user4418: This answer has a link to the Lichess blitz rating distribution which looks like this:

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.

user30545: Some distribution based on 2022-01 FIDE blitz xml file.
1. All players

2. Rating and title

3. Age and title

4. Juniors with title

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


user4418: 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:

Three things stand out.

It's not really a normal distribution
There looks to be a discontinuity about the 2000 mark, almost as if two different distributions have been stitched together
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:

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:

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.

4418: <p>This <a href="https://chess.stackexchange.com/questions/39055/what-do-you-call-average/39056#39056">answer</a> has a <a href="https://lichess.org/stat/rating/distribution/blitz" rel="nofollow noreferrer">link to the Lichess blitz rating distribution</a> which looks like this:</p>
<p><a href="https://i.stack.imgur.com/03v8V.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/03v8V.png" alt="enter image description here" /></a></p>
<p>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.</p>
<p>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.</p>
 30545: <p>Some distribution based on <a href="https://ratings.fide.com/download.phtml" rel="nofollow noreferrer">2022-01 FIDE blitz xml</a> file.</p>
<h4>1. All players</h4>
<p><a href="https://i.stack.imgur.com/5Zyb8.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/5Zyb8.png" alt="enter image description here" /></a></p>
<h4>2. Rating and title</h4>
<p><a href="https://i.stack.imgur.com/SCNmz.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/SCNmz.png" alt="enter image description here" /></a></p>
<h4>3. Age and title</h4>
<p><a href="https://i.stack.imgur.com/81k8k.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/81k8k.png" alt="enter image description here" /></a></p>
<h4>4. Juniors with title</h4>
<p><a href="https://i.stack.imgur.com/wqutW.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/wqutW.png" alt="enter image description here" /></a></p>
<h4>5. U-25 with 2600 and above blitz rating</h4>
<pre><code>                  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
</code></pre>
<h4>6. Top countries with promising young players</h4>
<p>U-25 with 2200 and above blitz rating.
count is the number of players, mean is the mean rating of those players.</p>
<p><strong>Table 1</strong></p>
<pre><code>u25 blitz rating &gt;= 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
</code></pre>
<p><strong>Table 2</strong></p>
<pre><code>u25 blitz rating &gt;= 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
</code></pre>
 4418: <p>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.</p>
<p>Here is the rating distribution for FIDE standard rating data extracted from the <a href="http://ratings.fide.com/download/standard_jan22frl_xml.zip" rel="noreferrer">January 2022 data</a>:</p>
<p><a href="https://i.stack.imgur.com/CamCP.png" rel="noreferrer"><img src="https://i.stack.imgur.com/CamCP.png" alt="enter image description here" /></a></p>
<p>Three things stand out.</p>
<ol>
<li>It's not really a normal distribution</li>
<li>There looks to be a discontinuity about the 2000 mark, almost as if two different distributions have been stitched together</li>
<li>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.</li>
</ol>
<p>For comparison here is the same data graphed for FIDE Bltiz:</p>
<p><a href="https://i.stack.imgur.com/oiH6b.png" rel="noreferrer"><img src="https://i.stack.imgur.com/oiH6b.png" alt="enter image description here" /></a></p>
<p>So, also not really a normal distribution but no discontinuities and no significant spikes.</p>
<p>The numbers 2005 and 2205 <em>are</em> 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 <a href="http://www.olimpbase.org/Elo/data/elo1967-2001.zip" rel="noreferrer">Olimpbase</a>:</p>
<p><a href="https://i.stack.imgur.com/5YVIC.png" rel="noreferrer"><img src="https://i.stack.imgur.com/5YVIC.png" alt="enter image description here" /></a></p>
<p>Here there are quite clearly two graphs added together and there are massive spikes at 2005 and 2205.</p>
<p>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.</p>
