Bosses play an important role in workplaces. Yet little is currently known about a foundational question. Are the right people promoted to be managers, team leaders, and supervisors? Gallup data and the famous Peter Principle both suggest that incompetent bosses are likely to be all around us. This paper's results uncover a different, and more nuanced, conclusion. By taking data on 35 nations, the paper provides the first statistically representative international estimates of the extent to which employees have 'bad bosses'. Using a simple, and arguably natural, measure, the paper calculates that approximately 13% of Europe's workers have a bad boss. These bosses are most common in the Transport sector and large organizations. The paper discusses its methodology, performs validation checks, and reviews other data and implications.