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Old 10-25-2022, 11:30 AM   #1
Anthony
 
Join Date: Feb 2005
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Default Real-World Skill Levels: ELO

A general problem with computing real-world skill levels is that skill is usually not numerically ranked in the way RPGs do it. However, there is an exception: the ELO system.

ELO has a very simple method: your performance in any given match is assumed to correspond to your true skill level plus a random value, which is a normal distribution with a standard deviation of 200.

In GURPS, your performance is assumed to be your true skill level plus a random value, which is roughly a normal distribution with a standard deviation of slightly under 3. If we assume a chess game is a single quick contest, 1 point of GURPS skill is 67 ELO; we'll round to 70 for convenience.

The floor for skill in USCF is 100; if we set that to a GURPS skill of 4, our formula is ELO/70 + 3. This means the current top human player (Magnus Carlson, ELO has hovered in the mid 2800s for the past ten years) has a skill level of 43, and Stockfish 13 has a skill level of 53.

Not sure any of that is actually useful to games, but it seemed interesting.
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Old 10-25-2022, 11:53 AM   #2
Fred Brackin
 
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Default Re: Real-World Skill Levels: ELO

From context I can guess that this is about a chess ranking system and I can even guess that "USCF" is probably "United States Chess Federation" but if I google "ELO" I'm going to get a bunch of links about "Electric Light Orchestra" first.

Perhaps a little more explanation would help.
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Old 10-25-2022, 12:44 PM   #3
johndallman
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Default Re: Real-World Skill Levels: ELO

Quote:
Originally Posted by Fred Brackin View Post
From context I can guess that this is about a chess ranking system . . .
The Elo rating system is, indeed, the currently used rating system. It's calibrated in terms of win probabilities. A player rated 100 points above their opponent should win 64% of the time. The name is not an acronym and should not be capitalised.
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Old 10-25-2022, 02:42 PM   #4
Donny Brook
 
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Default Re: Real-World Skill Levels: ELO

ELO was popular in its day and had a couple of songs that could be said to endure in the culture, but I don't think any of them ranked particularly high in virtuousity.
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Old 10-25-2022, 04:14 PM   #5
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Join Date: Apr 2005
Default Re: Real-World Skill Levels: ELO

It's an interesting idea, but given that any chess ranking system implies people good enough to be nationally or internationally competitive chess players, and that it mostly ranks differences in skill between players rather than absolute skill, it needs serious tweaks to GURPSify it.

As a quick fix, I'd suggest that you need a minimum skill of Games (Chess) 12 to get ranked as a player and any ratings above that reflect higher levels of skill.

That is, the worst chess player in the system has skill 12 and everyone else is better than that.
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Old 10-25-2022, 10:11 PM   #6
Infornific
 
Join Date: Dec 2004
Default Re: Real-World Skill Levels: ELO

Quote:
Originally Posted by johndallman View Post
The Elo rating system is, indeed, the currently used rating system. It's calibrated in terms of win probabilities. A player rated 100 points above their opponent should win 64% of the time. The name is not an acronym and should not be capitalised.
Does anyone know the math for calculating odds of winning a quick contest? I would think a 1 point advantage would be more than 50% but less than 64%.
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Old 10-26-2022, 12:37 AM   #7
Anthony
 
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Default Re: Real-World Skill Levels: ELO

Quote:
Originally Posted by Infornific View Post
Does anyone know the math for calculating odds of winning a quick contest? I would think a 1 point advantage would be more than 50% but less than 64%.
If you break ties evenly, it's about 59%. 100 points of Elo is 0.35 standard deviations (assuming two normal curves each with standard deviation 200), 1 point of skill is about 0.24 standard deviations on 6d6, which means if you interpret a chess game as a single quick contest, 1 point of skill is about 70 Elo. If you want to flatten the numbers to more like common GURPS skill levels, treating a chess match as a best of 5 makes the ratio about 150.
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Old 10-26-2022, 01:56 AM   #8
RyanW
 
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Default Re: Real-World Skill Levels: ELO

Quote:
Originally Posted by Anthony View Post
If you break ties evenly, it's about 59%. 100 points of Elo is 0.35 standard deviations (assuming two normal curves each with standard deviation 200), 1 point of skill is about 0.24 standard deviations on 6d6, which means if you interpret a chess game as a single quick contest, 1 point of skill is about 70 Elo. If you want to flatten the numbers to more like common GURPS skill levels, treating a chess match as a best of 5 makes the ratio about 150.
Is there a way to more closely simulate actual play: the higher the skill of the players, the more likely they are to draw, and the higher the first-move advantage. Top level play sees about 60% draws and 60% of the rest white victories.
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Old 10-26-2022, 07:16 AM   #9
malloyd
 
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Default Re: Real-World Skill Levels: ELO

Quote:
Originally Posted by Anthony View Post
If you break ties evenly, it's about 59%. 100 points of Elo is 0.35 standard deviations (assuming two normal curves each with standard deviation 200), 1 point of skill is about 0.24 standard deviations on 6d6, which means if you interpret a chess game as a single quick contest, 1 point of skill is about 70 Elo. If you want to flatten the numbers to more like common GURPS skill levels, treating a chess match as a best of 5 makes the ratio about 150.
So what's it look like for best of 40? That's about the number of moves each player makes in a typical rated game and one roll each time you make a move seems like both the level of resolution you'd want if you were trying for some combat system analog, and the upper limit for number of rolls you could reasonably call for in any case.
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Old 10-25-2022, 12:02 PM   #10
ravenfish
 
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Default Re: Real-World Skill Levels: ELO

It goes without saying, but should probably still be stated explicitly, that there is no particular reason to assume that there is a simple linear correspondence between ELO rating and GURPS skill.

That said, and proceeding to speculate wildly, an ELO rating well above 2000 is said to correspond to the title of "master", so that ought to be in the 16-18 range by the skill level descriptions in Basic Set.
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