cool! nice work man, nice work
FIDE vs Chess.com ratings explained
I realized that FIDE Online Arena is no threat no chess.com. Chess.com is just way more convenient. Frist off free members can play unlimited rated games. No installation required whatsoever, the whole contents of Chess.com available on a web browser.
So, these are self-reported FIDE ratings you are matching up?
I think you left off the most important conclusion, then, and the one that might damn your other conclusions: players (on average) will inflate their own ratings when asked what they are.
This is one important bias. However, there are probably many others too. One possible bias that works in the _reverse_ direction is this:
A player may report their FIDE rating when creating their profile, or edit their profile at some point in time to report their FIDE rating. As time goes by, however, their strength changes (and many players have been on chess.com for several years). My guess is that for active players their strength on average increases. Therefore, comparing current chess.com ratings to possibly often-older FIDE ratings probably underrates the FIDE values.
By the way, on the usefulness of this post, I previously had the impression that chess.com ratings are highly overratded compared to FIDE ratings. So e.g. I'm doing about 1600 on chess.com (live, standard) when concentrating and 1400-1500 when distracted (which is all too often), anyway I guessed that this may place my FIDE as low as 1200-1300. The analysis of this post clearly shows my guess was misinformed. Of course, there are still various limitations on what we can infer about an individual player's expceted FIDE rating, as the post itself and various comments have discussed.

FIDE ratings cannot be compared to chess.com ratings because, despite some site action, too many chess.com ratings are inflated due to cheating/assistance.
Would love it if one day they could!
Until then a significant number of high-rated players here are false/fraudulent.

I am Online 1670 and blitz ca 1150. I have not got Fiderating yet, but I guess 1300-1400 Fideplayers are near my level. My blitzrating is low, because I am not fast enough, I need at least 20 miutes pr game to play anyway near my skills. I have not learned enough theory yet, and I need much time to check for errors, so I need thinkingtime to fight good.

By the way, on the usefulness of this post, I previously had the impression that chess.com ratings are highly overratded compared to FIDE ratings. So e.g. I'm doing about 1600 on chess.com (live, standard) when concentrating and 1400-1500 when distracted (which is all too often), anyway I guessed that this may place my FIDE as low as 1200-1300. The analysis of this post clearly shows my guess was misinformed. Of course, there are still various limitations on what we can infer about an individual player's expceted FIDE rating, as the post itself and various comments have discussed.
You are ca 100 points above me here, so I guess you will play above 1400 Fide, comparing .com -players with the clubplayers I met. I think you could join a club and play interesting games from day one.

what's the average rating on standard for chess.com players. I'm around 1500 and I wonder how well-bad I'm doing compared to everybody else...
There is no way the blitz mean is 1685. According to chess.com published distributions, the mean is around 1100. I think the problem is that you are computing statistics for active players which tend to be a lot a stronger. You are not accounting for the thousands that play a few games then drop out. These "invisible" players have a big effect on the rating pool, because you have 100 casual visitors who play only once or twice for every FIDE rated candidate master that plays every night for 5 hours. In the eyes of the rating system, those 100 casuals far outweigh the one active player. Your statistics are probably virtually all active players, but in reality 95% of your population should be one-time dropouts to reflect that actual statistical reality.
To find the explained variance between two variables one has to square the relational coefficients. That implies that correlations between 0.5 and 0.8 share 0.25 and 0.64 of their variance. The shared explained variance between FIDE rating and Online for instance is 0.45. That means that roughly 45% of the reasons why the FIDE ratings is affected is shared with the reasons why Online changes. It does not help to identify which the reasons are shared between the FIDE rating and Online rating.
It also implies that 55% of the change in FIDE rating is caused by reasons, that are not changing Online ratings. Which reasons are different is not indicated by those numbers. Further investigations are needed to find it out.