I think I have observed a pattern where school tier k has professors who attended school tier k + 1. If you are looking at the maximum tier, then there is no k

I think I have observed a pattern where school tier k has professors who attended school tier k + 1. If you are looking at the maximum tier, then there is no k+1 to draw from. So, you end up drawing from your tier, and, especially if your tier has few schools in it, you end up with a disproportionate representation of self-hires.