As far as I know..
Craftsmanship: Increases the success rate..
Magic Craftsmanship: Increases the quality gained during a synthesis attempt..
Control: Increases the stability of the synthesis and decreases durability loss..
People continue to say this, but SE pretty clearly stated that recipes are influenced by either or, not both. Is there any proof out there to support this?
I understand what you're saying, I agree with you, but let's just put a stop to this nonsense right here and right now. Let's not ask for proof. Just shut them down. Grind them into the ground under your boot if you must until people get it through their heads that it has been explained to us, it is relatively simple, and there are no excuses for guessing on that particular topic anymore.
Some recipes favor craftsmanship. Craftsmanship for those recipes = success rate and quality gains.
Other recipes favor magic craftsmanship. Magic craftsmanship for those recipes = success rate and quality gains.
How can you tell which stat a recipe favors? Look at a list on a site (or through your own experimentation) and find out which tool gives you additional quantity
and which tools gives you additional quality (HQ1/2/3)
. Whichever tool gives you the quantity
result is your hint to which stat the recipe favors.
Main hand = craftsmanship
Off hand = magic craftsmanship
(Finished items like gear favor both, with emphasis on craftsmanship, and will always give HQ1/2/3 results. That's why we were given tools like raising hammers (in addition to doming hammers), <whatever>beak hammers (in addition to cross-pein hammers, and ornamental hammers (in addition to chaser hammers). Different stat distribution. Slightly different purpose.)
And what that means is that unless SE changed it, control is your universal stat. If you're stacking craftsmanship and using your offhand tool for everything (like an armorer ranking up on rings/chain using pliers) you're missing the boat.