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What is the average rating of a GM, IM, FM, CM and NM on Lichess? Spreadsheet/graphs included.

Made some stats I found interesting, thought maybe others would too! (TLDR + spreadsheet at the bottom)

But if you like a challenge; write down your guess for what you think the average titled ratings are like this :

GM: XXXX Blitz, XXXX Bullet
IM: XXXX Blitz, XXXX Bullet
FM: ...
CM: ...
NM: ...
(I was pretty off with mine)

So I was just practicing some basic CSV work with python and figured I might as well make something interesting of it, luckily Lichess is a goldmine of CSV files so I basically pulled all the results from all Titled bullet and blitz arenas and made some stats. So this is obviously nowhere near a complete list of titled players on Lichess and it will obviously be featuring a huge amount of overlap since the same players tend to play these tournaments. And I would love to do something similar for all titled players on the site and it should be possible since all profiles are open, but I couldn't figure out how, any help on this would be greatly appreciated!

But regardless this was still over 50k datapoints for titled players ratings taken over 4 and 7 years for blitz and bullet respectively, and to me it had some really interesting insights:
1. The Bullet inflation. I expected to see some but to see that it continues so dramatically still was quite surprising, especially considering how stable the blitz ratings seem to be. No idea why, would love to hear theories!
2. How big the gap between IM and GM is. Like I guess it makes sense, but I did not expect it to be so significantly bigger than the gap between IMs and FMs.
3. NMs being generally stronger than CMs. I expected the oposite due to there being more ways to get the NM title and the variations in federations strength level could lead to some pretty big deviations.
4. The median FM rating and the average tournament rating is consistently absurdly close, essentially FMs are the perfect average of titled players.
5. Bortnyk is a beast in blitz with 8 wins, Naroditsky is a monster in bullet with 16 wins!
6. Carlsen has too many -stein accounts with arena wins! (4 accounts with 12 wins in total)

Some choice clarifications:
1. Women's titles: I did initially include them but there was so few that it didn't produce any statistically meaningful insights.
2. Median vs average: Extreme outliers seemed to cause a lot of noise when using averages so I mostly stuck to medians.
3. The participation graph was included because I heard the site was dying to chess.com, seems to be doing quite fine imo.
4. Threw some Winners stats in there just for fun quite hastily.

TLDR and Spreadsheet (Graphs are under the numbers):
docs.google.com/spreadsheets/d/11UnkGu0ccuMwYBGDeuQNTJmDS2VlBaNRZNlFRKf_nqM/pubhtml

Results:
GM: 2730 Blitz, 2950 Bullet
IM: 2560 Blitz, 2710 Bullet
FM: 2470 Blitz, 2600 Bullet
CM: 2360 Blitz, 2490 Bullet
NM: 2380 Blitz, 2510 Bullet

*Rounded to the nearest 10 for readability, exact values in the spreadsheet. Bullet seems to still be climbing so averages (actual averages in this case) are calculated over the last 12 months, while blitz has been remarkably stable since 2022.

Thanks for reading!
I got the NM bullet peak and I'm only missing 60 blitz points... I have 1850 FIDE rating
seems like my goal of 2500 in one time control ( blitz/rapid/classical ) is like me being nearly IM level. I sure hope that isnt the case, I am nowhere near IM :P
I didn't look at your graphs but my guesses were pretty good, next to what you reported as the values. I figured it would start at about 2800 at the highest level and then decrease by 200 rating points, progressively down to the lowest level. (I like to keep things simple.)

I was tracking pretty good over the highest three levels, but then the ratings don't keep falling linearly any more. Maybe it just becomes more dependent on who goes after the norms to get the higher title at that level.
not on Lichess, in the titled arena only.

Many lower rated titled players don't play titled bullet arena, I guess.
If you are not a decent bullet player you lose almost all games, no fun...
Thanks, now I can brag about my lichess ratings using these stats ^__^
Very interesting post. Btw it's very difficult to compare the NM and CM titles, usually you can get the CM if you reach the rating of 2200 but you can also get it by finishing in the top places in a Continental or World Youth Championship or if you score 50% or more over at least 7 games so not all CM are 2200 strength, some are considerably weaker.
I'd like to publish a FOSS tool with polls the Lichess API (within limits) and generates such regressions, but I'd need a way to discover titled player usernames.