It has come to my attention that on the homepage on any given SE you can sort by "active", "hot", "week", and "month". The tooltip says the latter three sort by "most views, answers, and votes" over different periods of time. So it seems that this is uses a different formula than the "arbitrary hotness points" that create hot network questions. What is the formula and what is the rationale for using views here, but not in the network hot questions?
Also, what is the rationale for offering such different sorting options between the homepage and the questions tab? I have been active for ~4 months and never realized there was a sort by hotness option on a different screen (as I have always looked at the questions tab to see what was new) until today.