To have a common denominator to start their appraisal with, most experienced appraisers start by looking at the per square foot price of recent closed sales to arrive at an estimated value for a home under contract. Then they add or subtract for amenities and features that the home under contract has or does not have in comparision to the more recent sales in a neighborhood. Those additions or subtractions can cover a wide range including larger or smaller size, decks, lot size, a view, a remodeled kitchen or baths, overall condition and other elements.
It's likely that your appraiser, who would have been hired by your lender, arrived at the value of your home through this or a similar formula and was able to add value for your view and the fact that your place was in significantly better shape than the other homes on the market. Based on the appraiser's conclusion of the value of your home, and the fact that the appraiser's evaluation, as a safeguard, would have been reviewed by your lender's underwriting department, you probably paid a fair price for your home. Enjoy it!
When I work with a buyer, I usually run a CMA - Comparative Market Analysis - for any property they are thinking about writing an offer on. This is the same report I would run for the seller if they asked me to list their property. The buyer should be armed with the same information to level the playing field and make an informed decision.