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Why am I not in the rankings in the bullet?

Just to say my little about that, of course that guessing the result based on ELO works properly for any difference of ratings. (that is how is ELO defined, I assume) But in the case of a 1600 playing against e.g. Komodo, you would probably need more 10 minute games than a man in life can play... Similarly, Carlsen would die bored sooner than a 1600 would beat him (in average) :D
chessico, when you have nothing to say, you start to offend. This is rude and ignorant.
saddam_disney, moreover, Carlsen wouldn't even play 1600-rated player. Unless he would pay him. :)
But you are right, the result based on ELO works properly for any difference of ratings.
Arthur Schopenhauer was very right. When someone has no more arguments, he starts to offend his opponent. How basely...
Chesstroll, limit your replies to one post. Stop multiple posting.

On the other hand, something you need to bear in mind is the fact these are bullet games. The forumla used (ie, if 100 ELO points apart, the stronger player should win roughly 80% of the time) is designed for classic length games, not bullet.

In bullet, there are an exceedingly large numbers of errors made in a game which wouldn't occur in a classic length game. It's like comparing apples to oranges, and you're using formulae which are used to measure oranges, when you should be trying to measure apples.
Ingot, you completely don't understand statistics.

Magnus Carlsen has a 1 in 1800 chance of losing to a 1600 rated player, yes. This doesn't mean that if he plays 1800 games he will lose once, it means that EVERY GAME he has a 1 in 1800 chance of losing. The next game it's a 1 in 1800 chance. The next game 1 in 1800 chance. Which means, theoretically, unless he trips and falls on the board or gets sick and has to forfeit, he has a virtual 100% chance of winning. Likewise, if Cynosure has even just a 1 in 500 chance of losing against a 1600, he is going to win virtually 100% of those games, unless his connection drops or he mouseslips, etc. Therefore the liklihood of Cynosure losing to a 1600 and Carlsen losing to a 1600 are VIRTUALLY the same. They will win VIRTUALLY 100% of their games, because each game has such a small chance of loss. The degree of possibility is irrelevant once you go beyond odds of something like 1 in 100 because you have less than a 1% chance of losing each time you play someone at that rating.

Therefore, only taking games against players that you have less than a 1% chance of losing against over a lengthy period of time without challenging anyone near your rating could be seen as inflating your rating.

Over the last several weeks I've won 100% of the classical games I've played against 1400-1500 rated players. If I continue to play only 1400-1500 rated players my rating will go up to at least 1800 by the end of the year. But I have lost about 50% of games to people of my own rating level. And I haven't won a single game against anyone 1800. So would I really be able to say I'm an 1800 player?

Numbers can lie, and that's why I agree with Toadofsky that we should have a ladder system for the rankings/trophies rather than basing it off ratings alone.

Cynosure, I'm not agree.
It's not errors, which are used for determination of a winner. It's score that is used to determine a winner.
Just look.
For example we have two tournaments.
In the first tournament we have ten players. They play classical games. They play each other and get some score and their ratings change.

In the seconds tournament we have also ten players, but their ratings are same, as ratings of those ten who played classical games. But these people play bullet games.
And, let's take a situation, where their final score is the same, as of previous ten players.
So, what we have:

Both two groups (10 players in each) have 10 players.
Both two groups have same ratings. (For example: if the first has people with 1480, 2000, 2303, then another group has also people with 1480, 2000, 2303, etc.)
Both groups have same final results (if in the first group someone with 1687 rating win 7 games and lose 3, then in the second group, as there is also a player with 1687 rating, he also win 7 games and lose 3. And so on for other players).
The only difference is that the first group played classical games, and the second group played bullet games.

You can obviously see that their (of both groups) final rating will be the same (if someone in the first group moved from 1509 to 1609, then in the seconds group the player with 1509 will also move to 1609).

So, as we see, rating is calculated on score. Not on mistakes or something. So, the rating for bullet games and for classical games works equally. And it depends only on score of people.
And isn't it how the rating system was designed? To determine ratings based on score? So if it works for the score that we get from classical games, why shouldn't it work for the score of bullet games?

And what is when we use ratings-formula? We just convert rating into score, or score into rating. If one says, that such conversion isn't correct, he thereby claims that rating and score are not related equally. But how is it possible?

Because if we have ratings/score in classical games, we can use formula and find score using rating, or find rating using score. Because rating was determined by score. And they are correlated.

But why cannot we do this in bullet? In bullet games is the same. Rating was calculated of score. So we can convert rating into score, or score into rating. And it will be the same, as in classical games. Because score doesn't lose it's function. Rating was calculated on score, so we can say it's accurate. Why it would be different in classical games?

If two players play bullet, 2000-rated against 1600-rated, and first wins 4 times and loses 1 time, they will get some score, and some new ratings.
But if it would be classical games with the same score, would their ratings another in the end? No. So, it's only score, which determine ratings. And it's same for bullet games, for classical games. And it will work even for any kind of sport, where we can get score like 14-2, 2-2 etc.

Fenris1066, I don't agree.
What chance do we have to get in accident?
Or get into crushing plane?
Not very big.
Look, if you say, that everything that is lower than 1% is getting to 0% then, according to your logic, we get the next thing.
We have not very big chance to die into plane.
May be 1/1 000 000. Maybe more, maybe less. But definitely less than 1/100.
But why people still die on planes?
Because there is 1/1 000 000 chance.
This isn't so large, yes?
But people take it into account very seriously.

If something has possibility of 1/1800, it doesn't necessary that it will happen on 1800th time. It can happen on 1st time, or on 4000th time.
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.

According to your logic, there could be 1/100 chance, but everything which is less is impossible.
So it would mean the next.

If the difference in ratings in 800, you have chance to win 1/101.
But if the difference is a bit higher, 810, then your chances are becoming 0. How is that possible?
If the difference is 900, not 800, then according to your words, such player, who has 100 points more, immediately gets some enlightenment, so he hasn't anymore 1/120 chance to lose.
And where is this borderline?
What is the chance that coin will drop Eagle 10 times in a row? 1/1024. And, according to your words, it's impossible.
But you can see this trick of Derren Brown.
If something has a chance of 1800, it means it would happen approximately once in 1800 cases.
Otherwise, anything which is less than 1/100 would never happen.
Do you know what is the chance of creating life on Earth? It's very, very low. Unbelievably low. But why are we alive? Because there is a possibility. Very little, but there is.
Or do yo think that people never get in plane crashes?
The rating will be the same, but I'm not arguing about the rating being the same or not. I'm saying in 1+0, an opponent who is 100, 200, 300 even 400 rating points below you can be more assured of victory than if you were playing a 90+0. The simple fact of the matter is, in a 1+0 you are more prone to make errors - sometimes significant such as dropping your Queen, or leaving major material en prise. In a 90+0 you are far less likely to do so.

Therefore, by even arguing that "100 ELO points apart means the stronger player should win 75% of the time" may certainly be true for classical length games, and I'm sure the percentage refers to classical length games. You are using classical length rules and applying them to bullet games. Bullet is an entirely different class of chess.

So, if Hiimgosu was 2800 in classical, 90+0 games, and Marta Singer also played Hiimgosu in classical, 90+0 games, and you said "Singer has a 36% chance of winning, therefore Singer is within 97.5 rating points of Hiimgosu." Then I'd probably agree with you. But these aren't 90+0 games. These are 1+0 games, and a 1 in 3 chance of someone winning a 1+0 isn't that high - it's odds I'd take because it'd guarantee my rating to go up.

If we use http://en.lichess.org/@/mukundranjan as an example again, his average rating in the period I played him (peak rating doesn't matter, you can get inflated easily in bullet) was around 1630. My own average rating was around 1950. That's a 320 rating difference, averagely. Yet, out of 16 games, Muk won 4 - that's a 25% chance of victory.

If Singer has a 36% chance of victory and that corresponds to a 97.5 rating difference, and Muk has a 25% chance of victory, does that mean Muk's true rating is about 120 lower than mine?

As I said, it's bullet. If these were classic length games, I'd agree with you, but the nature of the beast in bullet is that you will have bad luck more often than in classic.

On the other hand, I've played this user 45 times: http://en.lichess.org/@/azons. I've won 33 games, he's won 12. 12/45 is roughly a 20% chance of winning. Azons average rating was about 1720 (we have history all the way back from 2013 when we were both around 1600!) and my average rating was about 1750. A 20% chance of winning, if Singer's 36% chance of victory = 97.5 rating point difference, should mean my opponent had about a 140 rating point difference to me. Yet that's clearly not the case - when we played, I crushed Azons (to the point where he regularly aborts games rather than play me), yet our average rating was only about 20 points apart. Even now, judging from August 24th - present, Azons average rating has been about 1840, and mine has been about 1890.

The issue is, because we're playing bullet, the games are much more volatile. If we were playing classical, Azons should win probably about 45% of games, with 7% draws. But we're not playing classical, we're playing bullet, so with only a minor average rating difference, you can factor in far more factors for failure than in classical.

So Muk shows how a weaker player can win more than they statistically should, and Azons shows how you can't apply statistics which make sense in a classical format to a bullet format, because it cannot explain discrepancies in ratings.

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