I am preparing an NSF standard grant in mathematics, and I need to prepare a budget. As is typical I am requesting two months' summer salary, a travel budget, some money for student support, and a couple of other minor odds and ends -- but I'm not sure how much to request. I don't need anything, but I could make good use of essentially an unlimited amount of money.
One guideline is the average award sizes, which are published by the NSF. It seems quite reasonable to request approximately the average, and this is what I will probably do. But sometimes I wonder if I am wasting the opportunity to request more, for example to allow more of our students to travel to conferences. This is especially true since I would still be happy to be funded even if my budget was cut.
When I get the opportunity, I will ask my question in person to someone who has served on a panel in my discipline. For now, perhaps it is useful to ask the interwebs: generally speaking, what is the relationship between the amount of the requested budget and the likelihood of funding?