Win rate by players ranks in OGS

q4w56 · May 28, 2017, 7:18am

I made this chart that show the win rate of black in OGS. Row is black rank, column is white rank. The +k in column means that white is k kyu stronger than black. In summary, every kyu rank roughly increases the win rate by 10%.

black win rates, total: 17799
b/w    +0    +1    +2    +3    +4
20k    52    45    27    33    23
19k    51    48    32    26    29
18k    39    40    34    28    25
17k    56    40    35    28    28
16k    43    44    28    23    30
15k    50    37    34    23    23
14k    46    46    35    25    20
13k    46    41    36    24    20
12k    47    43    35    21    23
11k    46    38    32    25     8
10k    49    45    38    28    26
 9k    49    39    32    27    11
 8k    44    41    37    20    18
 7k    51    38    25    23    12
 6k    46    39    28    16    25
 5k    49    38    24    27    10
 4k    46    45    29    31    11
 3k    45    38    19    19    24
 2k    45    33    20     9     -
 1k    43    43    18     -     -
 1d    45    41    12     -     -
  *    47    41    30    24    21


game counts, total: 17799
b/w    +0    +1    +2    +3    +4
20k    67   139   102    89    47
19k    81   152   137    81    42
18k   104   160   144   124    57
17k   107   194   151   111    65
16k   125   223   185   137    74
15k   143   234   217   137    73
14k   161   285   265   155    64
13k   166   330   242   138    65
12k   202   348   254   154    57
11k   228   337   279   125    50
10k   287   405   272   167    53
 9k   286   385   234   132    54
 8k   252   299   237   158    61
 7k   252   390   323   176    49
 6k   280   471   264   139    32
 5k   395   432   303   112    30
 4k   290   391   164   103    37
 3k   377   400   225   124    21
 2k   173   223   128    32     -
 1k   112   146    40     -     -
 1d   129    71    25     -     -
  *  4240  6021  4194  2411   934

Some details:

Data is crawled from the OGS api in 2 days.
The sample size is not really big (~200), so the win rate is likely not accurate.
Only 19x19, non-handicapped, 6.5 komi, non-timeout games are counted.

Eugene · May 28, 2017, 7:46am

Right, that’s it. When I get to 18k I’m dropping black, white all the way for me

Conrad_Melville · May 29, 2017, 12:49am

Thank you for this interesting compilation. It doesn’t surprise me. I believe komi is too large for weaker players, as they lack the ability to exploit the advantage of the first move (I can personally vouch for this!). I talked about this on another thread, New Way of Deciding Komi.The outliers for 20, 19, and 17k are hard to explain, but the large swing at 18k suggests that these ranks are part of some statistical fluke—perhaps the effects of sandbaggers. You know something is not right when 18k players of black are losing more games against equal players than against players who are a stone stronger.

Farraway · May 29, 2017, 2:17pm

Note that the sample size was ~ 200 games for each stat so we can’t say much about the anomaly at 18k. One thing to note, though:

Isn’t it more likely that komi is irrelevant for weaker players? The game is far more likely to be decided by mistakes that cause huge swings in the score.

Eugene · August 12, 2017, 1:16pm

It’d be interesting to do this again with the new ranks …

flovo · October 28, 2019, 6:32pm

total number of games (live, 19x19, ranked): 267152
max deviation: 125
timerange: 2018-01-01 to 2019-10-01

column is blacks rank, row white-black. 0 is everything within ±1, the others (1, 2, -1, …) are 1 rank wide.

winrate black

rank	-9	-8	-7	-6	-5	-4	-3	-2	-1	0	1	2	3	4	5	6	7	8	9
25k	–	–	–	–	–	–	–	–	–	50.3%	23.2%	23.6%	16.5%	16.5%	13.5%	8.1%	6.8%	13.5%	12.2%
24k	–	–	–	–	–	–	–	–	75.7%	42.4%	32.4%	21.0%	16.5%	17.6%	8.7%	12.9%	4.1%	2.9%	6.5%
23k	–	–	–	–	–	–	–	79.7%	62.7%	45.9%	28.2%	17.9%	23.2%	13.0%	5.8%	8.0%	9.0%	6.5%	3.8%
22k	–	–	–	–	–	–	80.8%	71.1%	71.3%	49.9%	34.8%	32.1%	21.7%	17.4%	13.7%	16.0%	15.3%	8.5%	6.2%
21k	–	–	–	–	–	82.9%	78.4%	73.5%	66.4%	49.2%	33.7%	26.7%	19.2%	18.3%	14.0%	6.0%	12.4%	8.8%	3.6%
20k	–	–	–	–	79.8%	74.6%	76.0%	73.5%	69.5%	51.0%	34.4%	28.2%	22.7%	15.4%	13.2%	10.1%	7.7%	4.1%	4.4%
19k	–	–	–	80.4%	87.8%	78.9%	71.4%	73.6%	67.2%	51.6%	37.5%	27.6%	20.9%	15.4%	11.0%	9.4%	7.0%	5.4%	4.8%
18k	–	–	88.5%	85.1%	83.2%	74.1%	76.6%	74.6%	67.1%	52.4%	39.2%	32.2%	24.8%	20.5%	11.9%	12.3%	7.4%	5.8%	10.3%
17k	–	84.6%	86.3%	76.7%	76.6%	78.2%	75.6%	72.5%	69.5%	55.3%	39.5%	27.5%	22.4%	17.3%	12.6%	8.4%	7.7%	3.1%	5.4%
16k	90.7%	97.4%	80.9%	92.1%	81.5%	80.2%	77.3%	72.7%	66.5%	49.7%	34.4%	25.9%	18.6%	14.3%	9.7%	9.8%	5.8%	4.1%	8.2%
15k	95.2%	83.8%	88.0%	84.5%	85.2%	84.3%	77.6%	74.4%	69.5%	51.0%	36.9%	27.0%	19.5%	13.5%	9.5%	6.1%	6.0%	4.2%	3.1%
14k	93.1%	86.8%	89.4%	94.4%	82.6%	83.6%	82.3%	81.5%	75.3%	54.0%	37.7%	27.4%	22.8%	19.1%	13.2%	12.9%	9.5%	6.0%	2.8%
13k	83.3%	95.1%	83.6%	83.3%	86.1%	86.6%	83.3%	78.3%	72.2%	54.0%	34.1%	26.2%	18.2%	14.8%	12.2%	7.4%	5.6%	4.1%	7.1%
12k	95.0%	90.0%	80.8%	85.3%	86.8%	82.7%	84.6%	77.6%	72.0%	53.8%	33.0%	23.3%	15.5%	11.3%	8.7%	10.7%	5.4%	2.5%	1.9%
11k	86.7%	89.7%	84.8%	93.3%	87.7%	84.9%	83.6%	81.2%	74.9%	56.4%	36.9%	23.7%	16.1%	10.9%	8.6%	6.6%	6.6%	4.9%	3.9%
10k	91.8%	89.7%	92.8%	92.2%	84.1%	83.7%	85.6%	79.5%	74.3%	52.6%	31.3%	20.3%	15.1%	13.0%	8.1%	5.1%	3.9%	5.1%	0.0%
9k	96.3%	90.8%	92.9%	92.4%	89.9%	89.2%	82.4%	80.7%	77.3%	55.8%	33.6%	25.5%	16.8%	10.9%	7.8%	7.0%	5.7%	1.1%	0.0%
8k	92.3%	97.7%	90.2%	89.1%	92.0%	86.7%	86.7%	82.0%	77.6%	55.6%	34.5%	22.3%	13.8%	10.3%	11.6%	5.1%	1.9%	0.0%	10.5%
7k	100.0%	90.7%	75.5%	91.7%	90.0%	84.2%	79.1%	80.3%	77.2%	54.7%	32.2%	21.4%	13.6%	11.1%	4.7%	3.0%	0.9%	0.0%	0.0%
6k	93.9%	90.1%	89.9%	88.6%	87.0%	85.6%	82.2%	81.3%	75.7%	54.5%	32.8%	17.9%	13.3%	8.4%	9.6%	6.5%	0.0%	2.1%	12.5%
5k	94.2%	96.2%	95.9%	91.1%	85.4%	87.2%	80.9%	80.0%	72.3%	53.8%	32.7%	22.0%	13.2%	8.4%	6.4%	4.4%	5.6%	8.0%	0.0%
4k	94.9%	95.5%	96.5%	91.2%	89.4%	87.3%	86.8%	80.9%	73.8%	53.2%	33.9%	18.7%	11.4%	9.7%	5.8%	0.0%	7.1%	9.4%	0.0%
3k	98.1%	95.9%	93.2%	92.0%	90.9%	90.9%	86.9%	80.8%	74.3%	56.3%	34.4%	22.1%	13.9%	10.4%	4.8%	8.7%	2.4%	6.2%	0.0%
2k	83.3%	100.0%	88.2%	91.7%	91.7%	90.8%	84.9%	76.9%	72.5%	51.7%	28.5%	14.8%	13.2%	5.2%	9.4%	7.7%	0.0%	0.0%	0.0%
1k	100.0%	100.0%	100.0%	96.1%	94.1%	90.0%	82.9%	81.0%	80.7%	62.2%	29.7%	21.4%	10.6%	3.3%	1.9%	5.9%	0.0%	50.0%	0.0%
1d	100.0%	100.0%	100.0%	98.0%	91.5%	91.9%	88.9%	77.7%	88.0%	64.5%	37.0%	22.9%	13.8%	22.9%	3.7%	0.0%	0.0%	0.0%	–
2d	–	100.0%	94.4%	98.9%	93.4%	79.7%	90.7%	86.5%	83.3%	59.8%	22.9%	14.3%	33.3%	0.0%	–	–	–	–	–
3d	–	100.0%	50.0%	50.0%	81.2%	88.5%	81.8%	66.7%	85.7%	70.5%	0.0%	28.6%	14.3%	0.0%	0.0%	–	–	–	–
4d	66.7%	–	80.0%	80.0%	81.0%	81.2%	65.4%	50.0%	77.8%	47.4%	42.9%	25.0%	16.7%	0.0%	–	–	–	–	–
5d	100.0%	100.0%	100.0%	80.0%	80.0%	93.0%	67.9%	68.8%	11.1%	25.0%	11.1%	57.1%	14.3%	–	–	–	–	–	–
6d	100.0%	100.0%	75.0%	92.9%	94.7%	97.6%	66.7%	66.7%	70.4%	26.1%	28.6%	33.3%	–	–	–	–	–	–	–
7d	100.0%	100.0%	100.0%	100.0%	100.0%	57.1%	77.8%	54.5%	38.9%	27.3%	0.0%	0.0%	–	–	–	–	–	–	–
8d	100.0%	100.0%	100.0%	100.0%	100.0%	100.0%	93.3%	76.5%	71.4%	14.3%	–	–	–	–	–	–	–	–	–
9d	–	100.0%	–	100.0%	–	60.0%	93.3%	63.6%	0.0%	0.0%	–	–	–	–	–	–	–	–	–

number of games

rank	-9	-8	-7	-6	-5	-4	-3	-2	-1	0	1	2	3	4	5	6	7	8	9
25k	–	–	–	–	–	–	–	–	–	3051	293	254	230	158	141	124	74	52	41
24k	–	–	–	–	–	–	–	–	169	203	111	105	97	102	104	70	49	35	31
23k	–	–	–	–	–	–	–	153	110	344	206	235	224	231	139	112	100	62	52
22k	–	–	–	–	–	–	177	114	178	521	299	321	299	219	168	131	124	82	65
21k	–	–	–	–	–	181	88	155	214	644	374	371	312	262	229	182	121	114	83
20k	–	–	–	–	183	67	125	219	275	786	514	472	423	421	318	248	168	123	90
19k	–	–	–	143	49	95	175	208	348	1122	646	626	665	546	373	307	258	186	104
18k	–	–	131	47	95	143	197	323	514	1415	883	853	751	635	447	359	202	121	87
17k	–	104	51	73	111	193	234	374	663	1769	1060	920	782	664	541	356	246	128	74
16k	86	39	68	101	124	207	300	458	689	2116	1167	1167	995	813	607	397	277	170	97
15k	21	37	50	71	108	197	331	594	869	2618	1525	1587	1474	1181	885	626	418	287	193
14k	29	53	66	89	138	250	368	585	964	3180	2046	1973	1718	1362	906	581	398	268	178
13k	24	41	55	108	144	232	347	627	1141	3494	2139	2186	1835	1205	776	501	408	244	127
12k	20	60	52	95	144	214	422	692	1152	3902	2702	2386	1742	1073	689	447	331	204	106
11k	45	68	92	120	187	331	495	922	1464	5018	2828	2287	1638	935	604	424	244	122	77
10k	61	58	97	116	227	343	610	1092	1909	5644	2825	2182	1456	880	619	389	257	98	47
9k	54	76	99	145	267	407	687	1127	1769	5039	2237	1705	1243	895	540	284	176	87	44
8k	39	44	82	101	212	301	489	800	1349	3997	1985	1706	1279	759	440	196	104	63	19
7k	29	43	53	108	220	298	416	676	1220	4254	2434	2117	1393	748	422	232	111	42	23
6k	49	71	158	273	269	347	432	705	1364	5165	2840	2122	1274	808	313	153	52	47	16
5k	103	182	316	315	287	374	565	981	1811	5834	2759	1885	1165	548	250	90	71	50	6
4k	98	111	171	170	254	370	608	1073	1807	5088	2020	1421	765	402	206	101	42	32	15
3k	53	98	103	100	154	317	578	933	1334	3074	1272	768	380	240	104	46	41	16	12
2k	6	43	17	48	133	217	464	597	687	1845	759	467	295	193	53	39	35	9	3
1k	2	8	54	77	152	281	304	348	503	1263	505	364	199	61	52	34	13	2	4
1d	11	12	6	51	142	148	144	130	200	550	181	96	58	48	27	9	1	1	–
2d	–	2	18	94	76	59	43	52	84	194	35	35	12	4	–	–	–	–	–
3d	–	4	2	2	16	26	22	30	21	61	11	7	7	1	1	–	–	–	–
4d	3	–	5	15	21	16	26	14	18	19	7	4	6	2	–	–	–	–	–
5d	3	4	1	5	10	57	28	16	9	36	9	7	7	–	–	–	–	–	–
6d	2	5	8	14	19	41	18	15	27	23	7	3	–	–	–	–	–	–	–
7d	5	2	4	15	19	7	9	11	18	11	5	4	–	–	–	–	–	–	–
8d	1	1	16	19	4	10	15	17	7	7	–	–	–	–	–	–	–	–	–
9d	–	6	–	1	–	5	15	11	3	6	–	–	–	–	–	–	–	–	–

Eugene · October 28, 2019, 9:02pm

DDKs find komi to be not enough eh…

Lys · October 28, 2019, 9:54pm

Very cool.

I’d like to colour the first table based on the second table with a red-yellow-green code (few games=red, many games =green).
It looks like some intersections aren’t very reliable.

DVbS78rkR7NVe · November 9, 2020, 4:01pm

Is there a theoretical function the table should match?

flovo · November 9, 2020, 7:45pm

Yes. Chance to win is calculated the same way as for ELO:

gennan · November 10, 2020, 7:26am

For completeness, maybe you should include how OGS computes ranks from Elo ratings?

gennan · November 10, 2020, 7:42am

BTW, this is winrate data from the EGF database over 2018:
Note that the data presentation is sort of mirrored compared to Flovo’s data.

                            Winning Statistics - Even Games
                                                          
                   G + 1               G + 2               G + 3                G + 4       

         G     Nw    Ng    Pw      Nw    Ng    Pw      Nw    Ng    Pw      Nw    Ng    Pw  
        --- ------------------- ------------------- ------------------- -------------------  
        20k    298  1059   28.1    123   577   21.3     73   611   11.9    51   522    9.8
        19k    118   306   38.6     51   219   23.3     22   147   15.0    12   103   11.7
        18k    147   391   37.6     74   253   29.2     33   151   21.9    12    86   14.0
        17k    232   561   41.4    107   391   27.4     46   239   19.2    15   120   12.5
        16k    223   539   41.4    128   420   30.5     37   212   17.5    18   138   13.0
        15k    187   450   41.6    110   327   33.6     46   208   22.1    19   137   13.9
        14k    164   367   44.7    106   324   32.7     52   220   23.6    25   130   19.2
        13k    153   375   40.8     87   254   34.3     57   174   32.8    15   102   14.7
        12k    149   333   44.7    118   303   38.9     33   154   21.4    25   119   21.0
        11k    180   393   45.8    108   290   37.2     54   174   31.0    21   105   20.0
        10k    189   431   43.9    129   348   37.1     39   130   30.0    25   105   23.8
         9k    224   483   46.4    109   324   33.6     54   150   36.0    28   101   27.7
         8k    225   532   42.3    133   352   37.8     45   186   24.2    26   122   21.3
         7k    230   565   40.7    174   432   40.3     44   178   24.7    22    91   24.2
         6k    295   685   43.1    153   388   39.4     43   178   24.2    15   108   13.9
         5k    319   762   41.9    156   402   38.8     30   163   18.4    18   101   17.8
         4k    401   880   45.6    169   465   36.3     46   164   28.0    23   156   14.7
         3k    364   827   44.0    133   434   30.6     44   253   17.4    20   132   15.2
         2k    281   708   39.7    176   526   33.5     68   241   28.2    17   133   12.8
         1k    327   849   38.5    148   503   29.4     39   227   17.2    11   131    8.4
         1d    308   911   33.8    126   529   23.8     33   277   11.9     3   121    2.5
         2d    240   659   36.4    106   474   22.4     14   228    6.1          76    0.0
         3d    202   559   36.1     72   363   19.8     10   179    5.6     5    69    7.2
         4d    179   536   33.4     39   265   14.7      6    95    6.3                   
         5d    129   412   31.3     31   182   17.0                                       
         6d     65   216   30.1                                                           


         Legend: G       : declared grade
                 Nw      : number of wins
                 Ng      : number of games
                 Pw      : percentage of wins of the weak player
                 G + <n> : games vs opponents stronger by <n> stones

         records: 58831

The data is somewhat similar, but the OGS data shows (much) higher Elo differences between ranks (more skewed winrates) than the EGF data[*].

Examples:
1 OGS rank difference at 10k gives about 75%/25% winrate ~ 200 Elo rank width.
1 EGF rank difference at 10k gives about 57%/43% winrate ~ 50 Elo rank width.

1 OGS rank difference at 1d gives about 85%/15% winrate ~ 300 Elo rank width.
1 EGF rank difference at 1d gives about 65%/35% winrate ~ 100 Elo rank width.

So in terms of winrate (Elo difference), OGS ranks seem to be much wider spaced than EGF ranks.

Do you know why this is the case? Does it have to do with statistical differences between online correspondence games (OGS) and live tournament games (EGF)?

[*] Actually, the EGF data is more similar to the OGS data from 2017, shown in the original post of this topic.

BHydden · November 10, 2020, 8:53am

Here you go.

gennan · November 10, 2020, 9:19pm

Thank you.

If my calculations are correct, I get:

Computing Elo width of OGS ranks

From rank-rating conversion formula
1 OGS rank difference at 10k ~ 50 Elo rank width => 57%/43% predicted winrate.
1 OGS rank difference at 1d ~ 70 Elo rank width => 60%/40% predicted winrate.

From actual winrates (see earlier posts)
1 OGS rank difference at 10k ~ 75%/25% actual winrate => 200 Elo rank width.
1 OGS rank difference at 1d ~ 85%/15% actual winrate => 300 Elo rank width.

I’m curious what would explain these rather large discrepancies between predicted and actual winrates. It may be worthwhile to do some further investigation.

shinuito · November 10, 2020, 10:33pm

Well is about 10kyu the new player rating?

As in when you start a new account is the default rating still 1150?

That would throw everything up in the air at 10kyu