Lucky charms really do improve our performance—so don't toss out that shamrock at midnight on March 17. Damisch, Stoberock, and Mussweiler published a study examining how superstitions influence us in a 2010 edition of Psychological Science ("Keep Your Fingers Crossed! How Superstition Improves Performance," vol. 21, no. 7). They scrutinized physical tasks (for example, involving motor dexterity) and cognitive ones (such as solving word games and memory assignments) to learn more about superstitious behavior.
In short, lucky charms (and superstitions, for that matter) work because they make us more confident. The authors define superstitions as "irrational beliefs that an object, action, or circumstance that is not logically related to a course of events influences its outcome." In technical terms, acting on a superstition (for example, crossing your fingers) or keeping your lucky charm close at hand increases "perceived self-efficacy." This means acting on superstitions or toting around lucky charms boosts our "confidence in mastering upcoming tasks, which in turn improves performance."
Irrationality wins out again!