About 35 years ago, I had a friend who was interested in astrology, and he got me to take an astrology class with him. I read books and cast horoscopes and came to the conclusion that astrology works. That is, you can go to a competent astrologer and learn true things about yourself that you did not know.
Of course, it has nothing to do with the stars. Their random position in the sky is a mandala to structure the conversation, a coach's list of plays one might call in a given circumstance. A "competent astrologer" is a cold reader. It's a carnie trick. A skilled cold reader can, indeed, direct a conversation about you that will give you new insight into your character. I suspect this is the basis of psychoanalysis.
Now imagine a world in which everybody believes in astrology, believes the stars' and planets' positions in the sky affect our daily lives. If people saw that Mercury was in retrograde (which is supposed to hinder all types of communication), not only would they attribute any lost mail to Mercury (and ignore the mail that got through), but it is also likely that more mail would be lost than usual, because it would be a self-fulfilling prophesy. Knowing the likelihood of lost mail might make people more careless. Or people might be more expansive and loving when Jupiter is in conjunction with the Moon, because they expect to be.
In such a world, astrology would look true. It might as well be true.
Which brings me to this study on superstition. They had 28 college students who believed or did not believe in good luck (about 80% did) putt a golf ball into a hole and told some they were using a lucky ball and some that they were using the same ball everybody else had. Then 51 kids did a motor-dexterity task putting balls in holes by tilting a box. Some were told the observer would keep his fingers crossed, and others were just told to start. Then they took 41 kids who had a lucky charm and had them do a task with or without it.
The kids with the lucky ball, or who had been told the observer had his fingers crossed, or who had their lucky charm with them did better.
So it appears that believing a superstition can make you perform better. Or worse, if you've lost your lucky charm.
This has an obvious application to religion. People who believe their god will make them strong might well be stronger than people who do not.