Based on Rav Kook - whose yahrtzeit is gimmel Elul, on the nature of Tefilla.
Davening is NOT for Hashem - He doesn't need it.
Davening is also NOT for ME! Chas Vi'shalom that davening should be self-serving. My own selfish desires should not be on my radar screen.
Davening is a Mitzva from the Torah that we do that changes WORLDS - both billions of spiritual worlds and our own little tiny universe as well. These changes also affect our own fate which we care about because we have a job to do and if our needs aren't met we can't do our job.