 More than it will change anyone or anything else, prayer will change the one who prays. Prayer is less about doing and causing and more about becoming the will of God in the earth. Prayer is about becoming God's answer in the world. Now, of course, God does things by his own power, through the miraculous, he does healing and deliverance and he causes things like this to manifest completely apart from us, but he also chooses, he also chooses to work through us in this way.