Open the list of publications in any academic field and the same names show up unusually often. While one person writes dozens of papers, most researchers write only one or two in their entire careers. It may look like chance at first glance, but a remarkably consistent rule lies hidden in this skew.
Simply put, Lotka's law is an empirical law stating that ‘the number of people who write many papers falls in inverse proportion to the square of the number of papers.’ Its full name is Lotka's Law of Scientific Productivity, and in library and information science it is used as the most basic tool for measuring author productivity.
In this article, we will look in turn at how Lotka's law was discovered, what the law says, and how it is used in libraries and research, along with its limits.
Understanding and Using Lotka's Law
A Rule Found in Chemical Abstracts
The first person to describe this law was the American statistician Alfred Lotka. He is better known as a scholar who explained population change mathematically, but with a short 1926 paper, “The Frequency Distribution of Scientific Productivity,” he also left a major mark on library and information science.
Lotka counted two sets of data by hand. One was the chemists whose surnames began with A and B in the index of Chemical Abstracts from 1907 to 1916; the other was the physicists listed in Auerbach's chronological tables summarizing the history of physics up to 1900.
The two fields were entirely different in character, but when he tallied how many papers each author had written, nearly the same shape of distribution appeared. Lotka believed this might be not a coincidence of a particular field but a rule running through scientific activity as a whole.
The Number of Authors Falls by the Inverse Square
Lotka's law can be expressed with a very simple formula: the number of authors who wrote n papers is roughly the number of authors who wrote one paper divided by the square of n.
(1) Authors with One Paper
If 100 authors wrote only one paper, they form the largest group among all authors. According to Lotka's calculations, about 60% of all authors belong here.
(2) Authors with Two Papers
Dividing by 4, the square of 2, gives about 25 people. Just one more paper, and the number of people drops to a quarter.
(3) Authors with Ten Papers
Dividing by 100, the square of 10, leaves only about one person. The more someone writes, the more rapidly such people become rare.
A shape like this, with an exponent of 2, is called an inverse square law. It explains why a long-tailed distribution arises, in which a few researchers produce many papers and many researchers produce few.
Uses in Libraries and Research
Together with Bradford's law and Zipf's law, Lotka's law is counted among the three major laws of bibliometrics. It serves as a starting point in many fields that try to read academic activity through numbers.
- Core Author Identification: Researchers who consistently publish many papers in a field are identified and used as a basis for collection building or expert recommendations.
- Research Evaluation: The research output of an institution or country is compared with the typical distribution to see how it differs and what its characteristics are.
- Field Maturity Analysis: In a newly emerging field, the share of authors with one or two papers is unusually high, so the distribution gives a sense of how established the field is.
- Collection Planning: Libraries acquire the works of highly productive authors first to meet users' needs efficiently.
Later, the historian of science Derek de Solla Price built on this idea and proposed Price's law, which states that a number of people equal to the square root of the total number of authors produce about half of the papers.
Points to Keep in Mind When Reading the Law
Lotka's law holds surprisingly often, but it is not always exact the way a law of nature is. Because it is a rule derived from experience, those who use it should read it with care.
Frequently Cited Limits
- Exponent Variation: Depending on the field and period, the exponent comes out larger or smaller than 2, making it hard to apply the same formula as is.
- Co-authorship Problem: Results vary greatly depending on whose credit a paper written by several people is counted as.
- Name Ambiguity: Errors arise when different people with the same name are counted as one, or one person is split and counted as several.
Above all, the number of papers is only one aspect of productivity and does not directly show the quality or influence of research. That is why today it is common to look at it together with other indicators, such as citation counts.
Lotka's law shows, in simple numbers, how production in the world of science is concentrated in a few. This rule, obtained 100 years ago by counting the names of chemists and physicists one by one, is still used today as a basic framework for reading the flow of scholarly information.
Recognizing the rule hidden behind the numbers while also reading its limits: that is the first step in reading the landscape of scholarship.
