BM25
In 1994 Stephen Robertson's group at City University, London, preparing its Okapi system for TREC-3, combined its two weighting functions BM11 and BM15 into one, BM25, in which a parameter b sets how far document length changes the contribution of term frequency. Run citya1 with this function headed the six best automatic ad hoc runs.
Why it matters
Term frequency in a document, document length and a term's rarity in the collection could be brought into one formula with two parameters that can be tuned and carried to another collection.
In the paper: the term frequency component tf(k1+1)/(K+tf), with K = k1((1-b) + b dl/avdl); b = 1 gives BM11, b = 0 gives BM15; 'values around 0.75 were usually used'. The official ad hoc runs were BM25(2.0;0.0;8;0.75), that is k1 = 2.0, not the often-quoted 1.2. Run citya1 on topics 151-200: average precision 0.401, precision at five documents 0.752, at thirty 0.617; without query expansion, 0.337. Queries were expanded by up to 40 terms (about 20 on average) from the top 30 documents. 33 groups took part in TREC-3, 14 companies and 19 universities. NIST's overview does not use the word BM25; only the group's paper names the formula. The proceedings number differs: the TREC-3 page says SP 500-226, the TREC-4 overview 500-225.