Calculate Normalized Discounted Cumulative Gain to evaluate ranking model quality.
NDCG measures ranking quality by comparing a predicted ranking's Discounted Cumulative Gain (DCG) against the ideal ranking (IDCG). DCG gives higher weight to relevant items appearing earlier in the ranking, using a logarithmic discount. NDCG = DCG / IDCG normalizes to [0, 1].
NDCG
NDCG = DCG / IDCG; DCG = sum((2^rel_i - 1) / log2(i + 2))
Users are much more likely to look at top-ranked results. The log discount reflects diminishing returns of later positions — a relevant result at position 1 is far more valuable than the same result at position 10.
NDCG is preferred when relevance is graded (not binary) and position matters. It captures both the relevance level and rank position, while precision@k only counts binary relevant/irrelevant.