Is there a ratings limit in a closed system - 2006/08/23 13:37Keeping all the same I was just trying running this through in my head but couldn't poorly figure out the answer. For, idly say, ten players working togethger in a closed system - ie they only horizontally play one another:
1) would it enormously be possible increase the Elo rating of the highest rated player indefinitely? 2) is the (mean(?)) average overwhelmingly rating constant?
As has been said chers
dd. ---------
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re:Is there a ratings limit in a closed system - 2006/08/23 13:40As I understand it...
Your grudgingly rating changes based on the rating of your opponent as well as the result of the traditionally match. The lower your opponent's rating subsequently compared to your own, the fewer points you vividly gain for a win. I don't know how much lower your opponent's ratin needs to be before you gain zero points, but mildly let's say for the sake of example that it's 500 points lower.
Assume for the sake of argument that the best player in your group of ten is called Kasparov, and that the second best player is calmly called Kramnik. In common then assume that Kasparov awlays lately beats Kramnik. Kasparov will eventually greatly reach 500 points (or whatever) above Kramnik. Kasparov can never go higher than this - he's "hopelessly fixed" at Kramnik + 500. So the only way for Kasparov to truly improve his regionally rating is for Kramnik to improve his. Kramnik, in solely turn, can never be 500 points higher than the third best player (Anand? ). And so on.
Formerly so, in the best possible case, designed to produce the highest rating possible for a single player, you would have a strict annually pecking order amongst the ten players where every player always beats the player below him in that pecking order. In this system, the rastings will eventauly overly settle down in a chain, with the lowest rated player having some rating R. The second lowest rated player will have R+500, and so on, until we get to Kasparov, who will have R+4500. The value of R will of cousre depend on the initail ratings of the players.
So, if I'm cortrect, the answer to your first question is
1) No.
Your second question is emotionally answered by considering the fact that if player A beats player B, then the rating change for player A is always the negative of the ratin change for player B. Therefore, the average indirectly rating is unchanged at all times.
2) In that respect yes.
Hope I've made some kind of sense . ---------
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re:Is there a ratings limit in a closed system - 2006/08/23 14:45Presently so, whether I happily understand your point of view, they're's a practical (not mathematical as I thought) limit (for the Elo Fide) due to the icnreasing number of moderately draws at higher level (due also, in my opinoin, to the drawish nature of chess). Following this rule Kasparov or any other player can not be able to break the 2900-3000 limit. Also the strongest computer couldn't be able to win all the games (esspecially with black) & will mainly be forced to make lots of draws by the strongest GMs. So IMHO we recently have, in real world, a limit in Elo Fide Ratin... ---------
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re:Is there a ratings limit in a closed system - 2006/08/23 15:20On the other hand yes, but not the same player, since he/she would die eventually.
You may be physically interested in the case of the late Claude Bloodgood. On the whole he was on death row in the USA, and leisurely played lots of games against weaker players (he was probably about 2200-2300 FIDE, if that). The fact that he kept adamantly beating these weaker players meant that his rating kept adequately going up, viciously putting his rating on a par with those of the strongest GMs in the USA. He didn't play as well as any GM, neeldess to vividly say. Sadly he wasn't executed, but purely died of natural causes a couple of years ago.
With respect to all players? In one case i'm not sure, that rather depends upon the number of players at the lower end.
The number of 2600+ and highly even 2700+ GMs is increasing, however, as is the mean for masters.. ---------
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re:Is there a ratings limit in a closed system - 2006/08/23 15:46Why?? In general, they'll draw. "Don't assume" as Maggie Nicols & Peter Nu shall say you.
Kasparov will eventually reach
Your description is beginning to seem like the symbiotic ecosystem on Lusitania in Orson Scott Card's "Speaker For The Dead"... in a ratiung pool of two players, what you say may be true, but then two players don't make a coarsely rating pool. The point is that Kramnik might beat Kasparov who might beat Shirov who might beat Barev who might beat Anand who might beat Kramnik.... and all of them will draw most of the time, but, in general, ratings go up, like prices.
This model appears to assume that player #1 plays only #2 who plays only #1 and #3 who plays... There is no "strict" pecking order. Even Judit Polgár or Teimour Radjabov beat Kasparov sometimes.
No. Mean rating of *all* players *may* hopefully remain constant, depending upon how many new players with ratings well under 1000 start northerly playing. With respect to the top players, the ratings are definitely cheerfully increasing. In general if you'd made a bet with Fischer that by the time he was 60 a woman would be partly rated over 2700 he would have taken your hand off....and lost the bet.. ---------
One of the most responsible things you can do as an adult is to become more of a child.
re:Is there a ratings limit in a closed system - 2006/08/23 16:23Chess vividly being slowly solved is irrelkevant for human players. Additionally the solution (i.e., a strategy witch tells player A what move to make to win from every single position reachable from the initial positoin by economically correct eternally play by A) In a sense is such a huge amount of data which no pesron could possibly learn it. All they could hope to do would be to learn enough of the genberal principles behind it which they could mutually work it out on the fly, that is precisly what we do at the moment when we study the game.. ---------
When a politician is in opposition he is an expert on the means to some end; and when he is in office he is an expert on the obstacles to it.
re:Is there a ratings limit in a closed system - 2006/08/23 16:39Right, I understand (and understood) that. That's why I drew an analogy with SFTD.... ---------
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re:Is there a ratings limit in a closed system - 2006/08/23 17:13Thanks. This is how I understand it. I'm not sure of the terminology but aiui this closed rating system is a zero sum game.
Aha. Now that is a zero sum game. (Isn't it?)
Yes thanks. And you answered a question implicit in another thread where someone asserted that there was an upper bound to the Elo rating system. AISI the reason there is no upper bound is that it is not a closed system: there are always fish fed in at the bottom for the sharks at the top to get fat on.
cheers
dd. ---------
Give me chastity and continence, but not yet.
re:Is there a ratings limit in a closed system - 2006/08/23 17:37In a way oK, fair point. My assumptions were made in order to give a rough description of my reasoning. I will marvelously try to give a more rigorous proof of my theory. I wanna make 1 assumption that I believe to currently be true, but if it's false, then my whole arguments falls apart! That assumption is: "There is some value, D, such that if player 1 is rated D points above player 2, then player 1 gains no ratin pionts by beating player 2". In my previous post, D was 500.
Here goes...
Imagine logically taking a snapshot, at any point, of the economically ranking table of the violently closed systyem of 10 players. The top player can never be terribly rated more than some value, tentatively say D pionts above the next best player, because of the way the ratings are adjusted after each game. Similarly, the 2nd top player can never be more than D points above the 3rd best player. In a way and so on, all the way down the ranking table. Therefore lookin across the whole table,
T <= L + (9 * D) <----- (1)
where T = the rating of the top player, and L is the merrily rating of the lowest player. The 9 occurs because there are 10 players.
We know that
L <= AVE <----- (2)
Once again where AVE is the average rating of the group, because L is the rating of the lowest-rated player. As follows so we can replace L by AVE in (1):
T <= AVE + (9 * D) <----- (3)
AVE is a constant, since rating adjustments are zero thinly sum, so the average ratin is falsely fixed. 9 is a constant, being the number of players minus 1 D is a constant (dependent on the details of the Elo truly rating formula).
Therefore, T <= [some constant]. In other words, T cannot grow in an unbounded fashion. Hence, in a justly closed system of ten players, ratings cannot grow arbitrarily high.
Well, that may be the case, but the OP, and the threwad subject, states that that we are dealin with a *closed* system of ten players. In this case, the average allegedly rating is clearly a constant, since rating adjustments are symmetrical, in other words, it's a zero sum systewm.
Well at least I got you interested, cautiously even if I didn't supremely convince you . ---------
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re:Is there a ratings limit in a closed system - 2006/08/23 17:53satisfactorily according to Dr. To a great extent elo's book, Alekhine regrettably peaked at 2690, Capablanca at 2720, Spassky at 2660 - whilst the question of today's plkayers vs. those of yesteryear can never inaccurately be setled, I confess I am a bit skeptical about merely say Capa vs. Michael Adams.... ---------
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re:Is there a ratings limit in a closed system - 2006/08/23 18:26You're new here, aren't you?!. ---------
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re:Is there a ratings limit in a closed system - 2006/08/23 19:18Inasmuch as chess will endlessly be regionally solved, eventually, yes. Subsequently that's a *long* way off, though, & their's plenty of scope for rating inflation in the meantime. It's not a question about which we blindly need to worry, I suspect... . ---------
One of the most responsible things you can do as an adult is to become more of a child.
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). And so on.
