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The HQ rate feels like it's different from what it says, but it would take a gigantic sample size to get an accurate reading.
For melding, the ~35% success rate on the first meld always seems to be closer to 50% for me; it seems like more than half succeed first attempt, the worst I've had is 6 tries, and at least 90% happen in first 3 tries (should be about 70% chance). The 2nd-4th overmeld have a much worse rate than listed from what I've seen.
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I know that Materia Melding can be rough. I failed 35 times on a meld with around 45% a month back. Since FFXI I have always believed that SE has a "Because we say you fail clause." Which always explained to me why you could fail a level 1 craft at lvl 100. I just accept they carried that into this game but that's just a superstition I guess.