Here's the data from FFXIDB. It collected data on crafting for over a year, from 2006 into 2007. Here is the math done on the DB:
https://www.bluegartr.com/threads/120352-CraftyMathEasy Read:
Anyway, we're going to have to nuke the 7M synth database that we've built up in the last year. Before we do that, if I very tightly constrain my queries then I can get some very basic information out of it:
Tier -1 HQ rate: 0.06% ( 16 / 24127 )
Tier 0 HQ rate: 1.8% +/- 0.3% ( 144 / 8073 ) -- 95% confidence interval is likely underestimated because it's too close to a bound.
Tier 1 HQ rate: 6.6% +/- 0.5% ( 660 / 9951 )
Tier 2 HQ rate: 28.5% +/- 0.8% ( 3659 / 12865 )
Tier 3 HQ rate: 50.6% +/- 0.7% ( 8835 / 17462 )
Data:
Format is:
Conservative Tier : NQ, HQ1, HQ2, HQ3
The Tier estimation is "conservative" because I'm always assuming that any synthesis support buff present is Advanced and that any Furniture in the MH is giving its crafting moghancement. Thus I should be overestimating skill level rather than underestimating, which should bias the HQ rate estimates downwards. .... or I'd like to pretend that it matters, but in practice I ran the numbers with the opposite assumptions (furniture not active and NQ support) and it made almost no difference. Still, those are the qualifiers.
Code:
Silent Oil (Slime Oil recipe)
Tier -1: 4827, 3, 0, 0, 0
Tier 0: 436, 3, 0, 0, 0
Tier 1: 563, 32, 8, 0, 0
Tier 2: 2429, 603, 146, 53
Tier 3: 5338, 4074, 1022, 363
Holy Water (no Trit recipe)
Tier -1: 19279, 12, 0, 1
Tier 0: 7473, 138, 3, 0
Tier 1: 7889, 396, 151, 0
Tier 2: 5068, 1634, 419, 152
Tier 3: 2728, 2144, 519, 189
Holy Water (Trit recipe)
Tier -1: 5, 0, 0, 0
Tier 0: 20, 0, 0, 0
Tier 1: 839, 57, 15, 1
Tier 2: 1709, 493, 120, 49
Tier 3: 561, 395, 90, 39
As if this wasn't long enough of a post, here is what was reported by a friend who was T3 crafting:
Tier 3: 90/339 = ~26.5%, nearly half of what 2006-2007 reflected.
Please feel free to add more data below this line, but I think the point has been proven.