There was an official post a long time ago about this. Every recipe in the game either uses Craftsmanship or Mg. Craftsmanship to influence your success rate and progress. Each also has minimum values for both this stat and Control, below which the synthesis is much harder, similar to trying a recipe that requires the use of common support without support at all.

Unfortunately that seems to be all that's known for sure. The formula governing crafting success or failure has a lot of variation, so it's hard to tell if you're using the right stat or just getting lucky. That said, it's definitely better to use crafting gear that improves all 3 stats as opposed to none at all.