Thanks for Terence, who has done the hard work of sorting out the specifics in the GameFaqs forum:
"Each item that an enemy can drop has its own drop chance. You can only get one item from an enemy, and the items are checked from the bottom up, starting with the 3rd Slot. Note that you can only get the 3rd Slot if you complete the Conditional Drop Requirement for that enemy. However, some enemies have a 3rd Slot but there is no Requirement to complete.
The chance that the item drops is a strict percentage chance, and can be modified in two ways: LUC and Scavenge.
The LUC effect is calculated as follows:
So a full party of L70s will have a divisor of 2070 here, and the LUC will vary - but I believe the lowest at L70 is 60, so the worst bonus you'll have is 111% (100 * 2300 / 2070). And of course, any LUC increasing equipment you bring helps.
The Scavenge effect is calculated in a different way - they're all multiplied together for all characters involved in the battle. So having a Medic and an Alchemist both with max Scavenge would be a bonus of 130% * 130% = 169%. We'll call this Scavenge Bonus.
Once all this has been calculated, each item dropped by the enemy has its chance looked at, and modified with the answer between each step rounded down:
At this point, we will have a final percentage. This is the exact percentage chance you have of getting that item. If this random chance fails, then we move onto the next item in the list: if we were looking at the 3rd item, then we'd move on to the 2nd item next, and so on. This continues until we succeed at getting an item, or we run out of items on that monster to collect."
Etrian Odyssey IIEdit
In this game, some changes were made to drop chances. LUC doesn't increase the drop chance anymore. However, Scavenger now is an additive bonus to the drop chance. Per example, Lv.5 Scavenge (41% Increase in Item Drop Rate) will turn a 10% drop chance into a 51% drop chance. With two characters that have Lv.5 Scavenge, even the most rare drops in the game will be raised to a 92% drop chance.
Furthermore, monsters can now drop all their drops at the same time. In the first game, one monsters could only drop one drop at a time.