Alas that is not the formula chess.com uses. They use the considerably more complicated Glicko rating system. I'll get you the article, although if you wish to google it, there is a link somewhere to the formula itself...
https://support.chess.com/article/210-how-do-ratings-work-on-chess-com
Yeah I saw that too but the difference is really only in the beginning when you have played very few games, after that it is the same as normal ELO. I know for sure because I replicated my ELO graph, after some 50 games or so it was exactly the same.
I'd think there would still be some difference since your rating adjustment depends on a relationship between your respective Glicko RDs as well as the rating difference. Pity chess.com no longer makes our RD public. Nice work in any event, so well done!
Yeah I saw that too but the difference is really only in the beginning when you have played very few games, after that it is the same as normal ELO. I know for sure because I replicated my ELO graph, after some 50 games or so it was exactly the same.
The rating deviation (RD) value impacts ratings even after your first games, it's part of the overall algorithm for every game played.
I just started playing chess a few weeks ago and I got curious how the ranking works. So I found out that its based on the ELO forumla for player A is:
Ea = 1 / (1 + 10^((Ra-Rb)/400) )
and where Ra - Rb is the differens in ranking between the players.
I think its all quite clever, even if it ain´t no rocket sience.
Anyways, after having now played some 600 rapid games I thought I noticed a much larger difference in my oponent skill than what the ELO formula would suggest. For example, accoring to ELO my expected score against a player with +100 ranking would be 0.36. Which menas I would win 36% of the games (if there are no draws). But I won far less games when my oponent was that much stronger. And vice verse, I won a vast majority of the games where I was ranked 100 points higher.
So I got curious to find out if this feeling I had was factual. So I copied the list of all my games into excel and did som calculations in order to see if I could somehow calculate out the correlation between ELO difference and result. And this is what I found out.
From the 500 games I have played (I skipped the first 100) I calculated the accuracy (variance) of the difference between Acutal score and Expected score. So if forexample I won a game where the expected score was 0,6, the variance for that game would be (1-0.4)^2 = 0.36. And if I lost, the variance would be (0-0.4)^2 = 0.16.
Then I adjusted the "400-factor" until I got the lowest total variance for all my games played.
And the result was that I should use a factor 140 (instead of 400) if I want to have the best possible guess on the outcome of my games. And the gut feeling I had that the formula underestimates the difference in skill when one player is stronger was correct (at least for my games). Instead of 36% chance of winning against a +100 player, my odds are only around 16%.
You can also see the correlation in this graph.
I did not put any labels but blue shows my average score (Y axis) vs difference in ELO (x-axis). Orange is what would be expected from the ELO formula. Chess.com mostly picks me players ranked +/- 75 points so data outside approximately +/- 50 is based on very few samples and not very accurate. But the trend is clear.
So after that I got the idea to see if I could tune the ELO forumla to i further improve the Expected score accuracy. And I found out that I got the highest accuracy if I changed the K-factor (I think its called?) from 16 to 26. Which means my ranking will change faster than the original forumla, if you meet an oponent with same ranking give you +/- 13 points instead of +/- 8. But I am a beginner and my rating varies quite a lot and also improved some 300 points during these games, and the result may not be the same for a more experienced player.
Then as a last thing I modified the ranking so that I also used future games (which you can of course not do for games that are not yet played.). And maybe not so surprisingly I could further improve the Expected score accuracy. Here is what it looks like in a grap (red = chess.com ELO, blue = my own estimated ELO base on both history as well as future games).
Could this be any useful? Not for me (because I suck at chess and don´t really care about my ranking, I just get these nerdy ideas sometimes that I want to calculate something) but maybe it could be interesting for some chessplayers to get an ELO that in a more accurate way represents your current skill level?