This example is a short of explanation that I expanded on in the thread: http://forum.square-enix.com/ffxiv/t...g-Improvements

IN short it says: IF you are high enough above a synth that you get no SP or XP, and you are totally maximized in all regards to make HQ (best gear for your rank, max support, bold synth, foods, attributes tweaked perfectly, guild abilities, new moon, remembered to sacrifice your goat, sold your soul, and your first born child to the powers that be) then you should have about 75% chance to HQ +1, and you balance rarity of +2, +3 from there. Basically, if you go balls to the walls hardcore, you should HQ SOMEHOW. IN 100 synths, that is 75 +1 items, which if you think about it, is a lot. But it is also a LOT of effort to get ALL your variables maximized. (this % would need to be adjusted to reflect things like... can we see our guild marks on local leves, allowing us to selectively maximize our abilities... will pumping our class specific or elemental stats ACTUALLY help us instead of just looking cool... will food actually be worthwhile... etc.,)

Whereas if you have the baseline gear at rank, no support, no buffs, bold synth, neutral moon, no abilites, etc., you should have about 5% chance to HQ +1 (that's about 1 in 20) and decrease from there. So that in 100 synths you have five +1, say two +2, and one +3.