In other words, MRR is the average of the reciprocal ranks of results for the questions in Q.
if the set of correct candidate answers for a question q j ∈ Q is {d 1 , d 2 , ..., d m j } and R jk is the set of ranked retrieval results from the top result until you get to the answer d k , then MAP is calculated as follows: When a relevant answer is not retrieved at all for a question, the precision value for that question in the above equation is taken to be 0.