I'm still not sure what to think of the additional rolls theory. If it's only true for the trait tiers, it might work, it still sounds horribly overpowered. It would push 5% drop rate to about 20% drop rate (think how incredibly noticeable that effect would be on King Arthro and Simurgh). And if we include other TH tiers (from gear and upgrades) as well, it would push the 5% to about 33%, so from a 1 in 20 drop to 1 in 3 drop.
I would love to do some new TH testing, with the new system to accurately determine a pattern to drops. In case anyone has some recent killing sprees they wanna parse for drops, I've included a drop rate counter into my parser:
http://ffxiut.com/parser
I like your suggested system a lot Byrth, although your formulas have me a bit confused. Please correct me if I'm wrong, I may have misunderstood, but wouldn't it be something like this
R = 1-(1-(D+T%))^(k+1)
where D is the original drop rate, T the TH level and k is the level you achieved from your highest damage attack, R being the resulting drop rate?
Generally I would endorse a system like that, however this is still a bit overpowered I think. If you think about it, having a good THF with you would be equivalent to doing a fight five times. And it's actually quite a bit more than that, due to the +T%, if you think about it, items with really small drop rates would be getting a massive drop rate boost. Take Hocho for example, an item with 1% drop rate, would shoot up to 35% if you get level 5, which should be very doable, quite possibly higher. That would be the equivalent to about 42 fights without TH. I think that's going a bit overboard.
So while I like the idea, I think it would need some fine tuning. For one you could replace the "+T%" by "*(1+T%)", and maybe give diminishing returns for higher level, like, only 2/3 the bonus with each level. This would be harder to implement however, would have to calculate it in a loop instead of one arithmetic expression, but it should still be very fast and easily feasible.
As I said, I might have misinterpreted what you meant, if I did feel free to correct me.