Welcome aboard, David! Kirk's right about context, but I'm guessing from your sig you're interested in selling small metal finger tops.
As you probably know, the shorter the distance h from the contact point to the top's center of mass (CM), the smoother the spin, the greater the precession rate, and the lower the minimum speed for stable sleeping. All of these consequences contribute to longer spin times, and all are desirable in this context.
But there's a rub, of course. Smaller h also means less ground clearance c beneath the rotor, and that makes the top harder to twirl, as the twirler must then keep the stem that much closer to the vertical to avoid grounding the rotor prior to release.
In fact, the critical quantity to track here isn't the clearance c per se but the "grounding angle" given by
a = tan-1(c / R),
where R is the rotor radius at the level where the rotor would first strike the ground. The smaller the grounding angle a, the less wiggle room the user has during the twirl.
No matter how nice the top otherwise, customers will be frustrated by a finger top that they can't twirl with a decent success rate right out of the box.
So to determine the optimal grounding angle, what you really need is an empirical success rate vs. a curve collected from a focus group of regular folks with a range of twirling skills. If the outcome of that study results in a value of h that cuts too deeply into smoothness or spin time, then you'll have to strike a compromise somehow.
