A Model of the Commit Size Distribution of Open Source

A fundamental unit of work in programming is the code contribution (“commit”) that a developer makes to the code base of the project in work. We use statistical methods to derive a model of the probabilistic distribution of commit sizes in open source projects and we show that the model is applicable to different project sizes. We use both graphical as well as statistical methods to validate the goodness of fit of our model. By measuring and modeling a fundamental dimension of programming we help improve software development tools and our understanding of software development.

💡 Research Summary

The paper tackles a fundamental yet understudied aspect of software development: the statistical distribution of commit sizes in open‑source projects. A “commit” is defined as the atomic unit of work a developer submits to a repository, and the authors quantify its size by summing the number of lines added and the number of lines deleted in that commit. Using a large empirical dataset comprising over 11 million commits drawn from 30 diverse open‑source projects collected between 2005 and 2010, the study proceeds through four main stages: data acquisition, exploratory analysis, distribution fitting, and validation across project scales and time.

Exploratory visualisations (histograms, log‑scale plots) reveal a highly right‑skewed distribution: the mean commit size (~23 lines) far exceeds the median (~7 lines), indicating a heavy tail of unusually large commits. To model this behavior, the authors evaluate several candidate probability distributions—exponential, log‑normal, Pareto, Generalized Pareto, and Weibull—by estimating parameters via maximum likelihood and assessing goodness‑of‑fit with Kolmogorov‑Smirnov, Anderson‑Darling, and chi‑square tests. The Weibull distribution, with shape parameter k≈0.68 and scale parameter λ≈15, consistently outperforms the alternatives, achieving the lowest KS statistic and the highest p‑values across the full range of commit sizes. While the Pareto model captures the tail, it fails to fit the bulk of the data; the log‑normal and exponential models underestimate large commits; and the Generalized Pareto, though flexible, suffers from over‑parameterisation.

A key contribution is the demonstration of “scale invariance”: when the dataset is partitioned by project size (small ≤5 developers, medium 6–20, large ≥21), the Weibull parameters remain remarkably stable, suggesting that the same underlying stochastic process governs commit generation regardless of team size. Temporal analysis shows a modest decline in average commit size and tail heaviness as projects mature, supporting the hypothesis that seasoned projects favor smaller, more frequent changes.

The authors discuss practical implications. First, static analysis and code‑review tools can use the Weibull model to flag commits that fall in the extreme upper percentile (e.g., >95th percentile) as potentially risky, prompting additional scrutiny. Second, defect‑prediction models can incorporate commit size as a predictor, given prior evidence linking large commits to higher fault density. Third, project managers can monitor deviations from the expected Weibull shape as an indicator of process health, adjusting policies (e.g., encouraging smaller pull requests) when the distribution drifts.

Threats to validity are acknowledged. Measuring size purely in lines of code ignores semantic effort (design, testing) and may be biased by language‑specific conventions (e.g., verbose versus terse syntax). The dataset, while large, excludes certain domains (embedded systems, proprietary code) that might exhibit different patterns. Moreover, the reliance on a single metric precludes a multi‑dimensional view of change magnitude.

In conclusion, the study provides robust empirical evidence that commit sizes in open‑source software follow a Weibull distribution, a finding that holds across project sizes and over time. This insight enriches our quantitative understanding of software evolution and offers a concrete statistical foundation for improving development tools, risk‑assessment practices, and process‑improvement initiatives. Future work is suggested to explore alternative size metrics (e.g., token changes, abstract syntax tree edits) and to test the model on closed‑source or industrial repositories.