[–] 7 points8 points  (17 children)

There is no limit on ELO. That's one of the problems with the system. If a computer played perfectly and won every game it would continue to gain ELO points. Eventually it would get fractions of a point, but the number would still rise.

[–]Atomic 1800 2 points3 points  (9 children)

Would perfect play not correspond to an infinite Elo, though?

[–] 5 points6 points  (4 children)

Elo doesn't care about how well you play, it cares about who you beat.

[–]Atomic 1800 1 point2 points  (3 children)

Right. I guess I was assuming that with perfect play you would beat everybody and everything you played. It seemed like a reasonable guess given how much higher rated computers are than humans, and yet still have some pretty obvious ways to improve.

[–][deleted]  (1 child)

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[–] 2 points3 points  (2 children)

Would perfect play not correspond to an infinite Elo, though?

To have a infinite ELO the following things are required (I think):

1) An infinite number of opponents:

Because points are scored based on the difference in ELO, if there were a finite number of players, their ELO would go to zero as you won games. Over time your ELO would be so high and your opponents so low, you would never reach ELO infinity. You need an infinite number of players so that the sum of their ELO points is infinity.

2) You would need to play an infinite number of games:

As you got higher and higher with the ELO, you get less and less points. To reach infinity would require an infinite number of games against opponents that have nearly your rating.

[–]Ke7# 0 points1 point  (1 child)

Not trying to be a dick, but it's Elo, not ELO :) Named after Arpad Elo.

[–] 1 point2 points  (0 children)

You're correct. My mistake.

[–] 2 points3 points  (6 children)

Bear in mind that it is mathematically possible for a number to rise and never reach an infinity.

[–] 2 points3 points  (5 children)

Yes, that's why I think an infinite Elo requires an infinite number of players.

[–] 1 point2 points  (0 children)

You can have negative Elo ratings so you can have a finite number of players and as the winner tends to positive infinity the loser tends toward negative infinity.

[–] 1 point2 points  (3 children)

Even with an infinite number of opponents it's possible to not reach infinity. For example: 1 + 1/2 + 1/4 + 1/8 etc could go on forever but would never even reach 2!

[–] 0 points1 point  (2 children)

The Elo system is not a geometric series so there is no limiting sum.

[–] 0 points1 point  (1 child)

Not strictly, but there are some similarities, as the "always win computer" will receive diminishing returns as its rating goes higher. At some point, to increase its rating, it will need to face a computer significantly as high as it. Assume it gets to 100,000 ELO. Even if it plays something as high as 4000, it won't get a significant increase, and even as it wins more over time, that increase will get even smaller.

[–] 0 points1 point  (0 children)

You are correct. All I am saying is that the score will tend to infinity rather than a finite number. It well just take a damn long time.

[–] 1 point2 points  (9 children)

Technically no, however it is a logarithmic growth so it becomes incredibly as your score increases. Say for example I build a computer that is literally a million times better than Magnus it would have an Elo of around 5270 (if we use the current k factor used by FIDE) it would take around 800 consecutive wins over Magnus to increase by a point.

Looking at it from a probability perspective, an infinite Elo rating would correspond to a 100% chance of winning. The only way to achieve this would be to solve the game of chess. Considering any method which was not perfect could potentially result in a draw or loss, the Elo rating would be limited by the true probability of the event. If the solution was perfect then the Elo score could tend to infinity as it played an infinite amount of games.

[–] 0 points1 point  (8 children)

How does this scaling work in a pool of two players? ie.

Player A always beats player B. Player B's score approaches 0. Can player A forever gain points off of player B? Initial scores of 1400, normal k-factor, how many games until player A reaches 10,000 elo? I understood it to be limited (I actually never looked at the exact formula since I am not great at math and lazy).

[–] 0 points1 point  (7 children)

Its a closed system so the points will always sum to 2800 in that case so if player a had a score of 10000, player b would have a score of -7200. This would mean that player a would have to win 2172 games for every game won by player b (assuming a no draw scenario) to achieve and maintain that rating

[–] 0 points1 point  (6 children)

I thought you couldn't have a negative elo (in the typical systems that people use).

[–] 1 point2 points  (5 children)

You can but they are incredibly rare as you would have to losses tens of thousands of consecutive matches to get one. I build elo systems for part of my job and I only come across them when I run ridiculous simulations.

[–] 1 point2 points  (1 child)

I build elo systems

you are satan

[–] 0 points1 point  (0 children)

Actually I'm Lord Gamblor, but that is just splitting hairs.

[–] 0 points1 point  (2 children)

Wait. I have this opportunity, so I have to ask you: is there elo hell? Are you familiar with the term?

[–] 1 point2 points  (1 child)

Well I assume you are referring to League of Legends by that remark. I don't play but from I understand is that if you lose and hence drop down in ranking then you drop down in category. Since you are only allowed to play against people in your category, it is much harder to gain points as you are playing against people in your own category. Say for example you have a rating of 1100 so you are in the 1000-1200 category, if you lose a bunch of games against a 1000 ranked person or persons then you could quickly fall to lets say 750. By doing so you would only be able to play against 600-800 people, thus making it a lot harder to attain your original ranking after a sharp collapse.

I can't think of of any other examples where there are tiers based on an Elo rating. I'll give you the example of tennis for which i have designed a model. If a player drops in rankings and gets stuck in Challenger tour, as opposed to the Main ATP tour, then it is a lot harder for them to increase their Elo rating as they are forced to play worse players. Even though they might be a lot better than them, their score increase is limited by the fact they can only play poorer players, hence the time to increase your rating can take much longer.

[–] 0 points1 point  (0 children)

You have answered my question in the positive, for which I am relieved (full disclosure, I'm gold 1 (around 1700 elo), so I don't really consider myself in elo hell, but I've been there and I've always maintained that it exists. Around 700 elo, and it was much tougher to climb out of those zones than in the 1500+ zones). I've always claimed some rough and much stupider version of the model you sketched exists, based on my rough understanding of elo, but did not have the specialty knowledge needed to write it out as you have. There is all this talk about "there is no elo hell" in the LoL community. They don't want to believe that there is anything inconsistent with their beloved game...

[–][deleted]  (1 child)

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