user3237: 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?

user3118: 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.

user1201: 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.

user2789: 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.

3237: <p>Since all chess player’s ratings are between 800 and 2900, why don’t we make a new rating defined like this:</p>

<p>New rating = (Old rating – 800) / 2.2</p>

<p>So that all chess player’s ratings would be between 0 and 999</p>

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

<p>New rating = (Old rating – 1000) / 2</p>

<p>(Though here extremely weak players would have a negative rating.)</p>

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

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

<p>What do you think? Is there something obvious that I missed or am I really right?</p>
 3118: <p>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).</p>

<p>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.</p>

<p>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.</p>
 1201: <p>Sure, you could compress the current range like that. The issue, though, is that ELO is <em>not</em> an objective scale with absolute endpoints. It's only a measure of play strength relative to past opponents.</p>

<p>The fact that no current player has an ELO above 2900 does not mean that such ratings are impossible. Until 1990, <a href="http://en.wikipedia.org/wiki/List_of_FIDE_chess_world_number_ones" rel="nofollow noreferrer">no one had a rating above 2800</a>. In fact, there's no mathematical upper bound on ELO rating at all: see <a href="https://chess.stackexchange.com/q/5251/1201">this question</a>, for example. The "big range of [unused] numbers" is infinite.</p>

<p>So yes, you <em>could</em> 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 <code>log ELO</code> 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.</p>

<hr>

<p>Perhaps the most pertinent question of all is, <em>why</em>? 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.</p>
 2789: <p>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.</p>
