How CEOs affect strategy and performance is important to strategic management research. We show that sophisticated statistical analysis alone is problematic for establishing the magnitude and causes of CEO impact on performance. We discuss three problem areas that substantially distort the measurement and sources of a CEO performance effect: (1) the nature of performance time series, (2) confounding and (3) the discovery of many interactions associated with the CEO performance effect. We show that the aggregate of empirical research implies complex interdependency as the driver of the CEO performance effect. This suggests a ‘fit’ model requiring new research approaches.