An Example of how to calculate Ratings under the new IECG Rating Scheme.
This example refers to the IECG
Rating Rules.
Let us assume the following situation: Player A plays against Player B.
Before the game, we have the following entry in the old rating lists:
Player A: 1800 2 1 2 (2000) Player B: 2200 15 18 7
What do these entries mean?
Player A has a Starting Rating of 1800, but has already played five
games. His opponents' average currently is 2000. Player B has an
established rating of 2200 with 40 games played under the new scheme. Both
player finished the first game in this rating period.
In the following 1-0 means a victory for A, = means a draw and 0-1 means
victory for B.
We now calculate the provisional rating for Player A (see section
IV.1 of the Rating Rules):
Rp = Opponents Average + Expected Rating Change*Correction.
The Average of the opponents' ratings is (2000*5+2200)/6 = 12200/6 = 2033
A's percentage result is given by p=(2*W+D)/2*N
1-0: p = (2*3+1)/(2*6) = (6+1)/12 = 7/12 = 0.58 =: p = (2*2+2)/(2*6) = 6/12 = 0.50 0-1: p = (2*2+1)/(2*6) = 5/12 = 0.42
Then the correction is given by F = -2*p*p + 2*p + 0.5, i. e.
1-0: F = -2*0.58 * 0.58 + 2*0.58 + 0.5 = 0.9872 =: F = -2*0.50 * 0.50 + 2*0.50 + 0.5 = 1.0 0-1: F = -2*0.42 * 0.42 + 2*0.42 + 0.5 = 0.9872
The expected Rating Change is then given by:
1-0: D(0.58) = -400*log10((1-0.58)/0.58) = -400*(-0.14) = 56 =: D(0.50) = -400*log10((1-0.5)/0.5) = -400* (0) = 0 0-1: D(0.42) = -400*log10((1-0.42)/0.42) = -400*0.14 = -56
Therefore:
1-0: Rp = 2033 + 56 * 0.9872 = 2088 =: Rp = 2033 + 0 * 1 = 2033 0-1: Rp = 2033 - 56 * 0.9872 = 1978
This is the first provisional rating of Player A.
Player B has an established rating. So we have to use the following
formula to calculate the rating change for this game:
dR = k*(W-We)
k is given by the product of two coefficients, determined by the old
rating of B and his experience (i.e. the number of games played).
Following section V.3
of the Rating Scheme Document, we have
k = r*P with r = 70-2200/40 = 70-55 = 15
and because he already played 40 games
P = 1.4 - 40/200 = 1.4 - 0.2 = 1.2
therefore k = 1.2*15 = 18.
"We" in the above formula is the probability
that B wins, given by the rating difference of B and A. Since the
difference D is given by
D = 2200-1800 = 400
we get (see section
I.3)
P(D) = P(400) = 1/(1+10^(-400/400)) = 1/(1+10^(-1)) = 1/(1+0.1)
= 1/1.1 = 0.91
Now we can easily calculate the rating change dR:
1-0: dR = 18*(0-0.91) = 18*(-0.91) = -16.38 =: dR = 18*(0.5-0.91) = 18*(-0.41) = -7.38 0-1: dR = 18*(1.0-0.91) = 18*0.09 = 1.62
Then the Performance of B is (since the rating period has not ended yet):
1-0: 2200-16 = 2184 =: 2200- 7 = 2193 0-1: 2200+ 2 = 2202
During a rating period all dR for each game are added up and the new
rating is then calculated.
Back to the IECG Homepage