Scientific productivity as a random walk
The expectation that scientific productivity follows regular patterns over a career underpins many scholarly evaluations. However, recent studies of individual productivity patterns reveal a puzzle: the average number of papers published per year robustly follows the ``canonical trajectory'' of a rapid rise followed by a gradual decline, yet only about 20\% of individual productivity trajectories follow this pattern. We resolve this puzzle by modeling scientific productivity as a random walk, showing that the canonical pattern can be explained as a decrease in the variance in changes to productivity in the early-to-mid career. By empirically characterizing the variable structure of 2,085 productivity trajectories of computer science faculty at 205 PhD-granting institutions, spanning 29,119 publications over 1980--2016, we (i) discover remarkably simple patterns in both early-career and year-to-year changes to productivity, and (ii) show that a random walk model of productivity both reproduces the canonical trajectory in the average productivity and captures much of the diversity of individual-level trajectories, including the lognormal distribution of cumulative productivity observed by William Shockley in 1957. We confirm that these results generalize across fields by fitting our model to a separate panel of 22,952 faculty across 12 fields from 2011 to 2023. These results highlight the importance of variance in shaping individual scientific productivity, opening up new avenues for characterizing how systemic incentives and opportunities can be directed for aggregate effect.