MAP

Mean Average Precision (MAP)

MAP

MAP is the mean of the Average Precision (AP) scores across all queries. AP summarizes a precision-recall curve into a single number for a ranked list.

Average Precision

$\text{AP}=\frac{1}{|R|}{\sum }_{k=1}^{n}P(k)\cdot \text{rel}(k)$

where:

• $|R|$ — total number of relevant documents
• $P(k)$ — precision at position $k$
• $\text{rel}(k)$ — 1 if document at position $k$ is relevant, 0 otherwise
• Sum only over positions where a relevant document appears

MAP

$\text{MAP}=\frac{1}{|Q|}{\sum }_{j=1}^{|Q|}\text{AP}(q_j)$

What AP Captures

AP rewards placing relevant documents early in the ranking. A relevant document at position 1 contributes $P(1)=1.0$, while one at position 100 contributes much less. Unlike P@k, AP considers all relevant documents.

Appears In

• IR-L04 - Evaluation