Quantifying the dynamics of failure across science, startups and security.

Human achievements are often preceded by repeated attempts that fail, but little is known about the mechanisms that govern the dynamics of failure. Here, building on previous research relating to innovation1-7 , human dynamics8-11 and learning12-17 , we develop a simple one-parameter model that mimics how successful future attempts build on past efforts. Solving this model analytically suggests that a phase transition separates the dynamics of failure into regions of progression or stagnation and predicts that, near the critical threshold, agents who share similar characteristics and learning strategies may experience fundamentally different outcomes following failures. Above the critical point, agents exploit incremental refinements to systematically advance towards success, whereas below it, they explore disjoint opportunities without a pattern of improvement. The model makes several empirically testable predictions, demonstrating that those who eventually succeed and those who do not may initially appear similar, but can be characterized by fundamentally distinct failure dynamics in terms of the efficiency and quality associated with each subsequent attempt. We collected large-scale data from three disparate domains and traced repeated attempts by investigators to obtain National Institutes of Health (NIH) grants to fund their research, innovators to successfully exit their startup ventures, and terrorist organizations to claim casualties in violent attacks. We find broadly consistent empirical support across all three domains, which systematically verifies each prediction of our model. Together, our findings unveil detectable yet previously unknown early signals that enable us to identify failure dynamics that will lead to ultimate success or failure. Given the ubiquitous nature of failure and the paucity of quantitative approaches to understand it, these results represent an initial step towards the deeper understanding of the complex dynamics underlying failure.