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spring-ai/hybrid-search/output/01-rrf-by-hand.txt
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# Reciprocal Rank Fusion on two short rankings
vector ranking : [A, B, C, D]
keyword ranking: [C, A, E, B]
--- k = 1 ---
A score 0.83333 (vector rank 1, keyword rank 2)
C score 0.75000 (vector rank 3, keyword rank 1)
B score 0.53333 (vector rank 2, keyword rank 4)
E score 0.25000 (vector rank 0, keyword rank 3)
D score 0.20000 (vector rank 4, keyword rank 0)
--- k = 60 ---
A score 0.03252 (vector rank 1, keyword rank 2)
C score 0.03227 (vector rank 3, keyword rank 1)
B score 0.03175 (vector rank 2, keyword rank 4)
E score 0.01587 (vector rank 0, keyword rank 3)
D score 0.01563 (vector rank 4, keyword rank 0)
--- k = 1000 ---
A score 0.00200 (vector rank 1, keyword rank 2)
C score 0.00200 (vector rank 3, keyword rank 1)
B score 0.00199 (vector rank 2, keyword rank 4)
E score 0.00100 (vector rank 0, keyword rank 3)
D score 0.00100 (vector rank 4, keyword rank 0)
--- the arithmetic for A at k = 60 ---
rank 1 in the vector list: 1/(60+1) = 0.01639
rank 2 in the keyword list: 1/(60+2) = 0.01613
sum = 0.03252
--- an item in one list only ---
E is rank 3 in the keyword list and absent from the vector list: 1/(60+3) = 0.01587
D is rank 4 in the vector list and absent from the keyword list: 1/(60+4) = 0.01563