How does ELO relate to Skill Level?

[arikanev]

Hey guys, sorry for the 3x opening issues, just really enjoying using your Python package. I noticed that setting an ELO of 4000 gives weaker results than setting the skill level to 20. Do you guys have a direct equation describing the relationship between ELO and Skill Level?

Thanks! Ari

[kieferro]

Hey guys, sorry for the 3x opening issues, just really enjoying using your Python package

No problem <3

I noticed that setting an ELO of 4000 gives weaker results than setting the skill level to 20

The problem is that there is a maximum value (in this case 3190) for the Elo parameter. I don't know exactly what happens if you specify a higher value, but I would imagine that the value is simply ignored. Therefore we are also planning on adding checks for the maxima and minima (#28).

We can't say much about the general question, because it's about the engine itself and we only provide the interface. I found this stackexchange thread where a list is given. But if you really want reliable information, you have to ask in the official Stockfish repo. If you get some information, feel free to link it in this issue thread as well, and we'll be happy to include the information in our README.

[arikanev]

Thanks for the info! I opened an issue with the official repo. It looks like the Stockfish version I'm using is 14. Yes, a min-max threshold would be a good idea. Note that I observed that playing with a 4000 elo still gave decent moves, so I dont think its entirely ignored, maybe just mapped to the highest value possible.

https://github.com/official-stockfish/Stockfish/issues/4717

[johndoknjas]

Hi @arikanev, it's a bit confusing how elo and skill level work, but unfortunately that's just the way the uci protocol made things (and Stockfish implements this protocol). Basically it works like this:

• Only skill level or elo is used at any one time.
• By default, Stockfish uses skill level, and the value is at 20. This is the strongest setting for Stockfish.
• If you call (for example) our set_elo_rating function, this will tell Stockfish to switch from skill level to elo, and will also set the elo to the value you specify.
• When the elo value is passed to stockfish, this is what it does behind the scenes. So if you've given a value higher than 3190 (at least at the time of writing), then Stockfish will lower it to 3190.
• As for whether Stockfish plays stronger at a skill level of 20 vs a 3190 elo, I believe it's the former. At best, the latter would be equal strength, but I'm pretty sure that's not the case. Like you've probably found, the max elo isn't bad per se, but not as good as full strength Stockfish.

[arikanev]

Yes! I've found that the max elo is not as good as the skill level of 20. That's interesting. Why is that? Are both the elo and skill level values affecting the same function that determines the engine performance? If they enable different functions, then by definition I guess they mean different things. If they affect the same function, there must be some direct mapping between the two!

[johndoknjas]

@arikanev I believe for elo the way it works is Stockfish runs as usual, but then they have some algorithm to sometimes select a lower ranked top move. Not sure about skill level but I'd assume they would work similarly.

For max elo vs skill level 20 though, the reason they're different is probably just because Stockfish's normal elo strength is higher. I'm not sure why they don't let you choose a max elo closer to Stockfish's elo (3500+). Maybe something about the algorithm needing buffer room between the two? Just speculating though.

[arikanev]

Interesting! Thanks for the info.