I suppose the question could also be rephrased as how many handicap games are needed to confirm the shape of the Elo per rank curve with sufficient confidence over a sufficient range.
The EGD only has some 100,000 handicap games in it, some 10% of all the games. That wasn’t really enough to determine the shape of the curve. But the EGF uses declared ranks, so even game results already gave enough data to determine the shape of the curve and the handicap game data was found to be at least consistent with that curve.
Even though relatively few OGS games are played with (larger) handicaps, I assume there are still many more than 100,000 handicap games in OGS’s historical data. If there are like a million, I expect it to be enough.
The numbers below are from a period of like 2 months 3 years ago, where some 17% of all games were with handicap, although mostly with small handicap:
handicap | count | %
----------+--------+----------------------------
0 | 432969 | 82.63
1 | 68731 | 13.12
2 | 13528 | 2.58
3 | 2990 | 0.57
4 | 1969 | 0.38
5 | 1250 | 0.25
6 | 917 | 0.18
7 | 605 | 0.12
8 | 392 | 0.07
9 | 659 | 0.13
[2021 Rating and rank adjustments - #382 by anoek]
And 4 years ago, anoek posted OGS handicap game statistics for handicap up to 4 stones on different board sizes, where handicap games also seemed to make up some 20-30% of all games on OGS.
See the tables in item 2 of 2020 Rating and rank tweaks and analysis which I copied below:
9x9 ranks predicting 9x9 games
Handicap 0 Handicap 1 Handicap 2 Handicap 3
30k 47.8 : 49.6 [n=2579] 33.3 : 49.8 [n=39] 28.0 : 48.5 [n=25] 40.7 : 48.9 [n=27]
25k 48.4 : 49.7 [n=20436] 44.7 : 48.7 [n=4417] 54.7 : 49.6 [n=311] 65.4 : 50.1 [n=104]
20k 47.7 : 49.6 [n=60398] 45.0 : 48.9 [n=32404] 51.5 : 49.5 [n=555] 63.6 : 49.6 [n=176]
15k 47.4 : 49.4 [n=207911] 44.7 : 48.8 [n=70964] 54.0 : 49.3 [n=2123] 63.6 : 49.7 [n=558]
10k 48.9 : 49.4 [n=333649] 45.6 : 49.1 [n=44339] 55.5 : 49.6 [n=1802] 71.4 : 50.3 [n=245]
5k 49.3 : 50.2 [n=83326] 44.2 : 49.9 [n=2287] 61.4 : 50.0 [n=451] 75.0 : 51.4 [n=96]
1d 52.8 : 50.9 [n=4699] 58.3 : 50.1 [n=24] 100.0 : 52.2 [n=3] --
6d 46.7 : 54.1 [n=15] -- -- --
ALL 48.4 : 49.5 [n=713013] 45.0 : 48.9 [n=154474] 54.8 : 49.5 [n=5270] 65.8 : 50.0 [n=1206]
13x13 ranks predicting 13x13 games
30k 44.6 : 49.6 [n=121] 47.5 : 49.9 [n=219] 100.0 : 48.3 [n=1] 50.0 : 47.1 [n=2]
25k 48.0 : 49.5 [n=2773] 45.5 : 49.7 [n=1756] 52.9 : 49.5 [n=104] 32.6 : 48.9 [n=43]
20k 44.0 : 49.3 [n=14530] 45.4 : 49.8 [n=11125] 44.4 : 49.4 [n=941] 42.7 : 49.4 [n=293]
15k 45.8 : 49.3 [n=60647] 46.5 : 50.0 [n=16939] 49.7 : 48.8 [n=2864] 39.7 : 49.1 [n=648]
10k 47.3 : 49.4 [n=85200] 47.8 : 50.3 [n=12933] 59.7 : 49.4 [n=2635] 48.0 : 49.9 [n=306]
5k 49.3 : 50.3 [n=17200] 45.4 : 50.0 [n=866] 58.3 : 49.8 [n=357] 57.6 : 49.9 [n=33]
1d 46.2 : 51.0 [n=249] -- -- --
6d 66.7 : 60.7 [n=3] -- -- --
ALL 46.7 : 49.4 [n=180723] 46.5 : 50.0 [n=43838] 53.3 : 49.2 [n=6902] 42.5 : 49.3 [n=1325]
19x19 ranks predicting 19x19 games
30k 48.4 : 49.6 [n=1504] 42.9 : 49.1 [n=212] 39.2 : 49.4 [n=227] 34.3 : 49.7 [n=67]
25k 45.9 : 49.5 [n=18333] 40.9 : 49.6 [n=4517] 40.0 : 49.7 [n=4083] 41.2 : 49.8 [n=857]
20k 47.3 : 49.5 [n=98224] 42.4 : 49.2 [n=20335] 41.3 : 49.2 [n=14927] 42.2 : 49.3 [n=4369]
15k 49.0 : 49.4 [n=235420] 43.5 : 48.7 [n=40980] 43.3 : 48.6 [n=26238] 45.5 : 48.9 [n=10026]
10k 49.6 : 49.3 [n=344796] 45.0 : 48.6 [n=45871] 46.3 : 48.5 [n=23862] 47.3 : 48.9 [n=9851]
5k 49.7 : 49.5 [n=245545] 44.8 : 48.7 [n=17596] 44.7 : 48.4 [n=8277] 41.8 : 48.4 [n=3881]
1d 49.2 : 49.8 [n=33502] 42.6 : 49.5 [n=2086] 47.5 : 50.0 [n=1100] 47.5 : 50.0 [n=589]
6d 48.9 : 50.6 [n=1585] 54.1 : 49.4 [n=181] 70.0 : 50.3 [n=50] 76.9 : 53.3 [n=26]
ALL 49.2 : 49.4 [n=978909] 43.9 : 48.8 [n=131778] 43.9 : 48.8 [n=78764] 45.0 : 48.9 [n=29666]
Combined rating system
Predicting 9
30k 49.2 : 49.8 [n=17573] 47.8 : 48.6 [n=2060] 49.2 : 49.9 [n=240] 68.0 : 49.9 [n=125]
25k 48.6 : 49.7 [n=43982] 45.5 : 48.7 [n=22370] 56.2 : 49.8 [n=299] 63.0 : 50.5 [n=100]
20k 48.1 : 49.5 [n=117350] 45.1 : 48.4 [n=56551] 53.7 : 49.3 [n=779] 70.5 : 49.6 [n=325]
15k 49.0 : 49.5 [n=262529] 45.4 : 48.1 [n=53642] 57.7 : 49.5 [n=1413] 72.6 : 49.8 [n=332]
10k 50.6 : 49.7 [n=206142] 47.9 : 48.6 [n=14727] 57.1 : 49.7 [n=1120] 71.7 : 50.8 [n=237]
5k 49.9 : 50.2 [n=49161] 43.4 : 49.0 [n=648] 60.5 : 50.6 [n=124] 75.0 : 49.2 [n=12]
1d 54.9 : 50.6 [n=4802] 52.1 : 47.7 [n=73] 100.0 : 51.5 [n=9] 87.5 : 53.4 [n=8]
6d 59.6 : 51.8 [n=171] -- -- --
ALL 49.4 : 49.6 [n=701710] 45.6 : 48.4 [n=150071] 56.3 : 49.6 [n=3984] 70.6 : 50.1 [n=1139]
Predicting 13
30k 49.3 : 49.6 [n=2094] 49.5 : 49.8 [n=2393] 65.6 : 49.0 [n=32] 48.6 : 49.9 [n=37]
25k 47.5 : 49.5 [n=8051] 46.9 : 49.5 [n=8310] 41.6 : 48.8 [n=308] 33.3 : 49.1 [n=33]
20k 46.5 : 49.2 [n=24573] 46.3 : 49.6 [n=20826] 49.8 : 48.6 [n=1222] 46.2 : 49.6 [n=279]
15k 47.6 : 49.2 [n=78278] 47.3 : 49.5 [n=24001] 50.5 : 48.2 [n=2349] 41.1 : 49.5 [n=445]
10k 49.0 : 49.4 [n=86805] 47.9 : 50.0 [n=13165] 57.8 : 48.3 [n=1500] 48.4 : 50.0 [n=182]
5k 50.5 : 50.2 [n=19668] 45.6 : 49.9 [n=1041] 56.2 : 48.9 [n=169] 46.7 : 47.2 [n=15]
1d 54.5 : 50.7 [n=985] 60.7 : 51.2 [n=28] 100.0 : 45.8 [n=4] --
6d 40.5 : 51.8 [n=42] -- -- --
ALL 48.3 : 49.4 [n=220496] 47.1 : 49.6 [n=69764] 52.1 : 48.4 [n=5584] 44.0 : 49.6 [n=991]
Predicting 19
30k 50.5 : 49.6 [n=2299] 44.3 : 48.9 [n=221] 36.9 : 48.5 [n=222] 31.7 : 49.5 [n=63]
25k 48.0 : 49.5 [n=10385] 42.3 : 48.9 [n=3479] 40.6 : 48.9 [n=3215] 38.3 : 49.2 [n=664]
20k 47.7 : 49.4 [n=61028] 41.1 : 48.7 [n=18301] 39.3 : 48.9 [n=15631] 39.9 : 49.0 [n=3557]
15k 48.7 : 49.3 [n=224916] 42.1 : 48.4 [n=48650] 41.1 : 48.6 [n=34843] 41.8 : 48.9 [n=12427]
10k 49.2 : 49.3 [n=410840] 43.1 : 48.3 [n=68206] 43.2 : 48.5 [n=40606] 44.0 : 48.9 [n=15422]
5k 49.6 : 49.4 [n=381050] 44.3 : 48.4 [n=32244] 44.5 : 48.3 [n=15511] 43.1 : 48.4 [n=6854]
1d 49.4 : 49.9 [n=60938] 41.3 : 49.0 [n=3580] 46.5 : 49.2 [n=2010] 44.3 : 49.0 [n=1061]
6d 49.0 : 50.6 [n=2519] 53.2 : 50.0 [n=220] 66.1 : 50.4 [n=59] 84.8 : 52.3 [n=33]
ALL 49.2 : 49.4 [n=1153975] 42.8 : 48.4 [n=174901] 42.2 : 48.6 [n=112097] 42.7 : 48.8 [n=40081]
Combined prediction of all games
30k 49.3 : 49.8 [n=21966] 48.5 : 49.2 [n=4674] 44.7 : 49.2 [n=494] 54.7 : 49.8 [n=225]
25k 48.3 : 49.6 [n=62418] 45.5 : 48.9 [n=34159] 41.9 : 48.9 [n=3822] 41.2 : 49.4 [n=797]
20k 47.8 : 49.4 [n=202951] 44.6 : 48.7 [n=95678] 40.7 : 48.9 [n=17632] 42.7 : 49.1 [n=4161]
15k 48.7 : 49.4 [n=565723] 44.5 : 48.5 [n=126293] 42.2 : 48.6 [n=38605] 42.6 : 48.9 [n=13204]
10k 49.6 : 49.4 [n=703787] 44.5 : 48.6 [n=96098] 44.1 : 48.5 [n=43226] 44.5 : 48.9 [n=15841]
5k 49.7 : 49.5 [n=449879] 44.3 : 48.5 [n=33933] 44.7 : 48.3 [n=15804] 43.1 : 48.4 [n=6881]
1d 49.8 : 49.9 [n=66725] 41.6 : 49.0 [n=3681] 46.8 : 49.2 [n=2023] 44.6 : 49.1 [n=1069]
6d 49.6 : 50.7 [n=2732] 53.2 : 50.0 [n=220] 66.1 : 50.4 [n=59] 84.8 : 52.3 [n=33]
ALL 49.2 : 49.5 [n=2076181] 44.6 : 48.6 [n=394736] 43.1 : 48.6 [n=121665] 43.5 : 48.9 [n=42211]