You've spent how much time looking at homes? You've looked at how many homes? You finally find "the one," and you want to risk offending the seller by just throwing a number up in the air and seeing where it lands?
Any offer I submit is always accompanied with comps. It's my way of saying "Here's what's sold, here's what the appraiser is going to base what your home is worth when he/she comes out and does their homework."
Base your offer on what is fair market value. You're buying a house, not a pair of shoes on clearance or a fridge from the Scratch and Dent department.