How is NDCG@K built and what exactly does the normalisation buy?

DCG@K = Σ_{i=1..K} (2^rel_i − 1) / log2(i + 1): item gain is divided by the log of its position, so contribution decays with depth, while the exponent in the numerator sharply favours strong signals. IDCG@K is the same for the ideal ordering, and NDCG = DCG / IDCG. The normalisation exists so you can average across users with different numbers of relevant items: without it, a user with twenty purchases always out-scores one with two, and the mean measures audience activity rather than model quality. NDCG is the standard whenever relevance is graded.