The ELO rating system as developed by Prof. Arpad Elo is simple,
tested
(by the international Chess Federation the FIDE) and easily adoptable
to Go tournaments. The structure of the ELO system is mathematically
very simple; it uses a table and a formula:
ELO difference 
Expected score 

0 
0.50 
20 
0.53 
40 
0.58 
60 
0.62 
80 
0.66 
100 
0.69 
120 
0.73 
140 
0.76 
160 
0.79 
180 
0.82 
200 
0.84 
300 
0.93 
400 
0.97 
... 
... 
Table 1: Expected score 
Based on the difference in ELO rating between two players
Basically, the table shows the Normal Probability Function which
is used to estimate the player's strength distribution.
The formula to calculate a player's new rating based on his/her
previous one is:
Rn = Ro + C * (S  Se) (1)
where:
Rn = new rating
Ro = old rating
S = score
Se = expected score
C = constant
So, if we assume a rating difference of 100 ELO points between dan grades,
scale a 1d at 1900 and use 30 for the constant C then we can calculate
some examples:
Example 1: 3d beats 3d
Ro = 2100
Se = 0.50
S = 1.00
Rn = 2100 + 30 * (.50) = 2100 + 15 = 2115
Example 2: 3d beats 2d
Ro = 2100
Se = 0.69
S = 1.00
Rn = 2100 + 30 * (.31) = 2100 + 9 = 2109
Example 3: 1d beats 3d
Ro = 1900
Se = 0.16
S = 1.00
Rn = 1900 + 30 * (.84) = 1900 + 25 = 1925
Notes
 When a player goes up D the opponent goes up D.
So in example 3 the 3d player drops 25 ELO points.
 The maximum drop/raise in rating per game is C.
The ELO system has two parameters which affect the dynamics
of the system: the constant C in formula (1)
and the variance of the player's strength distribution in table (1).
The parameters in Chess
For Chess, the variance of the Normal Probability Function is set
at 200 ELO points and the constant C depends on the rating of the
players involved. Below 2000 and above 2400 it is a constant, in
between it varies proportionally with the rating while creating a
continuous function:
Rating 
C 
< 2000  30 
2000  2400  130R/20 
2400 <  10 
Table 2: Variance affecting C 
Higher C values for lower ELO ratings allows
faster changes of the rating for weaker players
Proposal for the parameter values in Go
Now what would be a reasonable value for C
when applying the ELO system to the game of Go? If we set a
European 4 dan amateur at 2200, a 1p professional at
2500 (which would equal to a 7 dan amateur and would
give a 9p an ELO rating of about 2700) I would like to
propose the following table for Go ratings:
Rating 
Rank 
C 
< 2200 
30 kyu, ..., 4 dan 
30 
2200  2500 
4 dan, ..., 7 dan 
(2200R)/15 + 30 
2500 < 
7 dan/1p, ..., 9p 
10 
Table 3: Proposal for C in Go 
Low confidence in amateur ratings, high confidence in pro ratings
