Cynosure, I don't agree.
1. If 2800 rated has a big chance to make a mistake, then 2000-rated has very much bigger chance to make a mistake. So, it compensates. So, in some games 2800-rated will make mistakes, yes. But 2000-rated will make much more mistakes, and, by the way, he has same chances to make worse mistake in the same game, than 2800-rated. So, even if 2800-rated makes mistakes, it is compensated, because 2000-rated make worse mistakes.
2. Your calculations are wrong. And I already mentioned this.
25% isn't 120, but 190. And 20% chance is 240 rating difference.
#138 Okay, let's talk statistics...
I postulate that the rate at which a player errs (makes mistakes) depends on some factor L (lambda) which is a function of a player's rating. So a player with L=1 is likely to err every move, whereas a player with L > 20 goes many moves without error:
en.wikipedia.org/wiki/Poisson_distributionLet's assume that for a player to win, his opponent must err at least 3 more times than the player errs. So for the weaker player to win, his opponent must err multiple times without he himself committing an error. So say that a player with L=5 plays against an opponent with L=10. The L=10 player would lose a game lasting 30 moves if his L=5 opponent makes no mistakes in those same 30 moves. Here's a calculator to try the numbers yourself:
http://stattrek.com/online-calculator/poisson.aspx#cumprob(This leaves open the question of how from a player's rating to calculate L, but at least articulates the general concept that the weaker player does not win after a single error if his opponent is good at the game.)
This is further compounded in variant games where the weaker player might not understand the rules!
Of course, the Poisson distribution assumed independence, which I don't think is likely; a player will err more in bad games, and less in good games (e.g. if a player errs X times, a bad game can be assumed and more errors likely to follow)
#142
"the weaker player does not win after a single error if his opponent is good at the game."
Nobody says that the weaker player always wins after a single error of his opponent. But it doesn't mean that he cannot win.
Ingot, you stated "If you would play 1000 000 games with an opponent who can lose to you once in 1800 games, you would win about 555 games."
Once again, this shows your complete lack of understanding of statistical data. You are once again making the assumption that if you have a certain chance, that chance is objectively going to happen.
If I have a 1 in a million chance of beating Magnus Carlsen, it's theoretically possible that I could play a million games with him and win a million, because each time I have that 1 chance. It is highly unlikely, nearly impossible that I'd win a single game out of that million, maybe never even after playing a billion games because that chance is ridiculously small almost 0%. BUT it does not mean that I will ever win. Nor does it mean that he has to win a single game. That just isn't how statistics reflect reality.
If there is a 1 in 1 million chance my plane will crash, and my plane crashes, it doesn't mean there won't be another plane crash for a million planes. Every single plane has that same statistical chance of crashing. Every single plane can crash, or none of them can crash. Both are possible outcomes, one is more statistically likely to occur (not crashing). This is basic risk assessment, man!
Your logic is flawed, and you continue to put far too much stock in your numbers. Just because your equation may work in certain situations with some arbitrary "good enough" fudging (your predictions fall anywhere from being almost 100 points over the expected rating to within 17 rating points...with that much error margin with such small sample data, it's quite difficult to agree that your equation "works" for anything other than producing some reasonable estimate) but the fact is, it isn't even relevant to this discussion, yet you keep droning on and on about your numbers.
Ratings are intended to be a relative indicator of strength, not a ranking system. Ladders and pools are for rankings. Even FIDE doesn't rely on ratings alone, as was pointed out. The top players in the world aren't going around playing 1300 rated players in club outings to inflate their ratings either. They're playing grand slam tournaments, invitationals, etc. and playing against the other top players in the world. If their rating dips it's because they're losing against the best. If someone climbs to a higher rating, it's because they're killing it in tournaments against top players.
I once again stand firmly by the idea that if we wanted to be "fair" the rankings and trophies would be done by a ladder system or pools (we tried pools, they weren't popular outside of bullet). If you want to drone on about how the ratings are accurate reflections of ranked play, you may, but your data is flawed and uncompelling to people who understand mathematics and statistics.
Fenris1066, no, your logic is flawed.
If you say that if you would play 1 000 000 games where you have a chance to win 1/1800 and you wouldn't win about 555 games, it's the same if you would say, that two players, who are equally rated, will play 1000 games, and one of them will win all games. It's possible, yes. But we don't take this into account.
555/1 000 000 is the average possibility. It means on the very long period of time, for example, infinity, it will happen with such chance.
If the chance for plane to crash is 1 000 000, according to your words, it's possible that all planes will crush. It's possible. But there is a very little chance of it.
If something has a possibility of 1/1800, it can be that you play 1800 games and you win all games, instead of one.
But it's the same if we would consider Magnus Carlsen would play Nakamura 1000:0. It's possible. But it has a very little chance. Just so little that we don't consider it.
And why if reasoned people don't doubt in obvious statistics, they think it's possible to doubt in statistics of small percentages?
Secondly, I don't argue against making ratings not to be rankings. Where did I say that? And you are refuting something fictional that I didn't even state.
Of course top players don't play 1300-rated to determine their rating. It would take tens or hundreds of thousands of games to be clear here. And also because you can't be sure, that 1300-rated players don't cheat, they are not so watched. And their ratings are not so accurate, because it can be boosted intentionally.
But players like Magnus, Nakamura, Anand, all their games are clear, their ratings are clear. You know that you cannot cheat on that level. But on lower levels, there are more possibilities to gain ratings unfairly.
But it's OTB. In online chess, there are same possibilities to cheat if you are 1800-rated and 2800-rated. You will be caught. And we talk about bullet. Where cheating is a program, scanning windows, and in most cases it's neutralized.
Then, how you can see, 1600-rated in OTB also don't play with world champions. But not because it would be not accurate results. But again, because it will take 10 000-s games to win some games.
You continue arguing that if you play with a player, who's chance to win is less than 100, he will win less than 1/100, may be he will not win at all. But why don't you take another side? I see no reasons not to do. Maybe if your chances are less than 1000, you will win more than 1/1000? As you said, it can be, that better players doesn't win a single game, and it can be that a weaker player doesn't win a single game no matter how many games are. So, there are two sides. And in average, it's still 1/1800.
Otherwise let's consider such case, where Magnus Carlsen wins Nakamura 1000:0. Why don't you think about this? Because you saw how Carlsen lose to Nakamura? So, you need things to be on practice to believe in them? But how then do you believe in weather forecast? It's possible that the rain will not go, but you still take an umbrella.
"Secondly, I don't argue against making ratings not to be rankings. Where did I say that? And you are refuting something fictional that I didn't even state."
Then what are you even arguing, because the whole point of this thread is about why someone who has a high RD from not playing games loses their trophy. You've turned it into some ridiculous statistical warfare. I don't even know what you're arguing.
Maybe someone should just close this thread, it's just going in circles and nothing new has been said in the last 4 or 5 pages I think?
Why close it?
We have a discussion. Not a warfare.
What I'm arguing for is:
1) Rating of Singer__Marta is enough accurate to be 2709-2903.
2) People have the right to play with any opponents, no matter what are their ratings.
3) You will get approximately the same rating, if you play with 2800-rated and with 1800-rated, if their ratings are stable.
4) Therefore, it's impolite to call somebody a coward for playing much weaker opponents with stable rating.
1 - irrelevant to anything
2 - irrelevant to determining RD for Glicko-2
3 - Except that if you play consistently players rated signifanctly lower all the time and never anyone near your own level, your RD is going to go up because the confidence in your rating decreases. So if you want to keep trophies, you need to play regularly and you need to play someone within your rating zone now and then. This is how the Glicko-2 system maintains rating stability and thereby if you play nothing but someone 1000 rating below you, your own stability will decrease. This has been explained.
4 - Therefore, while yes, it is impolite to call somebody a coward for playing much weaker opponents with stable ratings, it is not unjust if that player loses their trophy because the rating system loses confidence in that player's own rating variance. Once that player's stability returns by playing someone of their level, they get their trophy back.
So uh....yeah, again, what was the point of your like 10 pages of diatribe again? You seem to just refuse to accept the answers and want to argue petty details instead. And then when people challenge your petty details, you simply say "no, I'm right, you're wrong" and restate the same thing you've said for 10 pages. What am I missing here?
Fenris doesn't believe point number 3.
Fenris doesn't see that you're arguing mainly for point number 4
You don't have statistically significant evidence for point number 3, and never will
Nothing more needs to be said
