This question seems reasonably focused and of interest, but is perhaps unanswerable. I'm a mathematics student graduating and would like to apply for the NSF postdoctoral fellowship. I wanted to know whether choosing an NSF sponsoring scientist who already has postdocs under their supervision damages one's chances of obtaining the fellowship. I'm not as interested in the question of whether such a sponsor will do as good a job in their role. I'm especially interested in answers which provide some evidence which bears on the matter. This seems slightly(very?) field specific, so answers from people with experience in mathematics or related fields are preferred.
I am not directly familiar with the NSF scheme, but for the NIH NRSA scheme choosing a PI with previous post docs is a huge benefit. In fact, from what I have heard from young colleagues, if the PI does not have current or previous post docs, the NIH likes to see a more experienced co-supervisor listed.