As always, thanks for the response.
However, you do realise that you wrote "item tier gain probability formula" and "complete overhaul of"? Maybe it is more complex than it should be, but surely the relationship is with the number each item has for its relevant tier. It's just one little formula in a sea of formulas (linear, or non-linear). I can easily understand that (L) and unlimited items should respond differently to a particular value, but how hard can it be? You make it sound like a monumental task...