Tell me how God, as opposed to natural explanations, can come up trumps on explanatory power."

That looks suspiciously like a question to me, Steve. and has nothing to do with Occam's razor.

Well, it was intended to be a piece of rhetoric, but never mind. Natural explanations are sufficient for phenomena such as improvements in people's health. We might have to dig and delve a bit for individual cases, owing to the fact that medical science hasn't revealed everything. Claiming that a supernatural force intervened is entirely superfluous. Were it to add some explanatory power it would perhaps be valid, but in fact it does the exact opposite. It gives us infinitely more explaining to do. So out with the razor, say I.