Real-World Skill Levels: ELO

[Anthony]

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.

[Fred Brackin]

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.

[ravenfish]

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.

[Anthony]

Originally Posted by ravenfish

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.

The odds of winning a quick contest in GURPS depends on the difference in skill between the two competitors. The odds of winning a chess match by ELO rating depends on the difference in rating between the two competitors. This makes them immediately comparable, because they actually do exactly the same thing, and does in fact imply a linear correspondence.

[johndallman]

Originally Posted by Fred Brackin

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.

[Donny Brook]

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.

[Pursuivant]

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.

[Infornific]

Originally Posted by johndallman

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%.

[Infornific]

Originally Posted by Anthony

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.

Except a game as a quick contest of skills is a simplification. If you played out a chess game with the same detail as combat there would be more dice rolls, and randomness should even out. You're much more likely to get one lucky/unlucky roll than three in a row.

[Anthony]

Originally Posted by Infornific

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.