  The expectation that scientific productivity follows regular patterns over a
career underpins many scholarly evaluations, including hiring, promotion and
tenure, awards, and grant funding. However, recent studies of individual
productivity patterns reveal a puzzle: on the one hand, the average number of
papers published per year robustly follows the "canonical trajectory" of a
rapid rise to an early peak followed by a graduate decline, but on the other
hand, only about 20% of individual researchers' productivity follows this
pattern. We resolve this puzzle by modeling scientific productivity as a
parameterized 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. These results highlight
the fundamental role of a panoply of contingent factors in shaping individual
scientific productivity, opening up new avenues for characterizing how systemic
incentives and opportunities can be directed for aggregate effect.
