I don't think I'm godlike, I've just been contracting for most of 20-something years and I've got good at it. I always give a range. It's never "X weeks" it's "between X and Y weeks" (showing all my workings, too). "X weeks" is always wrong and "X points" is not only meaningless, it also gives no indication of any uncertainty. By giving a range I give the managers enough information to understand the risks - they can choose to go low with their own estimates if they need to win the business, there's no need to pressure the team into giving an artifically low estimate.

I agree that if you start giving a single number of days/weeks, that's bad. Then there's a strong incentive for everyone to start padding their single figure estimates to cover their asses, and the managers end up just halving them in their gantt charts and pushing the team to work quicker. That's an adversarial environment, where nobody trusts each other.