The problem with professional dan ranks is that they're capped at 9p, and each association has different rules for awarding that rank. Because of this there is a lot of variance among 9p.
For instance, Fernando Aguilar 6d (aguilar1 and aguilar on KGS), an amateur dan from Argentina, has defeated Hasegawa Sunao 9p as well as Yo Kagen 9p. In theory this should not have happened.
If the cap didn't exist, I think Alpha Go may be around 13p, based on the fact that Lee Sedol and Ke Jie may be able to give reverse komi to many top 9p players, and that Alpha Go may be about 3 stones stronger than both. Park Yeong-hun is less often mentioned but he may be playing at a higher level to that of Lee Sedol.
I don't know Fernando Aguilar but is the reason he's 6D not that he's capped at it before becoming professional? IIRC when I played in SF bay area (probably all of USA in the AGA), you couldn't get higher than 6D(7D?) without becoming a pro. I think in tournament lineup you would see something like Mr. A 6D (7.2) where the 7.2 was his estimated rating but it was a long time ago.
Not entirely sure about caps at the amateur level. At least go servers don't have such cap, and there's certain mapping between KGS ranks to offline amateur ranks. The highest attainable rank at Go servers is 9d, aguilar is 6d there.
