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The random impact rule allows us to build a null model of a career. Using the null model, we can examine what a scientific career looks like when its driven by chance alone. We call this the R-model. But the R-model only accounts for differences in productivity, not differences in ability or talent. In response to this discrepancy, we create the Q-model, which assumes that the impact of papers we publish is determined by two factors, luck and a Q parameter unique to each person. We can then calculate how a person’s highest impact paper is expected to change with productivity. We find that the Q-model’s predictions are in excellent agreement with real world data. In fact, the Q parameter alone seems sufficient to explain what differentiates one scientist from another. We also find that it remains relatively stable over the course of a career. We then show how we calculate the Q factor for individual scientists, how we can use their Q factor to predict their impact, and how doing so provides a more accurate forecast of a scientist’s future impact than the h-index can. In the case of great scientists, we see that the Q factor turns luck into a consistently high impact career.
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