Lesson 0002 · Relevance & Scoring

BM25 scoring

Where _score actually comes from — three intuitions, one formula, two knobs.

~10 minWarm-up + quiz + labCheat sheet: here

In Lesson 0001 you learned whether a clause is scored. Now: how. Since Elasticsearch 5.0, the default similarity is BM25 (“Best Match 25”), which replaced classic TF/IDF. — Connelly, Practical BM25 (Part 2) Don't memorize the formula cold — understand its three moving parts, and the formula reads itself.

Three intuitions

1 · Rare terms matter more — IDF

A match on elasticsearch tells you more than a match on the. Inverse Document Frequency weights each query term by how rare it is across the collection: the fewer documents contain a term, the higher its weight.

2 · Repetition helps — but with diminishing returns (TF saturation)

A document mentioning tuning five times is more about tuning than one mentioning it once — but not five times more. BM25 lets term frequency raise the score while saturating: each extra occurrence adds less than the last. This is the key thing BM25 fixed about raw TF/IDF, where frequency grew without limit.

3 · Short fields count more — length normalization

A term in a 4-word title is a stronger signal than the same term buried in a 900-word body. BM25 compares each field's length to the average length for that field and discounts longer-than-average fields.

The formula

Put the three together. For a query term t in document D:

Sum that over every query term to get the document's score. The pieces:

• f(t,D) — how many times t appears in the field (term frequency).
• |D| — the field's length in terms; avgdl — average field length across docs.
• IDF(t) = ln(1 + (N − n + 0.5) / (n + 0.5)), with N = total docs, n = docs containing t.

The two knobs

k1

Controls TF saturation. Default 1.2. Higher → frequency keeps mattering longer before it saturates; k1 = 0 → term frequency ignored entirely (presence/absence only).

b

Controls length normalization. Default 0.75, range 0–1. b = 0 → field length ignored; b = 1 → full normalization (long fields penalized hardest).

Defaults and tuning guidance: Connelly, Practical BM25 (Part 3) · Similarity settings

Interview-grade nuances

Check yourself

From memory — effortful recall is the point. Feedback is immediate.

Hands-on: watch BM25 explain itself

The _explain API prints the exact BM25 arithmetic for one document. Reuse the lab_articles index from Lesson 0001 (re-run its seed if you deleted it).

1 · Explain a single-occurrence match

GET /lab_articles/_explain/3
{ "query": { "match": { "title": "tuning" } } }   // doc 3: "postgres tuning"

In the response, find the idf and tf sub-explanations. You'll see the literal inputs: n (docs with "tuning"), N (total docs), freq, k1=1.2, b=0.75, and the field's avgdl.

2 · Compare a double-occurrence match — see saturation

GET /lab_articles/_explain/2
{ "query": { "match": { "title": "tuning" } } }   // doc 2: "...tuning tuning" (freq=2)

3 · Turn a knob and predict

PUT /lab_bm25_b0
{ "settings": { "index": { "similarity": {
  "default": { "type": "BM25", "b": 0 }            // length normalization OFF
}}}}

Re-index the same docs into lab_bm25_b0 and compare a query's scores against lab_articles. Predict first: which docs should rise when long-field penalty is removed? Then DELETE /lab_articles /lab_bm25_b0 to clean up, and bring any surprising numbers to your teacher.