If what you say is correct, then the chance of getting a pink item with a 25% re-roll elixir and a 15% luck amulet would be 40% greater than without any luck boost. But if I run KM3 without any elixir I can spend hours there and be lucky to get a single locked crate. If I run with both of those items totaling a 40% luck boost, I typically will get at least 5+ locked crates in an hour. While leveling up to 36, I spent about 8 hours in KM3 (all with luck elixir and luck amulet) and I looted 50 locked crates and a nexus egg. I suspect if I had no elixir or luck amulet, I'd be lucky to have looted 5 crates.
The math does not support what you say. The math supports that I am getting a huge boost on my chance of getting a pink, because 40% of the time I am getting an epic item, that item is being upgraded to a legendary item. Since epic items have a much higher percentage drop rate than legendary in the drop table, my total chance of getting a legendary item is boosted exponentially.
Let's suppose the drop rate for each color rarity for a certain boss looks like this: 65% rare, 31% epic, 4% legendary -- I'm guessing the real numbers are somewhere in this range. 1 out of 25 drops being legendary sounds about right for running with no luck boost.
If your theory was correct, then whenever I got a re-roll, I would have a 4% chance of landing a legendary item during the re-roll. Since I'm only getting that re-roll 40% of the time, that means I only boost my chances of getting a legendary item by 1.6% (simple math: 4% of 40% = 1.6%). So running with 40% luck boost I now have a 5.6% (4% on first roll + 1.6% on re-roll) chance of getting a legendary item instead of 4% without any luck boost. However, I think we all know that we get a much greater luck boost than that when we run with a luck elixir and/or amulet. Nobody is spending all that plat for a lousy 1.6% extra chance of getting a legendary item.
If my theory is correct, then 40% of the time I get an epic item, it would be re-rolled to a legendary item.... 40% of 31% = 12.4%. So in my theory, the total chance of getting a legendary item would be 16.4% (4% on first roll + 12.4% on the re-roll). So that would mean approximately 4 times greater chance of getting a legendary item than without any luck boost (16.4% with luck boost compared to 4% without luck boost). I think we all know that this is around where the real figure lies. Anyone who runs both with and without luck elixirs, especially in places like KM3 or Jarl, knows that your chances of looting a legendary item with the luck elixir is much much higher than without.
And BTW, the reason these luck elixirs have not ruined the AL economy like they did in PL is because there is no 100% shamus elixir. If there was, we would be looting legendary items like crazy and the prices would crash.
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