You could define consistency at different levels of play by the Elo width of ranks (where ranks are assumed to be determined by handicap, as in n ranks difference can be compensated for by black getting to play n moves before the game starts with black’s turn and white getting komi, up to about n = 15).
Determined from EGF historical winning statistics, ranks around 15k are about 50 Elo wide, ranks around 1d EGF are about 100 Elo wide and ranks around 7d EGF are about 250 Elo wide. Going into the pro range, you get ranks (not pro ranks, but handicap ranks as defined above) of about 300+ Elo wide.
At perfect play, the Elo width per rank would approach infinity (or perhaps a finite, but very large value, due to the fact that score is an integer value instead of a continuous value, so komi handicap increments of less than 0.5 points are meaningless).
So you can fit an asymptotic curve through those Elo widths derived from winning statistics at different levels of play, to get an estimate for the highest rank possible = perfect play.
Using this method on EGF historical data, I arrived at an estimate of 13d EGF for perfect play, from the blue curve in this Elo width per rank graph, which is used by the EGF rating system since April 4th 2021 (red curve is what OGS uses):
Vertical axis is the Elo width per rank.
Horizontal axis is EGF rank expressed like internal OGS rank scale:
- 0 = 30k
- 10 = 20k
- 20 = 10k
- 30 = 1d
- 39 = 10d = more or less highest level achieved by humans like Go Seigen and Shin Jinseo,
- 42 = 13d = max rank in EGF rating system ~ perfect play?
(2021 Rating and rank adjustments - #59 by gennan)