I focus on the shot, but as I flip the baton my subconscious is analyzing it like crazy. Is it heavy/light? Is there a chip/dent/irregularity in one end? Anything about the texture that might affect the release (newer wood tends to be rougher, worked-in sets are smooth, wet wood can be "sticky", etc.) Again, I'm not actually thinking about these things, but I'll notice something out of the ordinary as I flip the baton. It also makes sure that I'm using my standard grip. And lastly it's ritual. Doing things the same way over & over helps with consistency, and consistency is at the heart of this game.
The analogue to this is spinning field kubbs before drilling them, which I also do. Weight, feel, defects in the edges, etc.
I guess I can't say for sure that any of this actually helps me throw better, but it makes me FEEL like it does, and that placebo effect probably has a greater impact on my accuracy than all the rest of this stuff combined.