NDCG and Ranking Metrics

Ranking systems order candidates for a user or query. Evaluation should reflect where relevant results appear and how relevance is defined. Precision at k is the fraction of the top k results judged relevant. Recall at k is the fraction of all relevant candidates retrieved in the top k. Precision emphasizes the quality of the displayed set; recall emphasizes how much of the relevant set was found.

Average precision summarizes precision at ranks where relevant items occur, and mean average precision (MAP) averages that value across queries. Mean reciprocal rank (MRR) uses the reciprocal of the rank of the first relevant result and averages across queries. MRR is useful when finding one good result quickly is the priority, but it largely ignores the quality of later ranks.

Discounted cumulative gain (DCG) supports graded relevance. A gain function assigns larger value to more relevant items, while a logarithmic discount reduces credit for items lower in the list. Normalized DCG divides a ranking's DCG by the ideal DCG for that query, giving a score typically between zero and one when definitions align. This normalization makes values more comparable across queries with different relevance distributions, but aggregation choices still matter.

Suppose a query has one highly relevant item and another mildly relevant item. Placing the highly relevant result first yields more DCG than placing it second. NDCG captures both graded relevance and rank position. It does not establish whether the relevance labels are unbiased or whether the candidate-generation process omitted useful items. Metrics can change with cutoff k, gain formula and label threshold. Report these choices and evaluate across the same query set. Offline metrics also do not fully capture user satisfaction, diversity, freshness, exposure bias or long-term outcomes. Use them alongside online experiments or human review when appropriate, while avoiding claims that a higher score alone proves a better user experience.