  Human achievements are often preceded by repeated attempts that initially
fail, yet little is known about the mechanisms governing the dynamics of
failure. Here, building on the rich literature on innovation, human dynamics
and learning, we develop a simple one-parameter model that mimics how
successful future attempts build on those past. Analytically solving this model
reveals a phase transition that separates dynamics of failure into regions of
stagnation or progression, predicting that near the critical threshold, agents
who share similar characteristics and learning strategies may experience
fundamentally different outcomes following failures. Below the critical point,
we see those who explore disjoint opportunities without a pattern of
improvement, and above it, those who exploit incremental refinements to
systematically advance toward success. The model makes several empirically
testable predictions, demonstrating that those who eventually succeed and those
who do not may be initially similar, yet are characterized by fundamentally
distinct failure dynamics in terms of the efficiency and quality of each
subsequent attempt. We collected large-scale data from three disparate domains,
tracing repeated attempts by (i) NIH investigators to fund their research, (ii)
innovators to successfully exit their startup ventures, and (iii) terrorist
organizations to post casualties in violent attacks, finding broadly consistent
empirical support across all three domains. Together, our findings unveil
identifiable yet previously unknown early signals that allow us to identify
failure dynamics that will lead to ultimate victory or defeat. Given the
ubiquitous nature of failures and the paucity of quantitative approaches to
understand them, these results represent a crucial step toward deeper
understanding of the complex dynamics beneath failures, the essential
prerequisites for success.
