Ideal Discounted Cumulative Gain

$REL_p$ is the ordered list of the documents relevant to the query up to position $p$.
$REL_i$ is the ideal ranking, up to position $p$, that the algorithm/model should return.
nDCG values for all queries are averaged to obtain a performance measure for a search engine, ranking algorithm, or model.

$$ IDCG_p \overset{\text{def}}{=} \sum_{i=1}^{|REL_p|} \frac{2^{rel_i} - 1}{\log_2(i + 1)} $$