Ok, I see. Thanks a ton for the explanation! I really appreciate you taking your time to help me. I am using the Catmull-Clark (ngons) mode. The problem I'm having is that I get some bald areas and some areas where it looks like the hair is clumping, even when I have clumping turned off. I assumed it had to do with the hair applying to the base model, because I thought the bald spots and clumps corresponded to the unsubdivided geometry. I now realize that doesn't seem to be the case at all.
However, the problem is still there and I'm not quite sure what's causing it. There are some odd bald spots and clumping going on around the mouth. Earlier, I tried copying the model, removed it from the rig and manually subdivided it and then added hair, and for some reason, that model got perfectly even hair distribution.
I've tried setting Root to "Polygon Area" under Guides > Roots in the Hair Object, instead of the default "Polygon Vertex", but that looks even worse. The copied model works fine with "Polygon Vertex", and all the default settings worked fine on this particular model before rigging it.
I'm attaching an image of what it looks like. To the left is the rigged model in an SDS, to the right is the same model, but manually subdivided and without the rig.