In part 1, I noted that citations in research are distributed by a power law: that is, the best few researchers get almost all the attention. Why is this? One factor is the Matthew effect, in which “the rich get richer and the poor get poorer.”1, 2
*For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken even that which he hath.
In this context, the Matthew effect is that the most accomplished researchers get increasing amounts of credit and attention.3 One recent study confirmed the Matthew effect in the careers of 400,000 scientists and 20,000 athletes. The authors suggested that the Matthew effect was a feature of “universal statistical laws” of competitive career progress: they predict that early success plays a crucial role in later success, and progress is much easier when you’re already ahead.4 They suggest that this trend is common to all competitive careers.
The Matthew effect may be a crucial consideration for assessing the probability that you rise to the top of your field. Because “the rich get richer,” early achievements and signs of success increase the likelihood that you’ll be even more successful later. For example, the figure below shows how the power-law exponent for a scientist’s article receiving a given number of citations decreases as s/he has more prior articles with more citations.5
The h-index in the figure above is the number of publications h by a given researcher with at least h citations. For instance, if you have 8 publications with at least 12 citations, then your h-index is 8. If you have 10 publications with at least 10 citations, and one publication with 9 citations, then your h-index is 10. So, the above figure shows that scientists with higher h-indices have lower power-law exponents for their articles getting cited. This means that their citation distributions have a “fatter tail.” We can use this to estimate, for example, that if your h-index is greater than 100, the expected number of citations of your future papers is twice that of the average researcher.
This manifestation of the Matthew effect may stem from the tendency to cite works by authors who are already highly cited when looking through an article’s references.5
The next figure is another illustration of the Matthew effect: it shows how the period between a scientist’s publications decrease as s/he publishes more articles.5
The Matthew effect seems crucial to the expected value of choosing an academic career. If you can do a lot of good as a high-profile researcher, then the expected value of this choice could justify this choice even if you’re unlikely to reach your goal. But, if you have good evidence of early success — indicated, among other things, by publications in top journals, high citation rates, and association with networks of prominent researchers citing each other6 — then the expected value of a research career may be extremely high.
Merton, R K. 1968. “The Matthew Effect in Science: The reward and communication systems of science are considered.” Science 159(3810): 5663. ↩
Petersen, A.M. et al. 2011. “Quantitative and empirical demonstration of the Matthew effect in a study of career longevity.” Proceedings of the National Academy of Sciences 108(1): 1823. ↩
Peterson, G. J., Pressé, S., & Dill, K. A. (2010). Nonuniversal power law scaling in the probability distribution of scientific citations. Proceedings of the National Academy of Sciences, 107(37), 1602316027. ↩↩↩
Radicchi, F., Fortunato, S., & Vespignani, A. (2012). Citation Networks. Models of Science Dynamics, 233257. ↩