NDCG — Normalized Discounted Cumulative Gain

The gold-standard retrieval metric used by search engines and RAG evaluations. Rewards highly relevant results appearing at the top.

Formula

`DCG@K = Σ rel[i] / log₂(i+2)` (i is 0-indexed)

Where IDCG is the DCG of the ideal (perfectly sorted) ranking.

Example

# relevance scores: [3, 2, 3, 0, 1, 2]
ndcg([3,2,3,0,1,2], k=4)
# DCG = 3/log2(2) + 2/log2(3) + 3/log2(4) + 0/log2(5)
# IDCG = ideal DCG for sorted [3,3,2,2,1,0]
→ 0.78514

Round to **5 decimal places**.