I would argue that if one is unable to do the back of the envelope estimate, then they would have a difficult time doing the rigorous calculation / determinatio

I would argue that if one is unable to do the back of the envelope estimate, then they would have a difficult time doing the rigorous calculation / determination. The main difference between the two is the quality of the numbers that go into them, right? I agree though, that overconfidence in one's ballpark estimate is not to be desired. But, that's more useful information gained from the question, not less.