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.

翻译：科学生产力在职业生涯中遵循规律性模式的预期支撑着许多学术评估。然而，近期对个体生产力模式的研究揭示了一个谜题：每年发表论文的平均数量稳健地遵循"典型轨迹"，即快速上升后逐渐下降，但仅有约20%的个体生产力轨迹符合这种模式。我们通过将科学生产力建模为随机游走来解决这一谜题，表明典型模式可以解释为职业生涯早中期生产力变化方差的减小。通过对205所博士授予机构的2,085位计算机科学教师的生产力轨迹（涵盖1980-2016年间29,119篇出版物）进行实证特征分析，我们（i）发现了职业生涯早期及逐年生产力变化中极为简单的模式，（ii）证明生产力随机游走模型既能复现平均生产力的典型轨迹，又能捕捉个体层面轨迹的多样性，包括威廉·肖克利在1957年观察到的累积生产力对数正态分布。我们通过将模型拟合到2011-2023年间12个领域22,952位教师的独立面板数据，证实这些结果在不同领域具有普适性。这些发现凸显了方差在塑造个体科学生产力中的重要性，为探索如何引导系统性激励与机会以实现聚合效应开辟了新途径。