Normon Vincent Peale wrote a book called "Expect a Miracle, Make Miracles Happen". Faith is a powerful tool. To me it is an important facet of life. However you choose to define "god" and whatever you believe about life and eternity we all place faith in something. Whether you pray, meditate or pratice yoga such a mindset does powerful things to a person physically and emotionally. Prayer in and of itself is a form of meditation. It provides one with the faith and will to accomplish things. It instills in ones self the belief that one can do. Another book is "The power of positive thinking". As simplistic as these statements may seem they accomplish powerful things. A positive, smiling, upbeat person inspires others and seems to go through life much better. They focus on the positive things of life- not the negative. By doing so they get more positive things out of life.
So simply put prayer works. Because it helps put one into the positive thinking mode. It empowers one to believe that big things can be accomplished.
IMHO