Scientometrics: The Discipline, Its Laws, and Where It’s Applied

Scientometrics is the discipline that studies science quantitatively — measuring scientific output, its growth, its structure, and its impact using publication and citation data. It asks questions bibliometrics narrows to publications and citations specifically (a distinction covered below): how fast is a field growing, how is its literature distributed across journals and authors, and how does one paper’s or researcher’s influence compare to another’s. Scientometrics supplies the underlying laws and measurement logic that research assessment, science funding policy, and library collection decisions all draw on.

What Is Scientometrics?

Scientometrics is the quantitative study of science, scholarship, and scientific communication — treating the scientific literature itself, and the activity that produces it, as data to be measured and modeled. The English term is a direct translation of naukometriya, coined in 1969 by the Russian mathematician and philosopher of science Vasily Nalimov together with Z. M. Mulchenko in their monograph of the same name. The term gained wide international use after the Hungarian information scientist Tibor Braun founded the journal Scientometrics in 1978, which he intended as a common venue for quantitative science studies broadly.

Scientometrics is closely related to, but broader than, three neighboring terms that are often used loosely as synonyms:

• Bibliometrics applies statistical methods specifically to publications, citations, and other bibliographic records — see CASRAI’s guide to bibliometric analysis methodology for the workflow. In practice the two fields overlap heavily and share the same classical laws, but bibliometrics is usually the term for the applied technique, while scientometrics is the broader disciplinary study of science as a system.
• Informetrics generalizes further still, covering the quantitative study of any recorded information, not only scholarly literature.
• Webometrics (or cybermetrics) applies the same measurement logic to web-based content — hyperlinks, web mentions, altmetrics — rather than the formal citation record.

In everyday use on a site like this one, “bibliometrics” tends to label the applied metrics (h-index, Journal Impact Factor, citation counts) that a researcher or administrator works with directly, while “scientometrics” is the umbrella discipline that explains why those metrics behave the way they do — including three foundational statistical regularities discovered decades before modern citation databases existed.

The Three Classical Laws of Scientometrics

Long before Scopus, Web of Science, or OpenAlex existed, three researchers independently found that scientific output follows highly skewed, predictable statistical patterns rather than being evenly distributed. These three findings are still the conceptual foundation the field is taught from.

Lotka’s Law (1926)

Alfred J. Lotka, a statistician then working at the Metropolitan Life Insurance Company, counted how many personal names appeared against 1, 2, 3, and more entries in the 1907–1916 decennial index of Chemical Abstracts (restricted to authors whose surnames began with A or B). He found that the number of authors making n contributions falls off as roughly 1/n² of the number making a single contribution — a small number of authors account for a disproportionate share of a field’s output, while most authors publish only once or twice. This is often called the “inverse square law of scientific productivity.” Lotka’s Law is the reason author-productivity distributions in any discipline look heavily right-skewed rather than roughly even, and it underlies later author-level metrics work, including the intuition behind the h-index.

Bradford’s Law (1934)

The British documentalist Samuel C. Bradford, building on the same skewed-distribution intuition as Lotka, found that the literature on a given subject scatters across journals in a predictable pattern: a small “core” of journals accounts for a large share of the relevant articles, a second zone of journals of roughly equal size yields a similar share with diminishing returns, and so on outward — each successive zone requiring disproportionately more journals to add the same number of articles. Bradford’s Law of Scattering is the direct ancestor of modern journal-selection and library collection-development practice: it explains why a research library or database can cover the great majority of a field’s relevant literature with a comparatively small, well-chosen set of core journals rather than needing exhaustive coverage.

Price’s Law and Cumulative Advantage

Derek de Solla Price, a physicist and historian of science, is generally credited as the founder of scientometrics as a rigorous field of study. His 1963 book Little Science, Big Science documented the exponential growth of scientific output and researcher numbers across the 20th century and asked what that growth trajectory implied for the future of science as an institution. Price’s own productivity law states that roughly half of all scientific papers in a field are produced by a core of contributors numbering about the square root of the field’s total author population — an even more extreme concentration than Lotka’s Law implies on its own. In a later 1976 paper, Price generalized this into a theory of cumulative advantage: papers, authors, and journals that already have citations or recognition tend to accumulate more of it at a faster rate than newcomers, a “rich get richer” dynamic that recurs throughout scientometric data, from citation counts to journal prestige.

Why the Classical Laws Still Matter

These three laws are not merely historical curiosity. They explain, mathematically, why so much scientometric data is highly skewed rather than normally distributed — which is precisely why arithmetic-mean-based summaries of citation counts or productivity are usually misleading, and why field-normalized and rank-based metrics (percentiles, the h-index and its relatives) were developed instead. They also motivate the core practical uses scientometrics is put to today, described next.

Where Scientometrics Is Applied

Scientometric methods and the classical laws above underpin several distinct, practical uses across research administration, publishing, and science policy:

• Research evaluation and funding decisions. Funders, universities, and national assessment exercises use citation- and publication-based indicators — alongside peer review, not as a replacement for it — to inform hiring, promotion, and grant decisions. This is also the area with the most active methodological reform: see CASRAI’s coverage of the San Francisco Declaration on Research Assessment (DORA) and the Coalition for Advancing Research Assessment (CoARA), both of which push back against mechanical, journal-level metrics like the Journal Impact Factor as substitutes for individual research quality.
• Science policy and national research strategy. Governments and funding agencies use scientometric indicators — publication growth, international collaboration patterns, field emergence and decline — to track where a national research system is strong, where it is falling behind, and where investment might be redirected.
• Library collection development and journal management. Bradford’s Law of Scattering directly informs which journals a research library subscribes to or a database indexes, since a comparatively small core covers most of a field’s citable output.
• Bibliometric analysis and science mapping. Scientometric techniques — co-citation analysis, bibliographic coupling, co-word analysis — are used to map the intellectual structure of a research field: its major sub-topics, its most influential works, and how it has evolved over time. See CASRAI’s guides to citation network analysis and VOSviewer, the most widely used science-mapping software, and the upstream overview at Bibliometric Analysis: Methodology, Workflow, and How to Conduct One.
• University and journal rankings. International rankings and journal-quality indicators such as the Journal Impact Factor and the CWTS Leiden Ranking apply scientometric methodology at the institutional and journal level, with the Leiden Ranking specifically built around responsible-use principles rather than a single composite score.

Data Sources and Tools

Modern scientometric work draws its underlying data from large citation databases — principally Scopus, Web of Science, and the open, API-accessible OpenAlex — compared directly in CASRAI’s Scopus vs. Web of Science vs. OpenAlex guide. See also what OpenAlex is actually used for in research assessment for how an open dataset changes what scientometric analysis at scale can do.

Limitations and Responsible Use

Because the classical laws describe skewed, concentrated distributions, scientometric indicators are easy to misuse if treated as precise, field-independent rankings rather than what they are: statistical summaries of processes with strong cumulative-advantage dynamics baked in. The Leiden Manifesto (Hicks, Wouters, Waltman, de Rijcke and Rafols, published in Nature in 2015) sets out ten principles for the responsible use of quantitative research-evaluation metrics, including that quantitative evaluation should support, not supplant, expert peer judgment, and that metrics should be field-normalized given how unevenly publication and citation rates vary by discipline. DORA and CoARA extend this reform effort at the institutional and funder-policy level. Anyone using scientometric data for evaluation — not just producing it for research purposes — should treat these as binding practical guidance, not optional commentary.

Frequently Asked Questions

What is scientometrics in simple terms?

Scientometrics is the quantitative study of science itself — measuring how scientific knowledge, publications, and researchers grow and interact using statistical methods applied to publication and citation data.

What is the difference between scientometrics and bibliometrics?

Bibliometrics applies statistical methods specifically to publications and citations; scientometrics is the broader discipline studying science and scientific communication as a whole, of which bibliometric technique is the main practical tool. The two overlap heavily in practice and share the same classical laws.

What is Lotka’s Law used for?

Lotka’s Law describes how scientific productivity is distributed among authors in a field: a small number of authors produce most of the output, while most authors publish only once or twice. It explains the heavily skewed shape of author-productivity data in any discipline.

What is Bradford’s Law of Scattering?

Bradford’s Law describes how the literature on a subject is distributed across journals: a small core of journals yields a large share of relevant articles, with diminishing returns as more, less-focused journals are added. It is the basis for core-journal selection in library collection development and database indexing.

What is Price’s Law in scientometrics?

Price’s Law holds that roughly half of a field’s publications come from a core of authors numbering about the square root of all contributing authors — an even sharper concentration than Lotka’s Law implies. Derek de Solla Price later generalized this into the theory of cumulative advantage, where existing recognition or citations attract more of the same.

Is scientometrics the same as research assessment?

No. Scientometrics is the underlying quantitative discipline; research assessment is one of its applications. Responsible research assessment, per frameworks like DORA and the Leiden Manifesto, uses scientometric indicators as one input alongside expert peer judgment, not as a mechanical substitute for it.