Divergence or Convergence? A Deep Insight into the Crowd Collaboration and its Productivity in Open Source Software based on Entropy

The Fork and Pull-Request model is widely used in collaborative development of open source software (OSS), fostering innovation through independent repository copies, but it can also lead to inefficiencies and fragmentation. A key underexplored aspect is the integration effectiveness—the degree to which distributed original commits across forks are effectively integrated back into the main repository. It plays a critical role in OSS project productivity but remains poorly understood. In response, we introduce convergence entropy, a novel metric that quantifies the integration effectiveness by measuring the similarity between distributions of original and merged commits across forks, adjusted for integration ratio. This metric highlights not only the volume of contributions but also their diversity and coordination, offering a unique lens to understand forking practices. Moreover, we explore the relationship between convergence entropy and three dimensions of OSS project productivity, showing significant correlations. We also observe that other factors can alter this dynamic.