Why would swapping positions matter with mice? Would this only matter if using dual trackballs (mapping problems)?
Okay, let me explain it this way -
Assume I have a trackball connected to OSCAR hack A. And two spinners connected to OSCAR hack B.
I have no other "mice" in the system.
I plug the OSCAR hack A in first followed by the OSCAR Hack B.
I fire up MAME (actually I think I might have to do this through the ctrl.cfg file) and set Centipede up to use Mouse 0 - the trackball. I set Arkanoid up to use Mouse 1 X-Axis. I set Csprint up to use P1 is Mouse 1 X-Axis, P2 is Mouse 2 Y-Axis.
All is well with the world. I am happily MAMEing away.

Now I shut the cab down and start it back up. OSCAR hack A is now identified by the OS and thus MAME as Mouse 1 and hack B is now Mouse 0.
I can play Centipede with the spinners like an Etch-a-sketch, but the tball doesn't work. Arkanoid works with the trackball moving side-to-side, but the spinner doesn't work. Cspint works with the trackball side-to-side controlling P1 and up-and-down controlling P2 (which would be real interesting, but frustrating to play).
I am not happy . . .

Btw, I
think this could be avoided by mapping each game to either Sysmouse or "Mouse 0 or Mouse 1", but then accidentally moving the spinners affects the trackball games, etc.