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Old 03-24-2011, 12:27 AM   #21
Not another shrubbery
 
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Default Re: Chess Skill Levels

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Originally Posted by Dragondog View Post
What I want to do is keep the internal probabilities given by the rating system. By doing that, I cannot arbitrarily assign how many points each skill level represents. From SL 14 and up, each skill level is about 90 points, but as RPK points out it can be rounded to 100 points to simplify things. But if we compare SL 13 with SL 15, that’s a difference of 240 rating points.

Setting 2800-2899 as skill 24, for Kasparov, 21 would be 2500 for GM. And using some simplifications, we have:
<SNIP>
But setting all living grandmasters, over a thousand of them, as Top Master Alive, seems too much to me.
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Originally Posted by Dragondog
Setting SL 6 as FIDE 800 gives GM skill 22+, and Kasparov a skill of 26. Which is too high.
This suggests a problem with your methodology. Instead of trying to fit the numbers to a fixed increase in the chance of winning, maybe you should just compromise between that goal, and a table that looks reasonable.
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Old 03-24-2011, 12:39 AM   #22
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Default Re: Chess Skill Levels

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Originally Posted by Dragondog View Post
Setting SL 6 as FIDE 800 gives GM skill 22+, and Kasparov a skill of 26. Which is too high.
I think that you could reasonably argue that top skills in chess will be higher than top skills in other fields, for a few reasons. First, chess is a very narrowly focused field, with no ancillary skills or techniques to support it -- the measure of skill at chess is just Games(chess). Second, chess is easier to train at than a lot of other skills, since there are no great requirements for equipment or facilities, and competitive tournaments are easy to find from very early in a chess player's career. Third, chess is highly prestigious and is played seriously throughout a great portion of the world, and so it's going to attract a much larger field of competitors than, say, croquet.

Put these three factors together and I think you could justify a skill of 26 or maybe even more for the best of all time.
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Old 03-24-2011, 12:46 AM   #23
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Default Re: Chess Skill Levels

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If we give Kasparov a skill of 22, a grandmaster has a skill of 18-19 which seems high considering how many grandmasters there are (more than 1,000 alive as of 12 feb 2011).
Chess doesn't require expensive equipment to practice, it is non-dangerous to play it or even to lose at it, and some cultures also strongly celebrate high chess skill (Russian culture in particular, is my impression).

3 arguments for why high Chess skill should be more common than high skill at other things?
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Old 03-24-2011, 01:11 AM   #24
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Default Re: Chess Skill Levels

Quote:
Originally Posted by Not another shrubbery View Post
This suggests a problem with your methodology. Instead of trying to fit the numbers to a fixed increase in the chance of winning, maybe you should just compromise between that goal, and a table that looks reasonable.
Not basing the skill on the probability in the rating system would defeat the purpose of this rating to skill transformation. Though for the sake of simplicity, I did round the numbers in my two latest posts.

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Originally Posted by Grouchy Chris View Post
I think that you could reasonably argue that top skills in chess will be higher than top skills in other fields, for a few reasons. First, chess is a very narrowly focused field, with no ancillary skills or techniques to support it -- the measure of skill at chess is just Games(chess). Second, chess is easier to train at than a lot of other skills, since there are no great requirements for equipment or facilities, and competitive tournaments are easy to find from very early in a chess player's career. Third, chess is highly prestigious and is played seriously throughout a great portion of the world, and so it's going to attract a much larger field of competitors than, say, croquet.

Put these three factors together and I think you could justify a skill of 26 or maybe even more for the best of all time.
I've considered some of these issues too and though I think that it seems to give excessively high skills, perhaps that is the solution.

Though Purple Haze has still not backed up his claim that 800 is the default adult level.
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Old 03-24-2011, 01:52 AM   #25
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Default Re: Chess Skill Levels

800 for the average adult beginner hass been well observed for a long time. Arpad Elo even mentions it in his book: The Evaluation of Chess Players Past and Present.

It is tough to prove of course since beginners rarely play in tournaments and thus tend not to have ratings.

The official USCF and CFC/FCE classes for tournaments are:

Code:
Open
Expert     2000-2199
Class A    1800-1999
Class B    1600-1799
Class C    1400-1599
Class D    1200-1399
Class E       0-1199
There are usually more E players than D.

When Elo developed the system a bell curve centered at 1500 roughly represented the members of the USCF at that point in the early 50's.
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Old 03-24-2011, 03:06 AM   #26
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Default Re: Chess Skill Levels

*sigh*

While I understand the idea of wanting to peg FIDE scores to actual GURPS skill levels, GURPS is just a game, and certain things are abstracted.

In GURPS, a skill level of 14+ makes you an expert, in this case a Master.

Higher levels of skill make you a Grand Master, obviously, but you can't tie them in to a FIDE score.....there are many expert players that don't compete in tournaments...

And I would peg Kasparov around skill level 22-25, myself.
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Old 03-24-2011, 04:34 AM   #27
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Default Re: Chess Skill Levels

Keep in mind the draw, which is quite important for highly skilled players. Elo doesn't give probabilities of winning, but rather expected scores. An expected score of .75 could mean that they have a 75% chance of winning, 25% of losing and 0% of drawing, or it could mean a 50% chance of winning, a 50% chance of drawing and a 0% percent chance of losing.

A regular contest with full normalization is a bad model, especially at the upper end, given the frequency of draws in real chess. The 1984 world championship between Kasparov and Karpov lasted 48 games, with 40 of them draws.
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Old 03-24-2011, 04:46 AM   #28
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Default Re: Chess Skill Levels

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Originally Posted by Grouchy Chris View Post
I think that you could reasonably argue that top skills in chess will be higher than top skills in other fields, for a few reasons. First, chess is a very narrowly focused field, with no ancillary skills or techniques to support it -- the measure of skill at chess is just Games(chess).
Actually I think that in a chess match between masters other factors than straight Games(chess) might have a big effect. For "normal" GURPS games it is totally not interesting but for a campaign focussing on chess I really would include Will rolls, allow for Intimidation to some extent, maybe even split the game into 3 phases (start, midgame, endgame) and allow specializations/techniques for that.
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Old 03-24-2011, 07:05 AM   #29
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Default Re: Chess Skill Levels

Remember also familiarity penalties. I would definitely give them for someone playing an opening he's never played before, for instance.
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Old 03-24-2011, 07:45 AM   #30
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Default Re: Chess Skill Levels

Quote:
Originally Posted by Dragondog View Post
What I want to do is keep the internal probabilities given by the rating system. By doing that, I cannot arbitrarily assign how many points each skill level represents. From SL 14 and up, each skill level is about 90 points, but as RPK points out it can be rounded to 100 points to simplify things. But if we compare SL 13 with SL 15, that’s a difference of 240 rating points.

Setting 2800-2899 as skill 24, for Kasparov, 21 would be 2500 for GM. And using some simplifications, we have:

19: FIDE 2300
17: FIDE 2100
15: FIDE 1900
14: FIDE 1775
13: FIDE 1650
11: FIDE 1450
9: FIDE 1250
7: FIDE 1050
5: FIDE 800

But setting all living grandmasters, over a thousand of them, as Top Master Alive, seems too much to me.
Setting skill level by "best alive" can cause major problems when the population base varies significantly. The modern serious chess-playing population base is vastly greater than in , say, 1500. A factor of 1000 between the two populations seems reasonable. So either 1500s Europe has no "Top Master Alive", or the modern world has many.

This grates on me, as it happens. The modern world spends vast, vast amounts on education, and puts people in learning positions for far, far longer than earlier times. We are also much closer (not that close, just closer) to a legitimate meritocracy. This suggests that modern skill levels in most fields should be significantly higher than comparable skills pre-mass education.
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