Why are Elo ratings for go higher than for chess?

Question

If we compare Elo(-like) ratings in chess and in go, we see that the highest ratings published for go (3621 for Ke Jie as of 2016-03-13 at goratings.org) are higher than those in chess (2851 for Magnus Carlsen as of 2016-03-01 at FIDE.com).

Is the best explanation one of the following suggestions, or something else?

• Go is in some sense better played than chess. While many in the West think of chess as the premier intellectual game, go has, I believe, been studied more intensively, had more support in Eastern culture than chess has where it is played and is financially more rewarding.
• Go is better at distinguishing slight differences in strength, e.g. because games are longer or because draws are rare (about 1 game in 50, I believe).
• There is some arbitrary difference in the way the Elo approach is applied to go and chess, e.g. an arbitrary baseline or scaling factor.

In any case, an explanation of how the rating system work and, if appropriate, interact with the nature of the games is needed to make an answer complete. If it is illuminating, a comparison with other games would also be welcome — for example, what would happen with ratings for a trivial game like noughts and crosses?

I realise that the systems are not intended for direct comparison, but I hope that they still allow some sort of conclusion to drawn. They are, after all, based on the same principles, though various parameters may be differently set.

Answer 1

There is no ELO rating in go. And even no official international rating at all. A common question in go forums is "how does my rating in [whatever country or online server] compare with [other country or online server]".

The European Go Federation is maintaining an international rating system where Ke Jie is rated 2956.

goratings.org is an individual initiative by Remi Coulom. It has become popular because it gave journalists a way to assign a World ranking to Fan Hui, but this is not an official rating system.

Bottom line is your answer 3, there is some arbitrary difference in the way the approach is applied to go and chess.

Answer 2

There are three determining factors for how high the highest Elo rating for a given game will be:

• Internal aspects of the rating system: First an foremost how the ratings are initialised. If you start out with everybody getting a rating of 2000, the numbers will stay higher than if everybody gets 1800. But also K-factor (how strong ratings fluctuate) and other details that might lead to inflation or deflation. So this is your arbitrary difference part of the answer.

• The level on which a game is played, i.e. how close the top players are to the human maximum playing strength. This depends a lot on how many players do play the game, how it is supported financially and what resources there are to get really strong. It strikes me as very likely that chess is played on a higher level than go, because chess players have had the benefit of superhuman helpers for at least 15 years now.

• The depth of the game, i.e. how big the difference between a beginner and the best (possible) human player would be. Here go is clearly ahead of chess, but I doubt this has much to do with the game tree complexity. Rather this is an effect of the broad drawing range in chess. If you reduce the drawing range in chess, for example by shortening the time control, you get "go-like" Elo ratings in chess. On chess servers with fast time controls ratings in excess of 3600 are not unusual.

Answer 3

I don't have an understanding of Go ratings, but I think you are comparing apples with oranges, i.e. Go elo ratings are not meant to be compared to Chess elo ratings.

This quote is from comparison of go rank with chess rating

It's not really possible. You could use the European GoR system to give a rough comparison, but the problem is that it's not anchored in the same way.

Answer 4

The ELO system, as it was originally designed, has a mean of 1500 and a standard deviation of 400 points.

The central limit theorem defines how many people can exist by this model depending on their distance from the mean. For example, a rating of 3100 is 4 standard deviations from the mean (1500 + 4 x 400 = 3100). According the central limit theorem there would be 99.993666% within 4 standard deviations, or about only 1 out 16,000 players which would be outside of this. Of course, we know there are no human players rated higher than 3100 so, we can see at once that the ELO system does not work correctly. If the players followed a normal distribution, then we would expect there to be, out of 1 million or so players, about 80 with a rating higher than 3100, but this is not the case.

Now, as to an igo player having a rating above 3600, that is 5.25 standard deviations above the mean (1500 + 5.25 x 400). According to the central limit theorem there should be one person out of 10 million that has this rating. If we assume there there 10 million rated go players and there is one above 3600 then that fits with the model.

There are two problems with comparing the two ratings for the champions. One is that the distribution of the players, certainly in chess, and possibly in igo, is not a normal Gaussian distribution, so the ELO system will always be wrong to an extent. Secondly, many rating systems, especially chess's FIDE system do not use pure ELO, but manipulate the rating in various ways. Also, the FIDE system has no set mean and has only a small number of players in it, not the entire world population of chess players. Therefore, it is difficult to draw any meaning from the comparison.

Answer 5

If you have two games each of which ranks players using the ELO rating system, then the game with higher rankings is generally viewed as "more complex" than the game with lower rankings. In the sense that there are more discrete levels of learning to mastery. It is not clear to me which ranking systems are being used in your statement, but for the conclusion to hold, the ranking systems used must be identical.

All that said, Go is definitely a more complex game than Chess, and is widely recognized as such. Anecdotal evidence to support that claim: Humans have been beat by computers in Chess for a while now, Go is apparently just happening today.

"Better" isn't a good word to use in this context, as that's a rather subjective term. "Complexity" is typically used in these kinds of conversations.

It is interesting to note, that the highest ELO ranking for League of Legends that I could find is 3069.

Answer 6

There are some good answers to the main question, and this is only to address the sub-question related to trivial games such as tic-tac-toe (because I think it is an awesome question;)

• Assuming adult, competitive play, where every competitor knows the solution, then outcome of every game would be a stalemate, and all players would have the same ranking.

But this leads to the very interesting question of what would an ELO distribution look like if there was formal, competitive play among small children?

I mention that because there has been some discussion in this thread of the relationship of game complexity (problem size) to ranking distribution.