All balls have a preferred spin axis through the pin. That is, the ball will have a tendency to reorient itself as it goes down the lane so that it is spinning about the pin. This reorientation is what we call track flare. When the ball is spinning around the pin, it is stable.
On a symmetric-cored ball, it can also spin stably 90* from the pin. If you put the pin at the north pole, 90* is any point on the equator. This is not as strongly preferred as spinning around the pin, but it is still stable. It's also not unique any spot 90* from the pin will be a stable orientation for the core.
An asymmetric-cored ball has a specific point that's 90* from the pin about which is will spin stably. Because it's a specific point (the MB mark, the secondary pin, or however the manufacturer chooses to mark it), it has a lot more influence on ball motion.
From a reaction standpoint, there is a wider range of ball reactions that you can get out of an asymmetric ball versus a symmetric ball. There's some room for tweaking the reaction with a symmetric ball, but you're really just limited to where you put the weight hole. Different placements of the MB will produce more different ball reactions than different placements of the CG on a symmetric ball. And you can still tweak the reaction with a weight hole.
SH
