Scattering (with Bradford's law)

Research has been made in Library and Information Science (LIS) about how the literature is scattered, for example, how the articles about a particular subject is scattered on scientific journals. One can also use the opposite expression: how articles on a given subject are concentrated on journals. Generally, how documents are scattered (or concentrated) in different sources or in Knowledge organization systems.


Scattering has mostly been considered in relation to what is known as Bradford's law. It is, however, possible to approach this phenomenon from other points of view. Here, we shall first present the traditional view and then suggest other ways of considering scattering.


"Bradford's law of scattering" first formulated by Bradford (1934, 1948) and coined so by Vickery (1948) is a particular bibliometric law (Garfield, 1971, correspondingly coined  Garfield's law of concentration). What precisely is said in Bradford's law is somewhat unclear because different formulations of the law, including verbal and mathematical  formulations are not in accordance with each other and because it is unclear how the concept of "subject" has been operationalized in empirical investigations.


Bradford's law states that documents on a given "subject" is distributed (scattered) according to a certain mathematical function so that a growth in papers on a subject requires a growth in the number of journals/information sources. The numbers of the groups of journals to produce nearly equal numbers of articles is roughly in proportion to 1: n: n2 …, where n is called the Bradford multiplier. (Bradford believed n to be constant in the different zones (n1=n2=n); Results reported by Rao (1998) indicates, however, that Bradford’s assumption was wrong: Bradford multipliers vary from zone to zone).


Explained in words, Bradford's law states that a small core of, for example, journals have as many papers on a given subject as a much larger number of journals, n, which again has as many papers on the subject as n2 journals. Bensman (1982, 286–87) analyzed Bradford's original data and found that in the applied geophysics subject, 9.2% of journals accounted for 51.7% of the articles on that subject with the other 48.3% of these articles spread out over journals of other disciplines. In the lubrication subject, 9.2% of the journals accounted for 40.8% of the articles on this subject with the remaining 59.2% spread out over the journals of other disciplines.


Bradford himself provided both a graphical and a verbal formulation of his law that have later been found not to be mathematical equivalent (Vickery, 1948). The exact mathematical function has been subject to much subsequent research, and the very question what a Bradford distribution is has been debated. As the distribution is very sensitive to different subjects and conventions, Heine (1998) found that it is unclear under which circumstances a distribution should be regarded a Bradford distribution.


Bradford's law has been regarded as identical with other bibliometric laws and also with laws in quite different domains. Brookes (1968,1969b), for example, considered 'the Bradford-Zipf distribution'. Zipf's law is about word distributions in a given text, while Bradford's is about subjects distributed over a range of sources. The most vague expression is "the law of the vital few" or "the phenomena of the few generating the many", which is also known as Pareto's principle after the Italian economist Vilfredo Pareto, who observed that 80% of property in Italy was owned by about 20% of the Italian population (see 80/20 rule).


Bradford's law is not claiming that scattering is the same from one subject to another. On the contrary might "soft" disciplines well be more scattered than "hard" disciplines (see Meadows, 1974).


It is often claimed that Bradford's law is useful and has been used to select journals for libraries or databases. However, not a single paper is available in the literature documenting this claim. The only 'real' application found is Garfield's application for selecting journals to his Citation Indexes. This example is not useful for scientific analysis because other selection methods have also been used to select journals for these databases and the influence of each method has not been identified or  communicated. See:


It is sometimes claimed that Bradford's law is not only about quantitative issues but also about qualitative issues: That the most productive journals on a subject are also the best journals (and thus the journals that should be selected by libraries and users). This claim is problematic given that different epistemologies are at play in disciplines and that the dominant view in one place and time need not be the best or the winning one. Journals which at a time represent a minority view and thus are regarded "less quality" in relation to a Bradford distribution may later represent a majority view (cf. Hjørland & Nicolaisen, 2005). What is popular methodologies among, say PhD students may be related to what seems easy to complete within a short span of years. Or, more generally: scientists sometimes think more about their career than about what is optimal from a scientific point of view. Experimental methods, for example, dominates in social psychology, but journals with a more macro-sociological orientation may be seen as being of an even quality (or perhaps higher quality) even if they publish much less papers. 


Hjørland & Nicolaisen (2005) presents three kinds of scattering:


Other kinds of scattering may also be considered, for example:

Bradford's law is claimed to be about subject scattering. However, it has never been carefully examined whether it makes a difference whether "subject" is operationalized one way or another when articles about a subject are identified and counted. It does make a difference whether what is counted are articles reflecting certain words or concepts in their titles or articles considered valuable for a given task, in other words: whether what is being counted are words, concepts or subjects. 

In some vague sense may Bradford's law be considered true: No matter how it is operationalized it is probable that "the law of the vital few" (Pareto's principle) will be verified. However, distributions are extremely sensitive regarding such operationalizations (consider Nicolaisen & Hjørland, in preparation): When journals are divided in Bradford zones (identification of "core journals") different ways of operationalizing "subjects" play an important role for what journals are included in the different zones. The considering of different kinds of scattering is thus important (contrary to what is said by Umstätter, 2005, who misunderstood what was claimed in the paper he discusses).


How should different patterns in scattering be understood and explained? Authors make decisions about where to publish their papers. They may choose to publish them in many different places (scattered) or to publish them in a few journals (concentrated). There may be individual variation in this form of publishing behavior (see individuality in information use). However, general patterns in scattering may reflect underlying norms, cultures and constraints. Some fields are more interdisciplinary, some cultures are more open, some fields have a high degree of consensus about which journals are the most important and so on. In some field are national traditions important, in other not.


The most scattered subjects may be the subjects that are broad and have a high probability of being researched in many different contexts. The least scattered subjects may be the subjects that require very special equipment that only exists in e few laboratories in the world.  In this way may the scattering of subjects reflect the social organization of knowledge.


Bhavnani (2005) studied the distribution of facts related to five common healthcare topics across high-quality sites and the reasons underlying those distributions. The analysis revealed the existence of few pages that had many facts, many pages that had few facts, and no single page or site that provided all the facts. While such a distribution conforms to other information-related phenomena, a deeper analysis revealed that the distributions were caused by a trade-off between depth and breadth, leading to the existence of general, specialized, and sparse pages. Furthermore, the results helped to make explicit the knowledge needed by searchers to find comprehensive healthcare information, and suggested the motivation to explore distribution-conscious approaches for the development of future search systems, search interfaces, Web page designs, and training.



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Wilson, C. S. (1995). The formation of subject literature collections for bibliometric analysis: The case of the topic of Bradford's law of scattering. Vol. 1-2.




See also: Compactness versus diffuseness; Diffusion research & Reception studies  (Epistemological lifeboat). Disciplinarity/Interdisciplinarity (Epistemological lifeboat).


See also: Canon



Birger Hjørland

Last edited: 15-06-2007