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Since all chess player’s ratings are between 800 and 2900, why don’t we make a new rating defined like this:

New rating = (Old rating – 800) / 2.2

So that all chess player’s ratings would be between 0 and 999

Or if we would like to be able to easily convert between old and new ratings we could define the new rating like this:

New rating = (Old rating – 1000) / 2

(Though here extremely weak players would have a negative rating.)

My point is that we would have almost the same precision, but we would only need to use 3 digits instead of 4.

I believe the current rating system is bad because a big range of numbers (3000 to 9999) isn’t used.

What do you think? Is there something obvious that I missed or am I really right?

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  • I think that there is a weakness in the Elo rating system and I have proposed a way to improve player rankings by comparing them in two dimensions. Here is the link to my paper: papers.ssrn.com/sol3/papers.cfm?abstract_id=2477868
    – Jamal Munshi
    Aug 12, 2014 at 1:20
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    Why? And how is that an improvement?
    – edwina oliver
    Feb 8, 2020 at 17:09
  • Since these numbers are stored on a computer, we should have consideration of their number system. On a 32 bit computer, the most often used number storage unit is integer, which has a range of 0-65,535. This means that compressing the ELO isn't the logical "answer" as it wastes space on the computer.
    – Mike Jones
    Feb 24, 2020 at 6:13

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Re-scaling the rating system doesn't improve it: it just changes the numbers. So what if the world's best players are rated 950 instead of 2900? It's like quoting somebody's mark in a test as 18/20 instead of 90%. The rating system would behave in exactly the same way.

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Sure, you could compress the current range like that. The issue, though, is that ELO is not an objective scale with absolute endpoints. It's only a measure of play strength relative to past opponents.

The fact that no current player has an ELO above 2900 does not mean that such ratings are impossible. Until 1990, no one had a rating above 2800. In fact, there's no mathematical upper bound on ELO rating at all: see this question, for example. The "big range of [unused] numbers" is infinite.

So yes, you could compress the ratings--but what do you do when someone achieves ELO 3001 in the uncompressed system? Recompress it with a different scaling factor, and change what everyone's ratings mean? And keep doing this every time someone "breaks" your current system? If the goal is to make ELO simpler to keep track of, this seems rather counterproductive. I suppose you could report log ELO to make it more tenable (also sillier), but the fact remains that there's no mathematical bound, so there's no guarantee that all ELOs will stay within the range you're looking for.

Perhaps the most pertinent question of all is, why? What do you gain from compressing Elo down to three (ish) digits? It diminishes (slightly) your ability to distinguish between players of similar ratings, but what is the upside? Or, why not compress it down to between one and one hundred, or zero and one? It's all the same values; "three digits" is quite arbitrary, and I can't think of any way that it "improves" on the current system.

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  • Using a log would not be very helpful. This would make players on the range of (100, 2900) equal to (2.00, 3.46) ! A 2000 rated player would be 3.30 while a 2900 would be 3.46.
    – Alan
    Jun 4, 2014 at 14:09
  • @Alan I never claimed that log Elo would be useful, just that it would be a more effective way to compress the range ;-)
    – Henry Keiter
    Jun 4, 2014 at 14:12
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    @Petrosian Then what's the point of the exercise in the first place? Why is having a 3-digit Elo desirable?
    – Henry Keiter
    Jun 4, 2014 at 14:49
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    @Petrosian What is your occupation, that you read/say/write so many Elo ratings each day that the time it takes to do so is actually a concern that outweighs the loss of precision? Memorizing Elo seems particularly sisyphean.
    – Henry Keiter
    Jun 4, 2014 at 14:56
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    @Petrosian How far do we take this? Why not make the scale 1-99? We'll make 100 = 3,000 and 1 = 30. Each point will be about 30 old points. I mean really.. do you consider someones rating between 30 points? Typically I'd really only consider every 100 points and that's not even completely reliable depending on frequency of play, possible improvement etc.
    – Alan
    Jun 4, 2014 at 15:56
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I suppose it is possible to change the rating scale. But, not all players are necessarily between 800-2900. I've seen plenty of players that have a rating below 800. In the last tournament I played, I saw a kid ranked 111 (who one round happened to beat a 500-600).

I don't think it is desirable to have players ranked negative, so let's just say we take the current rating and divide by 2.9 instead. It's also not guaranteed that players will always be ranked less than 2900, in fact, it is likely we will see a player achieve that rating soon. Magnus Carlsen's peak rating was 2882 and not too far in the past no player had achieved 2800. But, for us regular players we would see ratings in the range 0-999.

Other nations have different rating systems on a different scale. The English rating system would rank a 2000 USCF player around 175 ECF. Personally, I like a little more resolution in my rating than that, but the scale is mostly arbitrary. In the end, you either have a bit more precision or less digits. Either way is not too difficult.

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  • Someone with a FIDE Elo of 111? Wow, I've never seen that. I thought it was almost impossible to have a rating below 900-800... We could just attribute a rating of "000" to this kind of player, or say that they are "unrated". It doesn't really matter since it would only apply to extremely few players (who would probably quickly progress and then get a true rating).
    – Fate
    Jun 4, 2014 at 14:54
  • @Petrosian It was USCF but yes it was the lowest I've seen. I have seen and played 600 rated USCF players and they are not that uncommon. Looking at the cross table, the lowest ratings were: 261, 286, 428, 986, 523, 699, 310, 605, 208, 540, 756, 819, 838. So that's 10 players less than 800 rank in one tournament. At least one such player is 50+ years old and has played at least 13 tournaments. I'm not sure he will exceed 800, 900 easily if any time, but he likes playing and plays often. Anyway, lower ranked players do exist.
    – Alan
    Jun 4, 2014 at 15:49
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    Many, many children have USCF ratings well below 800.
    – dfan
    Jun 24, 2014 at 1:49
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    Now sure what the situation was when this answer was originally posted, but currently, the lowest possible FIDE rating is 1000. If someone's FIDE rating falls below 1000, they are removed from the ratings list and are thereafter treated as "unrated".
    – patbarron
    Feb 24, 2020 at 2:01
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No.

That is not an improvement just a scale change.

What would improve it is requiring people to play more frequently or lose points and also normalizing the average every 6 months or more so that the average is always at a fixed number.

I used 2000 as the average in the 60s when I was doing ratings and the ratings went from 0 to 4000. Nobody ever got close to zero and nobody got close to 4000 so that worked well for us.

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