Normalized discounted cumulative gain

The discounted cumulative gain (DCG) accumulated at a particular rank position $p$ is defined as:

$\mathrm {DCG_{p}} =rel_{1}+\sum _{i=2}^{p}{\frac {rel_{i}}{\log _{2}i}}$

Normalized DCG (nDCG) is a way to calculate this measure across multiple queries, the results for which might all be of different length. nDCG is computed as:

$\mathrm {nDCG_{p}} ={\frac {DCG_{p}}{IDCG{p}}}$

The nDCG values for all queries can be averaged to obtain a measure of the average performance of a search engine's ranking algorithm.