So...with a lot of help from various tools, I have managed to draft a new version of the AAAeq skill rating formula that is based on the tier point list, and (hopefully) more accurate towards near-AAA and high-good scores.
The formula is as follows:
AAAeq = (D-126.406)*((1 + (NGC/3.429871)^1.151702)^0.1682445) + 126.406
where D = the difficultly of the song, and NGC is the number of goods in the score to be ranked (where Average = 1.8 goods, Miss = 2.4 goods, and Boo = 0.2 goods.)
(NOTE: This formula alone will rank a lot of scores with a negative AAAeq value. I worked around that by assigning scores to the maximum of the above formula and the formula (1-NQC/1000). This will only matter if the score in question is ranked by the above formula to be below 1.00.)
Obviously that's just a mess of numbers and symbols, and doesn't tell you anything. Everyone loves graphs, so let's add some graphs:
And here's the original, for comparison:
As you can see, the new formula drops off far faster than the old one, but also maintains a higher score for longer on harder songs.
(Of course, I'm not suggesting this formula is perfect by any means...despite my attempt to patch this, there exists a huge hole for low D1 players. Maybe someone else can come up with a way to plug this hole.)