Symbol D
D is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Published equation contexts
Why this formula appears here
Lexical retrieval scores a document by how well its terms overlap the query’s terms, weighted by how rare each term is and normalised for document length. The canonical scoring function, still the default first-stage ranker across a large share of production search two decades after its formulation, is BM25: . Robertson and Zaragoza’s account of the probabilistic relevance framework behind this formula is worth reading past the equation for one design choice it exposes: the term-frequency component saturates rather than growing linearly, so a document repeating a query term fifty times is scored only marginally higher than one repeating it five times, and the…
Read the representative guide
Symbol Q
Q is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.
Read this term in its guide →Symbol i
i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol n
n appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Read this term in its guide →Symbol q_i
is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol f
f is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol k_1
is one of the signed contributions combined to compute the quantity on the left.
Read this term in its guide →Symbol b
b occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Read this term in its guide →Starting index or lower bound: i=1
This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.
Read this term in its guide →Ending index or upper bound: n
This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.
Read this term in its guide →Numerator: f(q_i, D)(k_1+1)
The complete quantity above the fraction bar.
Read this term in its guide →Denominator: f(q_i, D) + k_1(1 - b + bdfrac|D|avgdl)
The complete quantity below the fraction bar; it must be nonzero for this division.
Read this term in its guide →How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
Research cited beside this formula
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 1 · AI Agents & Systems
What Actually Happens Between a Query and an Answer in RAG
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
Lexical retrieval scores a document by how well its terms overlap the query’s terms, weighted by how rare each term is and normalised for document length. The canonical scoring function, still the default first-stage ranker across a large share of production search two decades after its formulation, is BM25: . Robertson and Zaragoza’s account of the probabilistic relevance framework behind this formula is worth reading past the equation for one design choice it exposes: the term-frequency component saturates rather than growing linearly, so a document repeating a query term fifty times is scored only marginally higher than one repeating it five times, and the…
Equation guide → · Article →