I can relate with this. When I beat T5, I decided to farm it indefinitely until I got the Allagan Cane because it looked cool. Set up a bunch of farm, and clear parties every day for weeks till I finally got it. Ended up taking like 3 weeks worth of farming and around more than 80 clears (I gave up counting at this point) to get the cane. I brought a lot of people together to beat T5, as well as get people who needed it to advance to 2nd coil. So it was gut wrenching watching everyone get their weapon one by one. I was determined though, so I kept going with the same intentions of getting the damned cane. Mind you that all the runs before the run that I got the cane, it did not drop once.

I can't say that I can prove it exactly, but I did save videos between my first clear and the clear that I got my cane on. I used the timestamps as estimates. I guess you could also ask around Cactuar about by T5 binge (I'm surprised some people actually remember that lol).