How many pizzas do you actually need? Finally, the math that matters.
Here's something most people don't realize: a large pizza has way more food than a medium, not just a little more. A 14-inch pizza has about 154 square inches of pizza. A 12-inch has about 113. That's 36% more pizza for usually just a few dollars more. Two large pizzas (308 sq in) are almost always a better deal than three mediums (339 sq in) at a similar price point.
Always round up. Nobody has ever been sad about leftover pizza. If you're ordering for a party with unknown appetites, the "hungry" setting is your safest bet. For kids under 10, count them as half an adult. And yes, one person will eat way more than you expect. There's always one.