Lichess' average centipawn vs. chesscom's percentage score

Can these two be equated?

I believe nope.

Chesscom woks under proprietary source, which means their code remains closed and is not available to the public; I couldn't find neither any page really explaining the mathematics behind it . This means we cannot be really sure how they define CAPS, so we can't make an analytical equation comparing that with average centipawns loss (also, note that average centipawns loss isn't specific to Lichess, it's something that Stockfish finds, as well as other engines).

The only way I can think of is taking a huge amount of games analyzed, and doing some regression.

Would it work if we played the same game with the same moves on both sites and then analyze?

@ryanjam That's a great idea. Or perhaps someone with some coding skills could take a large enough for sample size purposes number of chesscom games, do some kind of batch import to lichess, and then find a formula that equates one to the other...if indeed they are asking the same questions.

@MFXX Yes, the stuff under the hood is proprietary, but the general idea is pretty intuitive. It's simply a comparison with how well your moves matched up to what an engine would have done.

@watermelonbiscuit Yes, but to me it gives a rather qualitative idea instead of a quantitative one. For example, what does a CAPS of x% actually means? How is it calculated? A centipawn is well defined, but Chesscom gives rather a vague idea instead of a full, clear definition.

One difference between the two are that Lichess' average centipawn loss helps to easily determine cheaters (99%) of the times and on the other hand Chess.com's CAPS score is not very useful in determining cheaters unless you're a premium member as a basic member only gets analysis in depth 18 and a premium member can get a more accurate analysis (Depth 26).

I used this game (because classical might be the best variant to compare). Lichess says 31 and 48 ACPL respectively. Chess.com says 94.8 (white) to 81.6 (black). lichess.org/idbHhUMc#77

This game (lichess.org/XJZZ1TDt#17) is 17 and 46 ACPL, and on chess.dom the accuracies are 98.6 to 90.2. I'm not sure how to compare these, but here are a couple of games for reference. I don't think these would be comparable though, because they have two separate formulas.

They can be equal, but they are totally different. On lichess, it is from 0 to infinity and the lower the better. On chees com it is from 0 to 100 and the higher the better. I think it would be around 80, since 80 percent on chess com is quite good and on lichess as well.

No.

Chess.com's accuracy tracks every move's deviation from the best moves even in won positions. Lichess's centipawn differential does not punish you for suboptimal moves in won positions. Simply put, if your move does not significantly alter your lead, Lichess's centipawn metric is not hurt. With Chess.com though the accuracy will go down if you make suboptimal moves in a won position.

With that said, Lichess's centipawn differential is more useful for analysis than Chess.com's accuracy. The accuracy calculations are veiled behind a secret algorithm. We know how it works in general, but not the specifics of how it works. Moreover, accuracy doesn't really tell you a lot in many positions.

At the end of the day, average centipawn deviations and accuracy scores are not super useful. Go over your games after a loss. Analyze the game without an engine first if you have time. Look over engine analysis after that.