e. statistically 7*K (70 with K=10) rating points per 100 games.

petri999

#5

This possibility of run away due 400 pt limit is not feature of Elo ratings but FIDE implementation of adjustment algorithm for FIDE rating. Fide does not call it's rating as Elo rating. Other implementation have other funny things popping up. Like USCF rating floor something like : minimum rating a player's rating cannot drop below, determined by subtracting 200 points from their peak rating and rounding down to the nearest 100.

This should cause some inflation.

This possibility of run away due 400 pt limit is not feature of Elo ratings but FIDE implementation of adjustment algorithm for FIDE rating. Fide does not call it's rating as Elo rating. Other implementation have other funny things popping up. Like USCF rating floor something like : minimum rating a player's rating cannot drop below, determined by subtracting 200 points from their peak rating and rounding down to the nearest 100. This should cause some inflation.

tpr

#6

#3
"I'd be surprised if they invented a 4000 Elo bot that Stockfish / a 3500 bot was not able to draw against at least 10%"

Such a bot will emerge in the next 40 years.

#3 "I'd be surprised if they invented a 4000 Elo bot that Stockfish / a 3500 bot was not able to draw against at least 10%" * Such a bot will emerge in the next 40 years.

mkubecek

#7

To be honest, I would be more surprised if there weren't such engine in 40 years than if there were one in 10.

petri999

#8

I would be surprised on such an engine. I do not think there is enough room for improvement anymore. Without specially selected unbalanced starting positions all engine to engine games end in draw. In A0 study improvement plateaued well before planned training amount was reached. In go or shogi perhaps not in European Chess

Toscani

#9

As a player’s rating approaches 2900, the number of opponents who can offer meaningful rating gains becomes extremely limited. This creates a practical ceiling, not because improvement is impossible, but because the pool of equally strong or stronger players is so small. Expanding that pool by developing more high-level players raises the ceiling, much like expanding a room by moving its walls allows more people to enter.

Rating changes are based on expectations: if you beat someone you're not expected to, your rating increases significantly. If you lose to someone you're expected to beat, your rating drops sharply. Playing opponents with similar ratings may not result in big changes, but it helps stabilize your skill level.

Volatility in rating measured by the gap between a player's highest and lowest ratings shows how consistent they are. For example, a blitz rating that ranges from 1302 to 1832 shows a volatility of 530. Lower volatility suggests a more stable, well-rounded player. Gaining rating from such well rounded players is more reliable, as their performance reflects a consistent level of skill rather than emotional or stylistic swings of others.

Playing the position is important, but knowing the opponents rating volatility or rating deviation is also. I would rather want to be paired to a player that has a low rating deviation than with one that has a high volatile deviation in rating.

As a player’s rating approaches 2900, the number of opponents who can offer meaningful rating gains becomes extremely limited. This creates a practical ceiling, not because improvement is impossible, but because the pool of equally strong or stronger players is so small. Expanding that pool by developing more high-level players raises the ceiling, much like expanding a room by moving its walls allows more people to enter. Rating changes are based on expectations: if you beat someone you're not expected to, your rating increases significantly. If you lose to someone you're expected to beat, your rating drops sharply. Playing opponents with similar ratings may not result in big changes, but it helps stabilize your skill level. Volatility in rating measured by the gap between a player's highest and lowest ratings shows how consistent they are. For example, a blitz rating that ranges from 1302 to 1832 shows a volatility of 530. Lower volatility suggests a more stable, well-rounded player. Gaining rating from such well rounded players is more reliable, as their performance reflects a consistent level of skill rather than emotional or stylistic swings of others. Playing the position is important, but knowing the opponents rating volatility or rating deviation is also. I would rather want to be paired to a player that has a low rating deviation than with one that has a high volatile deviation in rating.

corvusmellori

#10

@tpr said in #2:

If an improved engine beats that engine 99 to 1 then it gets 3516 + 677 = 4193.
@lecw said in #3:
I'd be surprised if they invented a 4000 Elo bot that Stockfish / a 3500 bot was not able to draw against at least 10% of the time though

The problem with measurements like these is that the Elo system fundamentally assumes that win rates are transitive, in order for rating to be stable. For example, if A scores 60% against B, and B scores 60% against C, then A had better score 84% against C. With very high level engines, this really doesn't work out in practice, making Elo measurements of engines a bit arbitrary (of course, this can be a problem for humans as well).

@tpr said in #2: > If an improved engine beats that engine 99 to 1 then it gets 3516 + 677 = 4193. @lecw said in #3: > I'd be surprised if they invented a 4000 Elo bot that Stockfish / a 3500 bot was not able to draw against at least 10% of the time though The problem with measurements like these is that the Elo system fundamentally assumes that win rates are transitive, in order for rating to be stable. For example, if A scores 60% against B, and B scores 60% against C, then A had better score 84% against C. With very high level engines, this really doesn't work out in practice, making Elo measurements of engines a bit arbitrary (of course, this can be a problem for humans as well).