What is BM25 (Best Matching 25) Algorithm

BM25 (Best Matching 25) is a ranking algorithm used in information retrieval systems to determine how relevant a document is to a given search query. It’s an improved version of the traditional TF-IDF (Term Frequency–Inverse Document Frequency) approach and is widely used in modern search engines and databases.

• It measures term frequency and document relevance more accurately.
• It accounts for document length normalization, giving fair weight to all documents.
• It is widely used in tools like Elasticsearch, Whoosh and Lucene.
• It helps to deliver more relevant search results based on keyword matching and context.

In simple terms, BM25 helps rank documents or web pages based on how well they match a user’s search terms making it a cornerstone of effective search and retrieval systems.

Working of BM25

BM25 computes a relevance score between a query q and a document d using three main components: Term Frequency (TF), Inverse Document Frequency (IDF) and Document Length Normalization.

1. Term Frequency (TF)

Term frequency measures how often a query term appears in a document. Intuitively, a document containing a query term multiple times is more likely to be relevant. However, BM25 introduces a saturation effect i.e beyond a certain point, additional occurrences of a term contribute less to the score. This prevents overly long documents from being unfairly favored.

Mathematically, the term frequency component is normalized using the formula:

TF(t,d)=\frac{freq(t,d)}{freq(t,d) + k_1 . (1-b+b.\frac{|d|}{\text{avgdl}})}

where:

• t: Query term
• d: Document
• freq(t,d): Number of times term t appears in document d
• ∣d∣: Length of document d
• \text{avgdl}: average document length in corpus
• k_1​: controls term frequency scaling
• b: controls document length normalization

2. Inverse Document Frequency (IDF)

Inverse document frequency measures the importance of a term across the entire corpus. Rare terms are considered more informative than common ones. For example, the word "the" appears in almost every document and thus carries little value, whereas a rare term like "quantum" is more indicative of relevance.

The IDF component is calculated as:

IDF(t)=log(\frac{N-n_t+0.5}{n_t+0.5})

where:

• N: Total number of documents in the corpus
• n_t: Number of documents containing term t

3. Document Length Normalization

BM25 accounts for document length by normalizing scores to prevent longer documents from dominating the rankings. This is controlled by the parameter b which adjusts the influence of document length relative to the average document length (\text{avgdl}).

4. Final Score Calculation

The final BM25 score for a document d with respect to a query q is computed as:

Score(q,d) = \sum_{t\epsilon q}IDF(t).TF(t,d)

This sums up the contributions of all query terms t in the document d.

BM25 vs. Modern Dense Retrieval

Let's see the comparison between BM25 and Modern Dense Retrieval.

Applications

• Web search engines or open­source infrastructures such as Apache Lucene or Elasticsearch use it for initial document ranking.
• Enterprise search systems, for retrieving documents across internal corpora (intranets, knowledge bases).
• E-commerce search & recommendation uses it for matching product descriptions or search queries to products.
• Often used for first‐stage candidate retrieval before applying more expensive processing. This is widely used in question-answering system or information-retrieval pipelines

Advantages

• Robust and reliable: Works well across many datasets and retrieval tasks.
• Efficient and scalable: Computationally simpler than many neural retrieval methods making it practical for large‐scale search.
• Tunable: k1​ and b parameters allow adaptation to domain or document‐type characteristics.
• Interpretable: Because it is based on well‐understood statistical components, it is easier to debug and understand compared to many “black-box” models.

Limitations

• Lexical only: It matches terms, not concepts so synonyms, paraphrases, semantic relatedness are not captured.
• No user personalization or context awareness: The model does not incorporate user signals, query history or implicit context by default.
• Corpus characteristics matter: The effect of document length, term distribution and corpus size can influence performance significantly.
• Does not use dense embeddings: Cannot capture more abstract semantic relationships the way embedding‐based/dense retrieval methods can.