I always give a range, I've never gotten an offer at the bottom of the range. Generally, it's the top of the range, or very close to it, or top of their budget

I always give a range, I've never gotten an offer at the bottom of the range. Generally, it's the top of the range, or very close to it, or top of their budget (which is below the range). Granted, I tend to interview for roles I'm already demonstrably good at. So less experienced/suitable people might have different experiences. But this kind of negotiation clearly doesn't follow the "obvious" path. Remember, hiring managers are spending their own money and people do get excited for candidates. When you spent 20 hours interviewing people, and you finally get that unicorn, everyone is going to push for them.