Compare methods

	BM25 Probabilistic Ranking (Okapi)	Normalized Discounted Cumulative Gain (nDCG)
Field	Bibliometrics	Bibliometrics
Family	Process / pipeline	Process / pipeline
Year of origin	2009	2002
Originator	Stephen Robertson; Karen Spärck Jones; Hugo Zaragoza (Okapi team, City University London)	Kalervo Järvelin & Jaana Kekäläinen
Type	Probabilistic term-weighting and document-scoring pipeline for ranked retrieval	Graded-relevance ranking-evaluation pipeline with position discounting and normalization
Seminal source	Robertson, S., & Zaragoza, H. (2009). The Probabilistic Relevance Framework: BM25 and Beyond. Foundations and Trends in Information Retrieval, 3(4), 333-389.	Järvelin, K., & Kekäläinen, J. (2002). Cumulated gain-based evaluation of IR techniques. ACM Transactions on Information Systems, 20(4), 422-446.
Aliases	Okapi BM25, Best Matching 25, Probabilistic Relevance Ranking, BM25 Term Weighting	nDCG, Discounted Cumulative Gain, DCG/IDCG Normalization, Cumulated Gain Evaluation
Related	3	3
Summary	BM25, the Okapi 'Best Matching 25' function, is the dominant classical ranking function in information retrieval and the workhorse term-weighting scheme behind most lexical search engines and bibliographic databases. Developed by Stephen Robertson, Karen Spärck Jones and colleagues at City University London and formalized in Robertson and Zaragoza's 2009 monograph on the Probabilistic Relevance Framework, BM25 scores a document against a query as a sum, over query terms, of inverse-document-frequency weights multiplied by a saturating, length-normalized transform of within-document term frequency. Two free parameters control how quickly repeated terms stop adding evidence (k1) and how strongly document length is penalized (b). BM25 consistently outperformed plain TF-IDF in the TREC evaluations and remains the standard first-stage retrieval baseline against which modern neural rankers are measured.	Normalized Discounted Cumulative Gain (nDCG) is the standard metric for evaluating ranked retrieval and recommendation when relevance comes in grades rather than a simple relevant/non-relevant binary. Introduced by Kalervo Järvelin and Jaana Kekäläinen in their 2002 ACM Transactions on Information Systems paper on cumulated gain-based evaluation, nDCG rewards a system for placing highly relevant documents near the top of the ranking. It accumulates the graded relevance ('gain') of each retrieved item, discounts that gain by how far down the list the item sits, and normalizes the total against the best possible ordering so that scores fall on a comparable 0-to-1 scale across queries. Because it handles multi-level relevance and is rank-sensitive, nDCG has become the dominant effectiveness measure for web search, learning-to-rank, and academic-search evaluation.