Alexander token loot system using DF. How does it compare to COIL loot system. Math?

[DoctorPepper]

Looking quickly at loot lists, here is what I found.
(Note: The numbers are going to be different when in a static. This post is more for DF.)

COIL:
Picked a random turn (turn11). Has 18 pieces and 2 can drop per run (Ignoring mats). So at there is a 1/9 chance the item will drop. (There may be more than one person wanting that gear as well, but for now we will assume they don't.)

Alexander:
Let's take A1 (floor 1). Has 3 items and 2 can drop per run. Let's consider worst possible scenario. Let's say everyone is going for optimal looting choice to gear their character fully in week 5. This means that most people would want 1 of the 3 pieces and to scrap the others. This in effect gives a 2/3 pieces drop with 8 people lotting on that 1 item if that is one of the one's that dropped.

You need to take into account that the same item can drop multiples in alexander. For example, both drops from floor 1 can be for the waist slot. The math is the same either way because the chance is there for all items but I just thought I would throw it out there because you mentioned scrapping items.