"I'll pray for you."

[Zarith]

First you have no know what those supernatural phenomenon are. You have prayer requests but you don't know Gods answer.

Second you need a supernatural event detector. And you don't have one .

Third, you need to be able to distinguish supernatural events from natural events. If those events are truly supernatural, you shouldn't be able to detect them.

Looks like you've got your work cut out!

But people make prayer requests all the time asking for changes in the natural world.

You seem to believe supernatural = untestable, which is not at all the case, there have been many scientific studies on things like ESP, telekinesis, faith healing, fortune telling, water divination, and so on. It's not that these phenomena are impossible to measure in principle, it's that when we do measure them, we get the null result.

All of these things say that there exist detectable events in the natural world which have supernatural causes. Claims like this are entirely testable. So is a claim like 'praying for X makes X more likely' where X is a detectable event in the natural world. Perhaps you don't take this particular stance, but many people do, and there's nothing illogical about testing a claim like this, even if it turns out to be false.

Now, you seem to believe that they do get answered, but maybe in unpredictable and immeasurable ways. Fine. But if the question is, "Will my act of prayer make this sick person more likely to recover?" and the data says "No" ... what exactly is the point again?