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This answer has a link to the Lichess blitz rating distribution which looks like this:

enter image description here

It looks like a good approximation to a normal distribution, perhaps slightly skewed to the upper half, and has an interesting sawtooth appearance with spikes on the 100 marks. This is for blitz.

I'm really curious as to what is going on here and for comparison would like the FIDE standard rating distribution to see if it is similar as that might give some more insights into what is going on.

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It is first worth visiting the Lichess link and having a closer look at their sawtooth curve. They do not plot individual rating points. Instead they round to the nearest 25 point. So, it is not the case that you have local maxima exactly on each 100 point. We don't know how they round their numbers so we don't really know what is going on.

Here is the rating distribution for FIDE standard rating data extracted from the January 2022 data:

enter image description here

Three things stand out.

  1. It's not really a normal distribution
  2. There looks to be a discontinuity about the 2000 mark, almost as if two different distributions have been stitched together
  3. There are two massive spikes at 2005 and 2205. The 2004 count is 316 and 2005 is 440. The 2204 count is 141, 2205 count is 291.

For comparison here is the same data graphed for FIDE Bltiz:

enter image description here

So, also not really a normal distribution but no discontinuities and no significant spikes.

The numbers 2005 and 2205 are significant numbers in FIDE rating history. Take a look at this rating distribution for January 1992 extracted from FIDE standard rating data obtained from the Olimpbase:

enter image description here

Here there are quite clearly two graphs added together and there are massive spikes at 2005 and 2205.

The explanation for this is that in the early days you didn't get a FIDE rating unless you were over 2000 for females and over 2200 for males and because in those days FIDE ratings were in increments of 5 that meant you had to get at least 2005 if you were female and 2205 if you were male.

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    Just speculating, but humans like even numbers, so once someone reaches say 2000, they might choose to "retire" and not have a chance for the number to update, even if their skills decline. whereas if they are at say 1997, they might push themselves to get better/try again
    – user2813274
    Jan 29, 2022 at 22:37
  • @user2813274 this is definitely true, there are quite a few people who peaksit which is why you see this kind of pattern in various time controls. E.g. it is even more pronounced in bullet, and yet more in ultrabullet. Interestingly, the longer the time control the less people seem to care about it.
    – koedem
    Jan 30, 2022 at 2:47
  • There is the issue that FIDE rated events in US have higher entry cost unless over a set US rating. But US players just below that level need to enter FIDE rated events to play better player as the better players don't play in none FIDE events.
    – Ian Ringrose
    Jan 30, 2022 at 23:58
  • @koedem The explanation of what you noted isn't that people care less to sit on a rank at higher time controls. Instead, the faster the time control is, the more random the outcome is. In other words, much worse players can beat much better ones since there is less time for the skilled player to think and find strong moves. Less time means more guessing. The result is a person has a much higher chance of reaching an Elo higher than what they deserve through a streak gotten by luck in ultrabullet, and when someone sees that number they don't deserve, they kind of like to keep it.
    – user904963
    Nov 1 at 8:10
  • @user904963 that is quite possibly. It might also be that the sheer number of bullet games you can play means you will just by chance reach a rating that is a higher outlier eventually. I am not sure about the claim of better upset chances in bullet, since if those do happen, the ratings will reflect that; there might be more upset wins, but conversely there might be more upset draws at classical that still give good rating boosts against high rated opposition. In the end the exact cause doesn't really matter much.
    – koedem
    Nov 1 at 8:19
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Some distribution based on 2022-01 FIDE blitz xml file.

1. All players

enter image description here

2. Rating and title

enter image description here

3. Age and title

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4. Juniors with title

enter image description here

5. U-25 with 2600 and above blitz rating

                  name country sex title  rating  birthday  age
     Firouzja, Alireza     FRA   M    GM    2791    2003.0 19.0
        Erigaisi Arjun     IND   M    GM    2745    2003.0 19.0
           Nihal Sarin     IND   M    GM    2705    2004.0 18.0
Abdusattorov, Nodirbek     UZB   M    GM    2663    2004.0 18.0
     Muradli, Mahammad     AZE   M    IM    2645    2003.0 19.0
    Niemann, Hans Moke     USA   M    GM    2636    2003.0 19.0
    Sindarov, Javokhir     UZB   M    GM    2630    2005.0 17.0
      Sadhwani, Raunak     IND   M    GM    2616    2005.0 17.0

6. Top countries with promising young players

U-25 with 2200 and above blitz rating. count is the number of players, mean is the mean rating of those players.

Table 1

u25 blitz rating >= 2200, sorted by count:
         rating      
           mean count
country              
RUS      2313.0   143
GER      2311.0    67
IND      2369.0    46
UKR      2324.0    33
USA      2389.0    31
CHN      2333.0    26
ESP      2291.0    24
HUN      2316.0    22
IRI      2333.0    20
FRA      2309.0    19
POL      2359.0    18
CZE      2295.0    17
CUB      2276.0    17
SRB      2346.0    17
AZE      2329.0    15
KAZ      2357.0    15
ITA      2304.0    14
NOR      2387.0    13
ISR      2327.0    13
ARM      2403.0    12
AUT      2332.0    12
GRE      2322.0    12
SVK      2330.0    11
NED      2482.0     8
ENG      2275.0     8
SLO      2315.0     8
CRO      2338.0     8
TUR      2397.0     8
MDA      2318.0     7
SWE      2276.0     7
CAN      2292.0     7
UZB      2490.0     7
GEO      2269.0     6
ROU      2362.0     6
BLR      2306.0     6

Table 2

u25 blitz rating >= 2200, sorted by mean rating:
         rating      
           mean count
country              
UZB      2490.0     7
NED      2482.0     8
ARM      2403.0    12
TUR      2397.0     8
USA      2389.0    31
NOR      2387.0    13
IND      2369.0    46
ROU      2362.0     6
POL      2359.0    18
KAZ      2357.0    15
SRB      2346.0    17
CRO      2338.0     8
CHN      2333.0    26
IRI      2333.0    20
AUT      2332.0    12
SVK      2330.0    11
AZE      2329.0    15
ISR      2327.0    13
UKR      2324.0    33
GRE      2322.0    12
MDA      2318.0     7
HUN      2316.0    22
SLO      2315.0     8
RUS      2313.0   143
GER      2311.0    67
FRA      2309.0    19
BLR      2306.0     6
ITA      2304.0    14
CZE      2295.0    17
CAN      2292.0     7
ESP      2291.0    24
CUB      2276.0    17
SWE      2276.0     7
ENG      2275.0     8
GEO      2269.0     6
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