Both queries have six unique IDs with fixed toy relevance grades. Query-specific judgments need not agree for an ID. Positive grades are binary relevant; nDCG uses gains 2ᵍʳᵃᵈᵉ−1 (grades 0,1,2,3 give gains 0,1,3,7), discounted by 1/log₂(rank+1). A grade is not a probability. There are no learned ranking scores or score ties: the manual order is strict. Moving one ID preserves all other relative order and every identity.

Precision@k=found/k. Recall@k=found/total relevant when the relevant count is positive, otherwise Undefined. DCG sums the top-k discounted gains; ideal DCG sorts every judged item by descending grade and then applies the same k and discounts. nDCG=DCG/ideal DCG when the ideal is positive, otherwise Undefined. Equal-grade ideal permutations give the same denominator. Different gain conventions give different values; for example, scikit-learn uses supplied true scores directly, rather than automatically applying this demo’s exponential gain.

MRR is the arithmetic mean of two full-list RR values. Each RR is 1/first relevant rank, or explicitly 0 if no relevant item exists. Empty queries remain in the mean. Skipping or scoring them differently would be another policy; undefined recall/nDCG does not imply perfect retrieval. Selected-query precision/recall/nDCG are not averages across queries. More results or a higher one-metric score does not establish overall task success.

Actual rank/k/scenario edits clear stale explanations; Query and Item to move only select evidence. Reset restores the current baseline, and free-exploration Reset starts Experiment 1. Native selects, number editors and sliders make every order reachable without dragging. This small evaluation demo excludes training, embeddings, ANN/indexing, unknown judgments, label editing, significance tests and production-quality claims. Compare only with the same query set, judgments, cutoff, gain/discount and aggregation conventions.