I have been changed by prayer. Many people have said this to me as well. I would like to make a distinction between what I call material prayer and emotional prayer. There is a classic rock song by Janis Joplin that is a material prayer. This is not what I mean by prayer.
Many people have a childlike, magic view of prayer.
The fact that this kind of prayer seems to work sometimes is coincidence. We pray for something we want outside of ourselves. We receive it. We think, Aha, prayer works. Things are not that logical where prayer is concerned.