Normalized Discounted Cumulative Gain (nDCG)

Normalized Discounted Cumulative Gain (nDCG) is the standard metric for evaluating ranked retrieval and recommendation when relevance comes in grades rather than a simple relevant/non-relevant binary. Introduced by Kalervo Järvelin and Jaana Kekäläinen in their 2002 ACM Transactions on Information Systems paper on cumulated gain-based evaluation, nDCG rewards a system for placing highly relevant documents near the top of the ranking. It accumulates the graded relevance ('gain') of each retrieved item, discounts that gain by how far down the list the item sits, and normalizes the total against the best possible ordering so that scores fall on a comparable 0-to-1 scale across queries. Because it handles multi-level relevance and is rank-sensitive, nDCG has become the dominant effectiveness measure for web search, learning-to-rank, and academic-search evaluation.