I need help finding out some specifics. First, what I already know:
Non-named loot is affected by:
A1. Level of quest (as modified by the difficulty you run the quest on).
A2. Loot gem you are currently using (other party member's gems do not affect you)
A3. Chest's level modifier (some chests in the same quest are better than others in the same quest)
A3. Ransack timer on chest (number of times over 7 you opened it in the last 7 days is how many levels the chest is reduced by, down to chest level 0 = empty)
Note that some random items only drop on specific difficulty levels, so you may need to run this level 16 quest on Hard or Elite (or use a loot gem) to get to the needed "chest level 17" for a chance at a +2 Tome dropping.
Named loot in normal quests is affected by:
B1. Chest (named items only come from 1 or a few specific chests)
B2. Ransack timer (if you have opened this chest more than 7 times in the past 7 days, you get no named items from this chest). This rule doesn't apply in some cases where the name item is ALWAYS in the chest (runes in the Reaver's Refuge quests for instance).
B3. Difficulty you ran the quest on (for quests in IQ and newer). For example: the best types of Dream Edge only drop on hard/elite Mindsunder runs; Eardweller drops more often on hard/elite.
Named loot in raids is affected by:
C1. Chest (named items only come from 1 or a few specific chests)
C2. Ransack timer (if you have opened this chest more than 7 times in the past 7 days, you get no named items from this chest).
C3. Difficulty you ran the raid on: normal has a the lowest chance of raid items dropping, hard has a higher chance, elite has the highest chance.
Myths:
X1. Diplomacy, Charisma, who opens the chest first, inherent 'luck' of a specific character, etc. has no effect on chests.
X2. Other people's loot gems do not affect your chance at loot.
X3. Other people's loot pulls do not affect your chance at loot (the chest could give us all +2 Tomes at once)
X4. Loot gems have no effect on named items dropping, only on the level of random items.
Anything I missed?
Can anyone offer dev quote or other proof of the above, especially C3?