How many folks on chess.com are rated in each level, step by 100?

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YankeeBastid

Way back when I was creating the 4teamchess competitions, I calculated how many players there were by chess.com rating. I generated a spreadsheet to illustrate the differences. But now I have forgotten how I did it. Please take a look and see if you can figure out how I can update the percentage to current numbers?: Back then there were  6 million 15 thousand players. I know I used information that was readily available here. 

rank number pct 25000
100 89717 0.014914 373 1 373
200 195111 0.032433 811 374 1184
300 328633 0.054629 1366 1185 2549
400 470841 0.078268 1957 2550 4506
500 572374 0.095146 2379 4507 6885
600 631917 0.105044 2626 6886 9511
700 628286 0.104440 2611 9512 12122
800 594633 0.098846 2471 12123 14593
900 516472 0.085853 2146 14594 16739
1000 442244 0.073514 1838 16740 18577
1100 359953 0.059835 1496 18578 20073
1200 293519 0.048792 1220 20074 21293
1300 230314 0.038285 957 21294 22250
1400 177690 0.029537 738 22251 22988
1500 135053 0.022450 561 22989 23550
1600 101053 0.016798 420 23551 23970
1700 74537 0.012390 310 23971 24279
1800 54458 0.009053 226 24280 24506
1900 38479 0.006396 160 24507 24666
2000 29077 0.004833 120 24667 24786
2100 19299 0.003208 80 24787 24866
2200 12724 0.002115 65 24867 24931
2300 8153 0.001355 60 24932 24991
2400 5143 0.000855 55 24992 25046
2500 2500 0.000416 50 25047 25096
2600 1744 0.000290 45 25097 25141
2700 1020 0.000170 40 25142 25181
2800 490 0.000081 35 25182 25216
2900 220 0.000037 30 25217 25246
3000 90 0.000015 20 25247 25266
3100 14 0.000002 14 25267 25280
3200 2 0.000000 2 25381 25282
  6015760 25282
6015760
YankeeBastid

ok, the percentages are for a level 100 say, 89717 divided by 6015760 should be = 0.0149136601194197. so out of the total players that pct are rated in the 100's. I don't remember what the other columns represent right now.

rubik28917

The 4th column is what one gets by scaling down to 25,000. For example, at the rating level of 900, the percent is 0.085853. That times 25,000 is 2146.328976, which rounded off gives the value in column 4.

This holds true up to the 2100 level. Beyond that it goes haywire.

scooter_de

Cool stuff!

How can one obtain those data?

rubik28917

The 5th column is the sum of everything above it in the 4th column + 1. So the value for the 900 level in the 5th column is the sum of the 4th column from 100 to 800. Some of these numbers are off by 1, which I expect is some kind of rounding error. Also the value for 3200 is off by 100.

The 6th column is the sum of the 4th and 5th.

YankeeBastid

It is coming back. rubik, I am using 25000 instead of 6 million and applying the pcts to a population of 25000. so. 0.014914 times 25000 us 342.85 rounded up to 343. Do that for each of the pcts against 25000 and then the numbers kinda make sense.

scooter, that is what I am trying to remember.

rubik28917

The data in column 1 is obvious. The data in column 3 is percentages of the total. Columns 4-6 are based on scaling to 25,000. So the only thing missing is the one column that really matters.

The most annoying developer (of programs or statisics or whatever) I've ever met is myself. I do stuff like this, don't write anything down, because it's easy to remember, then don't. Good luck remembering.

YankeeBastid

at 77 years old, my memory is slipping. I know I did those calculations for a reason, but dam if I can remember today what they were. But, your responses got my brain fluid working so after a good long nap, I might wake up with an epiphany.

YankeeBastid

I think I remember how I was able to compile the percentages. WAY way back, when I first joined chess.com, the total number of players at each level was published and available here on chess.com. I was curious to see what percent of the total membership these numbers represented so that I could determine how many players would be represented no matter the total number of participants. So, that is why I made those calculations. whew.

jas0501

https://www.chess.com/leaderboard/live/rapid has an interactive chart:

YankeeBastid

ahhhh, that is cool. So, those numbers seem to seem to coincide with what I saw back then. Thank you for the update. I have closed my competition, by the way.

Crick3t

And you can easily get the json if you want to update your numbers.
https://www.chess.com/callback/leaderboard/live/sidebar/standard/stats

{
"rank": null,
"percentile": null,
"stats": {
"rating_distribution": {
"100": 1720825,
"200": 2945662,
"300": 3667848,
"400": 4412803,
"500": 4256737,
"600": 3872437,
"700": 3652472,
"800": 2890598,
"900": 2213907,
"1000": 1735383,
"1100": 1301699,
"1200": 998943,
"1300": 700177,
"1400": 495814,
"1500": 353630,
"1600": 255180,
"1700": 172663,
"1800": 116079,
"1900": 73464,
"2000": 51932,
"2100": 28610,
"2200": 15089,
"2300": 7161,
"2400": 2808,
"2500": 896,
"2600": 263,
"2700": 110,
"2800": 19,
"2900": 7,
"3000": 1
},
"avg_rating": "634.0615",
"player_count": 69394862
},
"user_stats": {
"win_count": 20,
"loss_count": 64,
"draw_count": 9
},
"user_rating": 1372
}

YankeeBastid

thank you for taking the time to resurect that API. I think that is what I did then. It is pretty cool to see where you stand against all 6 plus million chess players around the world. It might be interesting to associate where all the players stand by country to see which country is the strongest by chess.com standards. What do ya think?

Bobcat

I'm sure someone has the final say about

who is that?

on the phone

Superhero_og

Wholesome to see chess.com community helping a man