Using maximum likelihood estimation methods and complexity science concepts to research power law-distributed phenomena

Life is not normally distributed – we live in a world of extreme events that skew what we consider ‘average.’ The chapter begins with a brief explanation of the basic causes of skewed distributions followed by a section on horizontal scalability processes. These are generated by scale-free mechanisms that result in self-similar fractal structures within organizations. The discussion then focuses on one of the most cited mechanisms purported to cause power law distributions: Bak’s (1996) ‘self-organized criticality’. Using three longitudinal datasets of entrepreneurial ventures at different states of emergence, the chapter presents a method to determine whether data are power law distributed and, subsequently, how critical thresholds can be calculated. The analysis identifies the critical point in both founder inputs and venture outcomes, highlighting the threshold where systems transition from linear to nonlinear and from normal to novel. This provides scholars with a conceptual–empirical link for moving beyond loose qualitative metaphors to rigorous quantitative analysis in order to enhance the generalizability and utility of complexity science.