Roland Eisenhuth told me that when he was very young, the first time he had an examination in school his mother told him that she knew a secret for good luck. She leaned in and spit over his shoulder. This would give him an advantage on the exam, she told him.
Indeed it gave him a lot of confidence and confidence helped him do well on the exam. For every school examination after that until he left for University, his mother would spit over his shoulder and he would do well.
Here are the ingredients for a performance-related superstition. Something unusual is done before a performance, say a baseball player has chicken for dinner, and by chance he has a good game. Probably just a fluke. Just in case, he tries it again. Maybe it doesn’t repeat the second time, but maybe he does have another dose of luck and it “pays off” again. And there’s always a chance it repeats enough times in a row that its too unlikely to be a statistical fluke.
Now once you believe that chicken makes you a good hitter, you approach each game with confidence. And confidence makes you a good hitter. From now on, luck is no longer required: your confidence means that chicken dinner correlates with a good game. And you won’t have reason to experiment any further so there will be no learning about the no-chicken counterfactual.
If you are a coach (or a parent) you want to instill superstitions in your student. My wife has been stressing about our third-grade daughter’s first big standardized test coming up in a couple weeks. Not me. I am just going to spit over her shoulder.