Nice OP. Interestingly, the fact that prayer 'works' is one of the first things that caused me to question the Borg and then the existence of god. It may have been the first thing (it has been a while). There was good science several decades ago suggesting that prayer had a positive health impact. However, and this is the point that caused me to begin my Pink Floyd sojoun (another brick in the wall of my theism being removed): prayer 'works' regardless of which god one is praying to, including whether the 'god' is a rock, a pole or an imaginary creature in the heavens. All that matters is the one praying 'believed' or placed their psychological selves in a calmer more restful state.
Buddhist chants do the same thing only a lot better.