i'm not trying to argue about your methods, but i just want to explain how this looks to me, as a deist.
If I give an example of how I used prayer to help me in some facet of life... you counter with an explanation about how praying helped me by me actually maintaining focus, rather than by divine intervention, correct?
To me it seems a waste of time to try to contribute to a thread where the primary purpose is to look at prayer through the lenses of logic.
the thread was meant more for an open-ended discussion of what prayer is and what, if the traditional judeo-christian understanding of it is outmoded due to the flaws illustrated above, can be changed in our understanding (if anything) to maintain prayer as still meditatively useful, if not externally beckoning in any literal sense.
i also think that the discussion could lead, ultimately, to the factors present in the formation of belief systems and the supernatural as precursors to accepting prayer on faith in spite of the clearly massive, massive confirmation biases involved in filtering information to "prove" the efficacy of prayer.