Synthesis Guide Part 2 Done (with link)

[tymora]

Ah...found it.
http://lodestone.finalfantasyxiv.com...4558&tag=11552

Excerpt:

Simplify linear approximate

+1 Probability = ((Finish Quality) × 0.04% - 2.00%) per touch up
+2 Probability = ((Finish Quality) × 0.02% - 2.00%) per touch up
+3 Probability = ((Finish Quality) × 0.01% - 2.00%) per touch up

(These can fit 200-350 Range only)

So at 300 quality, you'll have a 10% +1, 4% +2 and 1% +3.
It also fits well with the observation that you can't get +2 under 100 quality and +3 under 200 quality.
His study didn't include touch-ups.

Taking that into account, using 300 quality as example...
Probability of +1 = 1 - (0.9)^x where x is number of touch-up attempts
Probability of +1 = 1 - (0.96)^x
Probability of +1 = 1 - (0.99)^x

So there is an additional depth to crafting which requires you to balance quality and final durability.

And just to add...moon phases and other elemental beliefs remain superstition for now.