This rating system is created for a game.

I. Mathematical details

Suppose there are 2 players, A and B, playing against eachother.

Let Ra and Rb be the ratings of A and B, respectively.

The K-factor of A is calculated by this formula:

Ka = 1 + 10^(2-(Ra-2000(-2+log99))/2000)

The K-factor of B is calculated by this formula:

Kb = 1 + 10^(2-(Rb-2000(-2+log99))/2000)

The β-factor of A is calculated by:

βa = 10^((Ra-2000(-2+log99))/2000)

The β-factor of B is calculated by:

βb = 10^((Rb-2000(-2+log99))/2000)

The expected score of A is calculated by:

Ea = 1/(1+3^(βb-βa))

The expected score of B is calculated by:

Eb = 1/(1+3^(βa-βb))

The bonus points for A is determined by:

BPa = (1/2)log(1+10^((2000-Ra)/100))

The bonus points for B is determined by:

BPb = (1/2)log(1+10^((2000-Rb)/100))

The new rating of A is calculated by:

Ra' = Ra + Ka(Sa-Ea) + BPa

The new rating of B is calculated by:

Rb' = Rb + Kb(Sb-Eb) + BPb

II. Ranking System

This ranking system is for amateur players. The rank will change automatically if the player's rating is in the predetermined range.

Rank Name	Rating Range
40-kyu（40級）	≤ -1901
39-kyu（39級）	-1900 - -1801
38-kyu（38級）	-1800 - -1701
37-kyu（37級）	-1700 - -1601
36-kyu（36級）	-1600 - -1501
35-kyu（35級）	-1500 - -1401
34-kyu（34級）	-1400 - -1301
33-kyu（33級）	-1300 - -1201
32-kyu（32級）	-1200 - -1101
31-kyu（31級）	-1100 - -1001
30-kyu（30級）	-1000 - -901
29-kyu（29級）	-900 - -801
28-kyu（28級）	-800 - -701
27-kyu（27級）	-700 - -601
26-kyu（26級）	-600 - -501
25-kyu（25級）	-500 - -401
24-kyu（24級）	-400 - -301
23-kyu（23級）	-300 - -201
22-kyu（22級）	-200 - -101
21-kyu（21級）	-100 - -1
20-kyu（20級）	0 - 99
19-kyu（19級）	100 - 199
18-kyu（18級）	200 - 299
17-kyu（17級）	300 - 399
16-kyu（16級）	400 - 499
15-kyu（15級）	500 - 599
14-kyu（14級）	600 - 699
13-kyu（13級）	700 - 799
12-kyu（12級）	800 - 899
11-kyu（11級）	900 - 999
10-kyu（10級）	1000 - 1099
9-kyu（9級）	1100 - 1199
8-kyu（8級）	1200 - 1299
7-kyu（7級）	1300 - 1399
6-kyu（6級）	1400 - 1499
5-kyu（5級）	1500 - 1599
4-kyu（4級）	1600 - 1699
3-kyu（3級）	1700 - 1799
2-kyu（2級）	1800 - 1899
1-kyu（1級）	1900 - 1999
1-dan（1段）	2000 - 2099
2-dan（2段）	2100 - 2199
3-dan（3段）	2200 - 2299
4-dan（4段）	2300 - 2399
5-dan（5段）	2400 - 2499
6-dan（6段）	2500 - 2599
7-dan（7段）	2600 - 2699
8-dan（8段）	2700 - 2799
9-dan（9段）	2800+

III. Professional Ranking System

This ranking system is for professional players. Players must complete / fall into all criteria for promotion / demotion.

Professional Rank

Promotion Status

Promotion Criteria

Demotion Status

Demotion Criteria

Reidan

（零段）

7-dan

（7段）

Rating 2600+

Shodan

（初段）

Rating ≤ 2619
In the last 20 Professional Ranked games after promotion / demotion, lose 14 games.

Shodan

（初段）

Reidan

（零段）

Rating 2620+
In the last 20 Professional Ranked games after promotion / demotion, win 13 games.

Nidan

（二段）

Rating ≤ 2639
In the last 20 Professional Ranked games after promotion / demotion, lose 14 games.

Nidan

（二段）

Shodan

（初段）

Rating 2640+
In the last 20 Professional Ranked games after promotion / demotion, win 13 games.

Sandan

（三段）

Rating ≤ 2664
In the last 20 Professional Ranked games after promotion / demotion, lose 13 games.

Sandan

（三段）

Nidan

（二段）

Rating 2665+
In the last 20 Professional Ranked games after promotion / demotion, win 14 games.

Yondan

（四段）

Rating ≤ 2689
In the last 20 Professional Ranked games after promotion / demotion, lose 13 games.

Yondan

（四段）

Sandan

（三段）

Rating 2690+
In the last 20 Professional Ranked games after promotion / demotion, win 14 games.

Godan

（五段）

Rating ≤ 2714
In the last 20 Professional Ranked games after promotion / demotion, lose 13 games.

Godan

（五段）

Yondan

（四段）

Rating 2715+
In the last 20 Professional Ranked games after promotion / demotion, win 14 games.

Rokudan

（六段）

Rating ≤ 2744
In the last 20 Professional Ranked games after promotion / demotion, lose 13 games.

Rokudan

（六段）

Godan

（五段）

Rating 2745+
In the last 20 Professional Ranked games after promotion / demotion, win 15 games.

Shichidan

（七段）

Rating ≤ 2779
In the last 20 Professional Ranked games after promotion / demotion, lose 13 games.

Shichidan

（七段）

Rokudan

（六段）

Rating 2780+
In the last 20 Professional Ranked games after promotion / demotion, win 16 games.

Hachidan

（八段）

Rating ≤ 2819
In the last 20 Professional Ranked games after promotion / demotion, lose 13 games.

Hachidan

（八段）

Shichidan

（七段）

Rating 2820+
In the last 20 Professional Ranked games after promotion / demotion, win 17 games.

Kudan

（九段）

Rating ≤ 2869
In the last 20 Professional Ranked games after promotion / demotion, lose 13 games.

Kudan

（九段）

Hachidan

（八段）

Rating 2870+
In the last 20 Professional Ranked games after promotion / demotion, win 18 games.

Making a Rating System

Super Admins