Intruder : In the UK, EAT's are issued by terminal control when holding is expected to be in excess of a certain time; it's basically if you have comms failure whilst holding so you and ATC both know when you will commence intermediate approach, but of course it also assists the crew in fuel planning for diversions.
Indeed, EATs (or EAC -- Expect Approach Clearance -- in the US) are associated with holding in the approach stack. However, there can be no "formula" for the Pilot to consult in that case.
So, I went back to the "other" -- and much less often used -- case, that of complete lost comms enroute. The formula I gave will yield the time ATC expects the aircraft to start an approach from the IAF serving the most likely active runway when the flight plan was filed.
I know that's a bit ancient, but you never know when someone might need it...
