Discounted cumulative gain

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Discounted Cumulative Gain is a measure for ranking quality and measures the usefulness (gain) of an item based on its relevance and position in the provided list. For comparing different lists of recommendations with various lengths, normalized Discounted Cumulative Gain or nDCG is used. It is based on dividing DCG by Ideal Discounted Cumulative Gain or IDCG. The more nDCG is, the better ranked list is provided.

Wikipedia: Discounted cumulative gain