Has anyone ever took note when you character was made? (Vana'diel time, day, moon phase, etc...) I was told that each character has a pre-asigned "luck" percentage which affects everything from drops, to synths to magic resists, to items you get out of chest or coffers. By knowing above mentioned information you might be able to calculate when perhaps it's best to synth or hope for a drop.
Someone asked me once: Have you noticed how items (re/ex) drop more frequent when you have that one person in your PT? (I'm not talking about THII, I had stuff drop better with non-thief in PT rather than THF.)
Perhaps the collective "luck" factor affects group drops like AF in dynamis or Gods on drops as well. This game is not random as some might think, after all it's numbers and calculations are made by system every second and most like that calculation is done against each character's "serial number".