It's 5 am and I can't seem to fall asleep. This random thought just hit me: Say each of the top 100 undergraduate programs generate on average 20 graduates with physics degree (To me it seems like this is an overestimation, but let's say it's the upper limit) every year. If you assume that 15 of those 20 graduates apply to grad school, that will make a national applicant pool of 1500 people. If 15 domestic applicants on average enter each of the top 20 departments, This would mean 1 out of 5 applicants enter top 20 departments. Does this seem at all like a reasonable estimate?