Normalized Discounted Cumulative Gain

Definition

nDCG scores a ranked list by adding up the graded relevance of its results with lower positions discounted, then dividing by the best score possible for the same results. It runs from 0 to 1 and rewards putting the most relevant items first.

In plain terms

People read from the top, so a good result at position 1 is worth more than the same result at position 5. DCG captures that: each result’s grade is divided by log₂(position + 1). Dividing the total by the DCG of the ideal ordering of the same results gives a number between 0 and 1 that can be compared across queries.

It needs graded judgments (see Relevance Judgments) and a cutoff, such as the top 5 or 10; scores at different cutoffs are different measures.

Example

Five results for one query, with grades 0 to 3 (3 is best). Discounts at positions 1 to 5: 1, 0.63, 0.5, 0.43, 0.39.

The ideal order for these results is 3, 2, 1, 0, 0. Precision at 3 is identical for A and B, yet nDCG separates them clearly.

Common misunderstandings

• “nDCG of 0.8 means 80% of the results are right.” It is a position-weighted score of graded relevance, not a percentage correct.
• “Scores from different cutoffs or grading scales can be compared.” The cutoff and the gain scale are part of the definition.
• “It needs no human judgments.” It needs grades; they have to come from somewhere, usually people.