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Elo Rating System
Part I of 2 Parts
This topic arose under the topic “2021 USA Championship” on Wed., 21/10/18. It is a totally separate issue, and so I think it deserves its own thread, since the topic is of some interest.
Below are the more recent of some of the threads there, that give some background to the discussion taking place (Mostly between Pargat Perrer, Bob Gillanders and Bob Armstrong, with others adding in)
Mon., 21/10/18 – Pargat Perrer
Originally posted by Bob Armstrong View Post
“Can we agree on an investigative model, somewhat reflective of reality?: that the 2021 women's pool at the moment has a lower average rating than an open pool of the same number of players. And the average rating of the elite women players is about 200 rating points below that of the elite in the open pool. And for the sake of argument, let's say that, at the moment, there are the same number of players in each pool (arbitrarily.....1000), though in fact the open pool is bigger. For our investigation, I think this fact does not affect the outcome........or do you think it does?”
Yes, I've been saying (and Bob G. agreed apparently) that the key variable is the relative size of the two pools. If you take the size of the open pool now, let's say worldwide it's 100,000 people for just a round number, then we see that with that many people and with some number N rated games between the members of the pool, the highest rating achieved so far is just over 2850.
If the pool grows by X number of members, the rating of Carlsen might reach 2900. Exactly what X needs to be could probably be worked out mathematically.
Now let's say this open pool is actually all men, it's not critical because we have already hypothesized that men and women are equal at chess ability by nature. You can still call it "open pool" if you like.
Now we create a new pool and it is women only. At first it only had let's say 1,000 members. Over time it grows to 10,000, then to 50,000, and finally to 100,000 members. And they are only playing against each other, no games against the men. Now all we need is for the right number of rated games played by all the members to achieve a Bell curve that is accurate enough. Maybe that number is actually less than N, the number of rated games that has been played up to today by the open pool. Or maybe it does need to be N.
Once we reach that number, the Bell curve for the women will be almost totally identical to the open pool curve. That means the outliers will be almost identical in number and in rating, there will be maybe 2 women near to the 2850 rating. This will happen without any woman playing any man in a rated game.
If we can agree on that, then we don't need any investigation, which of course a real investigation cannot happen because we can't actually separate out the men and women in real life.
Here is a question and answer on Quora.com which reinforces my point:
Question: What is the highest Elo chess rating possible?
Shaun Press
, FM, FT, IA, Member FIDE Rules Commision
Answered Jan 17, 2018
A2A
As the question is currently stated - there is no upper limit to Elo ratings. As the pool of players increases, the rating of the highest players get larger (not constantly, but eventually)
If you are looking for a specific number then the question could be restated as - “In a closed pool of N chess players, what is the highest theoretical Elo rating possible?” Then you can calculate the answer.
I underlined the critical statement. This is what you need to understand about Elo ratings.
Bob Armstrong – Tues., 21/10/19
Hi Pargat:
We are making progress.
Yes........what generally happens is that the open pool grows by new, low-rated players entering the pool. They are then beaten up upon by the top players in their section. These top players move up a section, becoming the lowest rated players one section up. But they are over-rated - they didn't improve; they just beat up on weaker players. So the top players in this section beat up on them, and gain rating points, enough to enter the next section up. And so on up the sections 'til the "Open" section. Then in the Open section the top players increase their rating a very small amount by winning away from the bottom, the new rating points brought into the Open Section pool by these bottom rated plalyers.
BUT.......
This increase will be very modest, because of the rating formula FIDE has at the top rating level. Furthermore, the average rating of the elite top 10, for example, will then stagnate and remain the pool's average top rating, since the top players will just trade points back and forth, randomly winning, drawing and losing. This is barring one of the 10 actually being Magnus Carlsen, who could then beat up on the other 9 elite players, and raise his rating to the top level, a ways above the average rating of the other 9 elite players.
Note also: if the new player into the pool is rated the same as the other 10 elite players, and is not Magnus Carlsen, the average ceiling rating of the pool will not change.
Do Pargat and Bob G agree that I have the system properly working so far in my investigation?
Cont'd in Part II below
Part I of 2 Parts
This topic arose under the topic “2021 USA Championship” on Wed., 21/10/18. It is a totally separate issue, and so I think it deserves its own thread, since the topic is of some interest.
Below are the more recent of some of the threads there, that give some background to the discussion taking place (Mostly between Pargat Perrer, Bob Gillanders and Bob Armstrong, with others adding in)
Mon., 21/10/18 – Pargat Perrer
Originally posted by Bob Armstrong View Post
“Can we agree on an investigative model, somewhat reflective of reality?: that the 2021 women's pool at the moment has a lower average rating than an open pool of the same number of players. And the average rating of the elite women players is about 200 rating points below that of the elite in the open pool. And for the sake of argument, let's say that, at the moment, there are the same number of players in each pool (arbitrarily.....1000), though in fact the open pool is bigger. For our investigation, I think this fact does not affect the outcome........or do you think it does?”
Yes, I've been saying (and Bob G. agreed apparently) that the key variable is the relative size of the two pools. If you take the size of the open pool now, let's say worldwide it's 100,000 people for just a round number, then we see that with that many people and with some number N rated games between the members of the pool, the highest rating achieved so far is just over 2850.
If the pool grows by X number of members, the rating of Carlsen might reach 2900. Exactly what X needs to be could probably be worked out mathematically.
Now let's say this open pool is actually all men, it's not critical because we have already hypothesized that men and women are equal at chess ability by nature. You can still call it "open pool" if you like.
Now we create a new pool and it is women only. At first it only had let's say 1,000 members. Over time it grows to 10,000, then to 50,000, and finally to 100,000 members. And they are only playing against each other, no games against the men. Now all we need is for the right number of rated games played by all the members to achieve a Bell curve that is accurate enough. Maybe that number is actually less than N, the number of rated games that has been played up to today by the open pool. Or maybe it does need to be N.
Once we reach that number, the Bell curve for the women will be almost totally identical to the open pool curve. That means the outliers will be almost identical in number and in rating, there will be maybe 2 women near to the 2850 rating. This will happen without any woman playing any man in a rated game.
If we can agree on that, then we don't need any investigation, which of course a real investigation cannot happen because we can't actually separate out the men and women in real life.
Here is a question and answer on Quora.com which reinforces my point:
Question: What is the highest Elo chess rating possible?
Shaun Press
, FM, FT, IA, Member FIDE Rules Commision
Answered Jan 17, 2018
A2A
As the question is currently stated - there is no upper limit to Elo ratings. As the pool of players increases, the rating of the highest players get larger (not constantly, but eventually)
If you are looking for a specific number then the question could be restated as - “In a closed pool of N chess players, what is the highest theoretical Elo rating possible?” Then you can calculate the answer.
I underlined the critical statement. This is what you need to understand about Elo ratings.
Bob Armstrong – Tues., 21/10/19
Hi Pargat:
We are making progress.
Yes........what generally happens is that the open pool grows by new, low-rated players entering the pool. They are then beaten up upon by the top players in their section. These top players move up a section, becoming the lowest rated players one section up. But they are over-rated - they didn't improve; they just beat up on weaker players. So the top players in this section beat up on them, and gain rating points, enough to enter the next section up. And so on up the sections 'til the "Open" section. Then in the Open section the top players increase their rating a very small amount by winning away from the bottom, the new rating points brought into the Open Section pool by these bottom rated plalyers.
BUT.......
This increase will be very modest, because of the rating formula FIDE has at the top rating level. Furthermore, the average rating of the elite top 10, for example, will then stagnate and remain the pool's average top rating, since the top players will just trade points back and forth, randomly winning, drawing and losing. This is barring one of the 10 actually being Magnus Carlsen, who could then beat up on the other 9 elite players, and raise his rating to the top level, a ways above the average rating of the other 9 elite players.
Note also: if the new player into the pool is rated the same as the other 10 elite players, and is not Magnus Carlsen, the average ceiling rating of the pool will not change.
Do Pargat and Bob G agree that I have the system properly working so far in my investigation?
Cont'd in Part II below
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