Rating of Performance on Game Analyses

I would like lichess.org to add the estimated rating of each player's performance to the analysis board when looking at a game. It would be a simple but useful addition in my opinion. If this already exists, and I just missed it, please point it out to me. Thank you.

How would this be done? You can't simply use averige centipawn loss (ACPL) loss for this, as you can have 20 ACPL on a game where you blundered a queen and both rooks, but because the game took extremely long, the vast majority of your moves would have 0 ACPL (staying at the max, 10 or -10). Of course, it's possible to do it using this (maybe something like 3000 - 30ACPL lichess blitz rating), though it would be extremely inaccurate and useless.

MessyAnswer, I am not sure how it is done, but I know that it is something already instituted in Tournaments on the final screen displaying the winners, and it is usually pretty accurate. An example here: en.lichess.org/tournament/yhkwE9kV where under "Berserk Rate" it is listed "Performance".

I was thinking about this post, while comparing some games with the post-game analysis feature and came up with this for a formula.

3000-ACPL(10)-B(100)-M(10)-I

where B=number of blunders, M=mistakes, and I=inaccuracies

The calculated game ratings (four) for the two games I was looking at seemed kind of high.

This was all just done off the top of my head so don't get too critical guys. Look at it as a draft.

#1 "It would be a simple but useful addition in my opinion... I am not sure how it is done."

Lichess Feedback in a nutshell. Don't get me wrong, if done correctly it could be useful; however, I highly doubt that it's possible to get everyone to agree to do it correctly.

@Asym #3

The performance ratings in tournaments are calculated purely with how you scored against certain opponents. For example, if you defeat a 1100 rated player and then lose to a 1300 rated player, your performance rating will be somewhere in between there (I think it should be 1200, though I'm not quite sure). See en.wikipedia.org/wiki/Elo_rating_system#Performance_rating for a detailed explanation.

For one single game, this would be useless, because with only the score and the rating of your opponent, the only results could be
- Infinite (or the rating of your opponent + 400) if you defeated your opponent;
- Infinitely low (or the rating of your opponent - 400) if you lost to your opponent;
- The rating of your opponent if you drew your opponent.

OK folks, I've refined my formula a little bit.

3000-ACPL(10)-B/Mv(10,000)-M/Mv(1,000)-I/Mv(100)

Where in addition to #4, Mv=number of moves

Now time to test it. I'll get back to you with some results.

OK, I did some calculations. The formula in #7, is at least within bounds (800 to 3000) from what I initially can see, but it gives very high ratings. It might be good for every bodies ego!

I tried tweaking the formula to find something empirically and came up with this:

3000-ACPL(10)-(B/Mv*100,000)^.75-(M/Mv*10,000)^.75-(I/Mv*1,000)^.75

This gives a more reasonable rating value, but may be too easy on a player that doesn't make mistakes and too hard on the rating value as you make more mistakes. Also, I don't know if it would stay within the lower bound of 800.

Fun to play with numbers, thanks guys for a very stimulating Sunday morning - or maybe it was the coffee. :-)

@LDog11 Nice to see you messing around with the numbers some, trying to get a decently working formula. If lichess really wanted to make up a formula that comes close to reality (which I highly doubt), they should probably use their statistics gathered by Chess Insights. This could give an idea of the playing strength in the game, though as I mentioned in #2, ACPL isn't really a good metric and blunders, mistakes and inaccuracies don't always work extremely well either.

@MessyAnswer Thanks, always nice to know you're not just talking to yourself.