Understanding the Verbal Form of Bradford’s Law

If you have ever searched for journal articles on a single topic, you may have noticed something odd. A handful of journals supply most of what you need, while the rest of the relevant articles are scattered thinly across a huge number of titles. This is not a coincidence. It is a measurable pattern, and the librarian Samuel Clement Bradford described it in words long before anyone wrote it as an equation. That description is what we call the verbal form of Bradford’s law, and it remains the starting point for almost every scattering study done today.

Where Bradford’s law began 🔗

Samuel C. Bradford was a librarian at the Science Museum in London. In 1934 he first described the pattern of diminishing returns that appears when you keep searching more and more journals for articles on one subject. He worked with two bibliographies he had compiled, the Current Bibliography of Applied Geophysics and the Quarterly Bibliography of Lubrication.

His method was simple. He arranged the journals in decreasing order of how many relevant articles each one carried, then split the full set of articles into three roughly equal groups. He noticed that the number of journals needed to fill each group grew in a regular way. A few highly productive journals formed the first group, a larger set formed the second, and a much larger set formed the third. Bradford called the first group the nucleus or core, and he labelled the others the succeeding zones. He published the finding in 1934 and later expanded it in his 1948 book Documentation.

The verbal form of Bradford’s law 🔗

Bradford did not give a mathematical model for his observation. Instead he wrote it down as a sentence, and that sentence is the verbal form of the law. In paraphrase, it says that if scientific journals are arranged by decreasing productivity of articles on a subject, they can be divided into a nucleus of periodicals devoted to that subject and several succeeding zones that each contain the same number of articles as the nucleus. The number of journals in the nucleus and the following zones will then follow the ratio 1 : n : n², where n is a multiplier.

You can read the full statement in Bradford’s own phrasing in many bibliometric papers, since it is quoted almost word for word whenever the law is tested. The key shift to notice is this. The zones are defined by holding the number of articles constant, not the number of journals. Every zone carries the same article load. What changes from zone to zone is how many journals you must gather to reach that load.

Breaking down the statement 🔗

Three ideas are doing the heavy lifting here. First, ranking by productivity means the most article-rich journal sits at the top and the rest descend from there. Second, the nucleus is the small core of journals that supplies the first third of all articles. Third, the succeeding zones each match that same article count but demand progressively more journals. The deeper you go, the more journals you scan for the same reward. This is the diminishing return Bradford was describing.

The mathematical representation: 1 : n : n² 🔗

The verbal statement carries a quiet mathematical claim inside it. When the journals are grouped into three zones of equal article output, the number of journals in those zones forms an approximate geometric series. The ratio is written as 1 : n : n², and this is often described as the number of periodicals across the three zones following 1 : n : n², where n is the Bradford multiplier.

A geometric series simply means each term is the previous one multiplied by a fixed number. If the nucleus contains a journals, the second zone contains roughly a×n journals, and the third zone contains roughly a×n×n, which is a×n². So if the multiplier is 5 and the core has 10 journals, the model predicts about 50 journals in the second zone and 250 in the third.

Why the zones hold equal articles 🔗

This is the part students most often get backwards, so it is worth stating plainly. The articles are split into equal thirds first. The journals are then counted within each third. Because journals in the core are far more productive, a small number of them fills the first third quickly. By the time you reach the third zone, the journals are thinly productive, so you need a flood of titles to gather the same number of articles. The equal article count is the rule; the rising journal count is the consequence.

A worked example 🔗

The INFLIBNET teaching material gives a clean illustration. Suppose a subject’s literature ideally fits the law and the journals number 310 in total. With a multiplier of 5, the split becomes 10, then 10×5, then 10×5×5, which is 10, 50 and 250. The first 10 journals form the core zone, the next 50 form the second zone, and the last 250 form the third. Each of these three zones contains the same number of articles. In reality the data is never this tidy, and the articles in the three zones come out only roughly equal, but the pattern holds well enough to be useful as a rule of thumb.

The Bradford multiplier (n) 🔗

The multiplier, written as n (and sometimes as k or r in different textbooks), is the engine of the whole distribution. It is the factor by which the number of journals grows from one zone to the next. A small multiplier means the journals spread slowly across zones. A large multiplier means the literature scatters fast and you must search far more titles to stay comprehensive.

How to calculate the multiplier 🔗

In a typical scattering study, the multiplier is found by dividing the number of journals in one zone by the number in the zone immediately before it. If the second zone has 50 journals and the core has 10, the multiplier is 5. If the third zone has 250 journals and the second has 50, the multiplier is again 5. Researchers usually compute it for each step and then take an average, because the data rarely produces an identical value at every stage. The zones themselves are drawn so that the percentage error in article distribution across the three zones stays as small as possible.

What the multiplier tells you 🔗

Springer’s study of core journals in pediatric neurosurgery shows the multiplier in action. Imagine six core journals supply 15 useful articles in a month. If you need twelve more journals to find the next 15 articles, the multiplier is 2. The zone after that would need about 24 journals for another 15 articles, then 48, then 96, and so on. Each field carries its own core size and its own multiplier, which is exactly why the multiplier is so valuable. It captures, in a single number, how concentrated or how scattered a discipline’s literature really is.

Verbal versus graphical: a known ambiguity 🔗

Bradford actually left behind two versions of his law, and they do not perfectly agree. The verbal form is the sequence of ratios we have been discussing. The graphical form comes from plotting the cumulative number of articles against the logarithm of the cumulative number of journals, which produces a rising curve that then straightens into a line. Brian Vickery first pointed out that the two statements are not identical, and later work by Brookes, Leimkuhler and others supplied the mathematical models that Bradford never wrote himself.

For students, the takeaway is that the verbal form is the conceptual anchor. It tells you what to expect and why. The graphical and mathematical forms are tools for testing whether a real dataset actually behaves the way the words predict. Most Indian doctoral citation studies, such as analyses of physics theses at the Indian Institute of Science, apply both forms together to check their findings.

Why the verbal form still matters 🔗

This nearly century-old idea is far from a museum piece. Librarians use it to decide which core journals deserve subscription priority, since a small nucleus often satisfies most user demand. Database designers use a related idea called Bradfordizing, which re-ranks search results to push core journals to the top. Researchers building literature reviews use it to identify the handful of journals they cannot afford to miss. In every case, the verbal form supplies the reasoning: concentrate on the core, and accept diminishing returns as you move outward.

It is worth remembering Bradford’s own caution. The law is not statistically exact, and it works best when the articles all belong to one fairly narrow subject. Mix several subjects together and the pattern tends to break down. Used within those limits, though, the verbal form remains one of the most quoted and most practical statements in the whole of bibliometrics.

What do you think? If you mapped the journals you rely on most for your own field, do you think they would fall into a small core the way Bradford predicts? And in an age of open-access databases and full-text search, does the idea of a scattered “core” still describe how you actually find information?

References

1. https://en.wikipedia.org/wiki/Bradford%27s_law
2. https://egyankosh.ac.in/bitstream/123456789/11366/1/Unit-6.pdf
3. https://digitalcommons.unl.edu/context/libphilprac/article/2569/viewcontent/auto_convert.pdf
4. https://ebooks.inflibnet.ac.in/liscp10/chapter/bradford-distributions-an-overview/
5. https://ebooks.inflibnet.ac.in/liscp10/chapter/classical-law-of-bibliometrics/
6. https://link.springer.com/article/10.1007/s00381-014-2481-9