A statistical theory of overconfidence is proposed and applied to the issue of occupational choice. Individuals who can choose whether to engage in an activity or not must estimate their performance. The estimates have error and that error has positive expectation among those who engage in the activity. As a result, an unbiased ex ante estimate of performance in an occupatoin results in an ex post biased estimate of ability among those enter. The statistical theory of overconfidence provides a number of testable implications, most significant of which is that overconfidence should be more prevalent in occupations where estimates of ability are noisier. This and other implications are tested and found to hold using the Current Population Survey and Panel Study of Income Dynamics data.