Great posts from all of my colleagues. The ratio you talk about can, and should only, be used as a guideline for a range in a particular area. As previous posters mentioned, each house has it's own worth to you, but purchase price should be based on previous sales of comparable properties, location, upgrades, and amenities (as William said, a pool can be a must have or an unwanted chore).
I had a potential client who crunched the tax assessment numbers himself, and insisted that his house should be listed almost 50K over what the comparables clearly showed. In this case, although the home was in a great location, and had a nice piece of property, he was comparing tax assessments of 4 and 5 bedroom colonials to his 3 bedroom split level. He listed with another agency at the higher price, and the house lingered and expired.
A qualified agent can and should present you with all the relevent numbers to help you agree on a recommended offer price . Remember they (we) do this for a lving, and sell homes many more times than an individual sells or buys one. Our insight into the current market, access to the current sales stats and trends is an invaluable tool. Good luck !!!