Does faith have a purpose? Is it useful?

I am talking about faith in general, as meaning a belief without proof. I am including things from "I believe I can win this race" to "I believe I can beat this cancer" to "I believe in God". And also "I believe I am a sinner", "I believe I won't get addicted in the first time" or "I believe that group of people should be killed for being infidels"