First off, we will define Luck.  coincidence, fate. Happenstance,  contingency.

New research conducted by psychologists has suggested that lucky charms actually do work.

On one test researchers gave golf balls to a number of golfers and told some of them that they were playing with a lucky ball, the golfers without it played noticeably poorer than those who believed that their ball was giving them luck.New research conducted by psychologists has suggested that lucky charms actually do work.

 

When one has beliefs, and emotions toward something, they start behaving differently. If i was to tell a best friend of mine, that I have a new baseball bat and it wins every game if  you play with it.  My best friend would start acting, and feel toward the game differently. The object raises your self-esteem, and makes you believe and think " I can do this, and I will do this". A person with a more emotional hunt toward winning or achieving a goal, has a much greater advantage than one who thinks lower and has a lower commitment.

Luck is proposed by Happenstance. The more you believe in something, hope in something, look forward in something, want something, the more likely something you like will happen.

This is why when people believe in luck, they have a much greater chance of getting in what they believe.

Which proves the luck theory.