I've used only a few assymetric balls, and, for my money all have been duds...EXCEPT for my latest, a Morich Onslaught. This ball has demonstrated, for me, the advantage of assymetrics. It gives me an entirely different look than any symmetrical ball in my bag; that is, it offers me options in playing the lane that I don't have otherwise. Advantages? I think not so much advantages, as differences. The disadvantage of assymetrics is, if it is one, you need to be much more on your game as a driller with them. I don't know if its true of all assymetrics but I think it possible to screw them up much more easily if drilled incorrectly (this may well be why my earlier forays into assymetrics was a flop.)
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"I do desire that we may be better strangers." Willie the Shake, As You Like it(III,ii)