Originally Posted by
AdelaaR
I said you gain "potential energy" and then afterwards you release it to go faster on the descent.
This is not some sort of magic but physics

This is absolutely accurate, but it has no bearing on the question at hand. How much of a difference do hills make for average speed? The answer would be it makes a difference depending on how many and how steep the hills are. The potential energy you build climbing and release descending isn't really relevant. You'd have a faster average on flat roads without any potential energy (well that gained to gravity anyway) than you would climbing steep hills and descending fast.