I feel like your post is also not rooted in actual applicable experience. What's your definition of "superior" here? Is it the few hundred quality that you're guaranteed to get? Most of the time this is not worth much due to how the chance HQ is not linear, which I'll show below. I already felt that hasty + innovation is better in my past experiences, but I went ahead and did comparisons on astral oil yesterday to double-check with actual crafting. An innovation-based rotation is better in general.
I'll use your numbers:
I can replicate this with the settings you've posted earlier:
Control: 806
Starting Quality: 1500
Item: a 2-star craft
The starting point for a fair comparison here where CP, durability, and chance of success are accounted for shouldn't start at 7 IQ stacks and 3665 quality, but instead should start at 6 IQ stacks and 3178 quality.
Possibility #1: Safe basic touches (100% chance):
Steady Hand II
(+487) Basic Touch -> 7 IQ stacks
(+540) Basic Touch -> 8 IQ stacks
Great Strides
(+2858) Beregot's Blessing
Total gain: +3885 quality (+3398 from 7 IQ stacks, noted in your post)
Durability used: 30
CP used: 117
Result: 7063 / 9430 total item quality, which is a 45% chance to HQ.
Extra note: Chance for a "Good" condition for the Beregot's Blessing _if_ you have an additional 14 CP to Observe (disregarding that this doesn't make this an equal comparison... anyone have this number for 2-star crafts? It's quite low.)
Possibility #2: Failed hasty touch and innovation (20% chance):
Steady Hand II
(+0) Failed Hasty Touch -> still 6 IQ stacks
Innovation
(+623) Basic Touch -> 7 IQ stacks
Great Strides
(+2991) Beregot's Blessing
Total gain: +3614 quality
Durability used: 30
CP used: 117
Result: 6792 / 9430 total item quality, which is 32% chance to HQ
Extra note: The actual quality loss from the safe basic touches in this example is 271 quality, but the % chance to HQ is what really matters.
Possibility #3: Successful hasty touch and innovation (80% chance):
Steady Hand II
(+487) Successful Hasty Touch -> 7 IQ stacks
Innovation
(+679) Basic Touch -> 8 IQ stacks
Great Strides
(+3540) Beregot's Blessing
Total gain: +4706 quality
Durability used: 30
CP used: 117
Result: 7884 / 9430 total item quality, which is 78% chance to HQ
If you choose safe basic touches in this example, your expected chance to HQ in a long run is: (100% * 45%) = 45% chance to HQ
If you choose hasty touch + innovation in this example, your expected chance to HQ in a long run is (rounded down): (20% * 32%) + (80% * 78%) = 68% chance to HQ
The math gets slightly fuzzier when you account for the additional "Good" condition chance. Even if we're super generous and say it's a 20% chance to 100% HQ, the safe basic touches is still inferior.
Let's say you change your starting point from 6 IQ stacks to 7 IQ stacks. The numbers still come out to (100% * 82%)=82% versus (20% * 78%)+(80% * 95%) = 91%.
At a starting point of 8 IQ stacks, safe basic touches will result in 100% HQ. Hasty + innovation comes out to (20%*95%)+(80%*100%)=99%.
At a starting point of 9 IQ stacks, both methods will HQ 100%.
The numbers here match my feeling from experience: Only in rare situations will basic touch be better than hasty + innovation, and even then, not by much (...which I noted in my first response in point #2 that you chose not to include in your response).


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