There is a formula sitting inside virtually every major search engine in the world. It has no flashy name, no Silicon Valley origin story, and its inventors never sought fame. But the equation that became BM25 a scoring function for ranking documents by relevance has quietly shaped how billions of people find information online for more than three decades.
The story begins in London in the early 1970s, in the corridors of City University, where two researchers were asking a question that seems almost obvious in retrospect: what if relevance itself could be treated as a probability?
The Problem of Too Many Answers
By the mid-1970s, information retrieval systems were generating a new kind of frustration. Boolean search matching documents that contained certain words produced lists of results that were technically accurate but practically useless. A query for "bank" would return everything from financial institutions to river embankments, with no sense of which documents a user actually wanted.
Stephen E. Robertson and Karen Spärck Jones were working at City University's Department of Information Science, surrounded by the challenge that defined their field: how do you rank the results of a search so that the most useful documents appear first? The traditional approaches relied on counting word frequencies, measuring document length, or applying fixed rules. None of them treated the problem as fundamentally probabilistic.
Their insight, developed across several years of research, was that relevance was not binary. A document was not simply relevant or irrelevant it had a probability of relevance given the query and the document itself. This probability could be estimated, weighted, and used to sort results.
In their foundational 1976 paper "Relevance weighting of search terms" published in the Journal of the American Society for Information Science, Robertson and Spärck-Jones formalized this idea into what became known as the probabilistic relevance model. The framework proposed that for any document dj and query q, the probability that the document was relevant could be calculated from the representations of both. Their formula calculating the ratio of the probability a document was relevant to the probability it was not gave the field its first principled mathematical foundation for ranking.
The Probability Ranking Principle
The theoretical implications of their work extended far beyond a single formula. In a 1977 paper titled "The probability ranking principle in IR" published in the Journal of Documentation, Robertson articulated what would become one of the most influential ideas in information retrieval: if a system ranks documents in order of their probability of relevance to a user's query, it performs optimally. This became known as the the Probability Ranking Principle.
The elegance of the principle lay in its simplicity. By making explicit the assumption that documents could be ranked by their likelihood of usefulness, Robertson gave the field a standard against which other approaches could be measured. The principle did not dictate how to calculate those probabilities only that ranking by them was theoretically sound.
According to the Springer Encyclopedia of Database Systems entry on the Probability Ranking Principle, Robertson formalized this with a specific mathematical model (the RSJ model), which calculated the probability of relevance as a log-odds ratio across query terms. The model assumed independence between terms a simplification that made calculations tractable while capturing the essential logic of relevance estimation.
From Theory to Practice: The Birth of BM25
Theoretical models are one thing. Practical ranking functions are another. The probabilistic relevance framework provided the foundation, but translating it into a usable formula required additional work and several more years of development.
The solution emerged in modified form through the Okapi system, an information retrieval system developed at City University in London during the 1980s and 1990s. The Okapi project, named after a library-assisted retrieval system, implemented and refined the probabilistic models that Robertson and his colleagues had been developing. From this practical experience came BM25 Best Matching 25 a ranking function that distilled decades of probabilistic theory into a single, implementable formula.
According to the Wikipedia entry on Okapi BM25, the function was developed by Stephen E. Robertson, Karen Spärck Jones, and others, building on the probabilistic retrieval framework from the 1970s and 1980s. The formula incorporated term frequency (how often a query term appears in a document), inverse document frequency (how rare or common the term is across the collection), and document length normalization addressing one of the key limitations of earlier approaches.
"BM25 is a bag-of-words retrieval function that ranks a set of documents based on the query terms appearing in each document, regardless of their proximity within the document. It is a family of scoring functions with slightly different components and parameters."
The formula's parameters k1 typically set between 1.2 and 2.0, and b usually set to 0.75 controlled how aggressively term frequency and document length were weighted. These values emerged from empirical testing more than theoretical derivation, giving BM25 a pragmatic flexibility that allowed it to work well across diverse collections and query types.
The Practitioner Publication
Robertson's career extended well beyond the original theoretical contributions. His selected publications list at City University reveals a sustained intellectual engagement with information retrieval across five decades. His 1977 paper on the probability ranking principle was reprinted in 1997 in "Readings in Information Retrieval" edited by Spärck Jones and Peter Willett, demonstrating the lasting significance of the work.
Perhaps most remarkably, Robertson continued contributing to the field through subsequent decades. His 1982 paper with Maron and Cooper explored "Probability of relevance: a unification of two competing models for information retrieval" an attempt to reconcile different probabilistic approaches under a common framework. Work on relevance feedback, query expansion, and indexing theory followed, building an interconnected body of research that treated information retrieval as a coherent discipline beyond a collection of ad hoc techniques.
In 2020, Robertson published Before Computers: On Information Technology from Writing to the Age of Digital Data with Open Book Publishers, a book that placed his technical work in historical context. The title itself suggests a scholar deeply interested in the lineage of ideas understanding not just how systems work, but how they came to be designed the way they are.
Why the Framework Still Holds
The probabilistic relevance model was not perfect. The original framework acknowledged several limitations: there was no accurate estimate for first-run probabilities, index terms were not weighted, and terms were assumed mutually independent. These constraints required further development, and the field responded with increasingly sophisticated approaches.
Yet the core intuition proved remarkably durable. When modern practitioners assess ranking systems, as documented in contemporary AI learning resources, BM25 remains "still the industry standard baseline for text ranking." The resource notes that "despite neural models, BM25 is still used as a baseline in 2025" a testament to the robustness of the original framework.
The reason for this endurance lies in what the probabilistic model actually captures. By treating relevance as a probability, Robertson and Spärck-Jones built a framework flexible enough to accommodate new evidence, new term-weighting schemes, and new understanding of how users express information needs. BM25 became the direct descendant of that framework, but the underlying principle rank by probability of usefulness proved more durable than any specific implementation.
Understanding the Foundation
For readers working in search, discovery, and answer engines today, the Robertson-Spärck-Jones framework offers more than historical interest. It provides a conceptual vocabulary for understanding why ranking works the way it does and why certain approaches succeed where others fail.
The key insight is that ranking is fundamentally a decision under uncertainty. A user submits a query with a latent information need. The system has incomplete evidence about what documents will satisfy that need. The rational response is to rank documents by the estimated probability that they are relevant not by raw matches, not by recency, not by authority scores alone, but by a principled combination of evidence that predicts usefulness.
This probabilistic lens explains why term frequency matters (repeated mentions suggest importance), why inverse document frequency matters (rare terms discriminate more effectively), and why document length normalization matters (a long document may accumulate term matches without being more relevant). Each element of the BM25 formula reflects a reasoned assumption about how evidence of relevance manifests in text.
What this means for WebSearches readers is practical: understanding the probabilistic foundation helps explain the behavior of modern ranking systems, even those that have moved beyond literal term matching into semantic understanding and neural embeddings. The questions of probability estimation, evidence combination, and uncertainty remain central even when the specific formulas have changed.
A Framework That Surpassed Its Origins
The probabilistic relevance model was designed as a framework for deriving ranking functions. It succeeded beyond its creators' expectations. BM25, its most prominent derivative, became so widely adopted that it effectively became synonymous with baseline text ranking. Variations like BM25F extended the approach to handle document structure and anchor text. Learning-to-rank approaches built on the same underlying intuition, treating relevance as something to be predicted beyond simply matched.
Robertson and Spärck-Jones did not set out to build the foundation of modern search. They were solving a technical problem in information retrieval, working within an academic context that valued theoretical rigor and empirical validation. That their framework endured while many contemporary approaches faded suggests something important: good theory outlasts its implementation.
Karen Spärck Jones passed away in 2007, having seen her work underpin systems she could scarcely have imagined. Stephen Robertson continued publishing and thinking about information retrieval into his later career, including the historical synthesis of Before Computers. Together, they built a framework that survived the transition from mainframe batch retrieval to web-scale search engines to the neural era a testament to the power of asking the right foundational question.
What this means for WebSearches readers
Understanding the probabilistic relevance model is not merely an academic exercise. For anyone working with search systems whether building them, evaluating them, or optimizing content for them the framework provides essential context. BM25 remains the baseline against which improvements are measured. The Probability Ranking Principle remains the theoretical justification for most ranking approaches. And the underlying intuition that relevance is probabilistic, that ranking should reflect estimated usefulness, that evidence must be combined systematically continues to animate the field.
When debugging why a search engine returns unexpected results, or when evaluating a new ranking algorithm, practitioners benefit from understanding the foundations. The Robertson-Spärck-Jones framework is not a historical curiosity. It is the conceptual toolkit that makes sense of modern ranking and that will continue to inform how we build and understand search systems for decades to come.
Where to read further
For readers interested in exploring the primary sources directly, Robertson's publications page at City University provides a comprehensive bibliography spanning his entire career, including the foundational papers from the 1970s and their later elaborations. The Wikipedia entry on Okapi BM25 offers a detailed explanation of the scoring function's components and their empirical origins. For a curated guide to the broader landscape of ranking and recommendation foundations, the classic foundational papers resource by Renee Jia places Robertson and Spärck-Jones's contributions within the larger trajectory of information retrieval and machine learning research.