The title says it all really. In an even game on OGS, a 1.00 dan against a 1.00 kyu should win 1.60 games for every game he loses. While in the AGA, a 1.00 dan against a 1.00 kyu should win 4.81 games for every game he loses. This corresponds to a Glicko rating difference of 81 and 273 points respectively.
How does the AGA think the rating gap between these two ranks is over three times larger than OGS does? This does not seem consistent. Can anyone explain this?
Calculations
Here is a simple Python script showing the calculations I did to get the above figures:
import math
e = math.e
#OGS Calculation
print("An OGS 1.00 dan has a rating of: ")
print(525*e**(30/23.15))
print("\nAn OGS 1.00 kyu has a rating of: ")
print(525*e**(29/23.15))
print("\nThis rating difference is: ")
OGS_diff = 525e**(30/23.15)-525e**(29/23.15)
print(OGS_diff)
print("\nThis corresponds to a win ratio of: ")
print(10**(OGS_diff/400))
#AGA Calculation
#These equations come directly from the official AGA PDF I linked
k = 7.5
sigma_px = 1.0649-0.0021976k+0.00014984k**2
RD = 1
print("\nThe AGA win probability of a 1dan vs a 1kyu: ")
win_prob = 0.5*math.erfc(-RD/(2**0.5)/sigma_px)
print(win_prob)
print("\nThis corresponds to a win ratio of: ")
win_ratio = win_prob/(1-win_prob)
print(win_ratio)
print("\nThis corresponds to a rating difference of: ")
AGA_diff = 400*math.log10(win_ratio)
print(AGA_diff)
#Compare OGS to AGA
disparity = AGA_diff/OGS_diff
print(f"\nThe AGA thinks the rating difference between a 1 dan and 1kyu is {disparity} larger than OGS does")
Links
Formula of ln(rating / 525) * 23.15 for converting OGS ranks to ratings from here
Explanation of AGA win probabilities between ranks from here
Basic explanation of how rating difference relates to win probabilities can be found here