Why don't normal painkillers such as paracetomol and ibuprofen work against migraine?

We put this question to Dr Richard Lipton:

Well sometimes they do and you know, and like every condition, there's a broad spectrum of severity. So, ibuprofen and paracetamol may work if you treat the migraine very early. If you wait and wonder if you need to treat, oral medications become less effective because migraine also affects the gut and you may not absorb the medication as well. For people who don't do well with over-the-counter medications, there's certainly a wide range of prescription drug options that are very effective.