Are External Contributions Important to Project Productivity in Open Source Software? A Deep Insight based on Issue Entropy

In the realm of open source software (OSS) development, the resolution of issues is not just a technical task but a pivotal activity that drives ongoing enhancement and secures a project's sustainability. Contributing to issues is the majority form for external contributors to take part in OSS projects. Although the significance of external contributors is recognized, their contributions in issue process still lacks full quantification and clarity, and the correlation between their contributions and the project productivity remains unclear. In response, we propose issue entropy, a novel metric that quantifies the complexity of event sequence in issue process applied to study the external contributions. The metric applies principles of information theory to scrutinize granular details within a project's issue-related activities, providing a unique lens to understand and assess external contributions. To explore the correlation between external contributions and project productivity, we employed issue entropy as a novel way to examine external contributions, and analyzed its correlation with new bugs, commits, and bug fix time, serving as proxies for OSS project productivity. Our findings reveal a strong positive correlation with new bugs, variable relationship with commit volume based on company sponsorship, and significant negative correlation with bug fix time. We also observe the significant interactions between external contributions and other factors, such as project age and the number of files. Moreover, issue entropy offers a new perspective on the health of the OSS project ecosystem, potentially supporting further research and practical applications.