Precision and recall are single-value metrics based on the whole list of documents returned by the system. For systems that return a ranked sequence of documents, it is desirable to also consider the order in which the returned documents are presented. Average precision emphasizes ranking relevant documents higher. It is the average of precisions computed at the point of each of the relevant documents in the ranked sequence:

where r is the rank, N the number retrieved, rel() a binary function on the relevance of a given rank, and P(r) precision at a given cut-off rank:

This metric is also sometimes referred to geometrically as the area under the Precision-Recall curve.

Note that the denominator (number of relevant documents) is the number of relevant documents in the entire collection, so that the metric reflects performance over all relevant documents, regardless of a retrieval cutoff. See:.

^ Turpin, Andrew; Scholer, Falk (2006). "User performance versus precision measures for simple search tasks". Proceedings of the 29^th Annual international ACM SIGIR Conference on Research and Development in information Retrieval_r(Seattle, Washington, USA, August 06-11, 2006) (New York, NY: ACM): 11–18. doi:10.1145/1148170.1148176

MAP(Mean Average Precision)：?jiǎn)蝹€(gè)主題的平均準(zhǔn)確率是每篇相關(guān)文檔檢索出后的準(zhǔn)確率的平均值。主集合的平均準(zhǔn)確率(MAP)是每個(gè)主題的平均準(zhǔn)確率的平均值。 MAP 是反映系統(tǒng)在全部相關(guān)文檔上性能的單值指標(biāo)。系統(tǒng)檢索出來的相關(guān)文檔越靠前(rank 越高)，MAP就可能越高。如果系統(tǒng)沒有返回相關(guān)文檔，則準(zhǔn)確率默認(rèn)為0。
        例如：假設(shè)有兩個(gè)主題，主題1有4個(gè)相關(guān)網(wǎng)頁，主題2有5個(gè)相關(guān)網(wǎng)頁。某系統(tǒng)對(duì)于主題1檢索出4個(gè)相關(guān)網(wǎng)頁，其rank分別為1, 2, 4, 7；對(duì)于主題2檢索出3個(gè)相關(guān)網(wǎng)頁，其rank分別為1,3,5。對(duì)于主題1，平均準(zhǔn)確率為(1/1+2/2+3/4+4/7)/4=0.83。對(duì)于主題 2，平均準(zhǔn)確率為(1/1+2/3+3/5+0+0)/5=0.45。則MAP= (0.83+0.45)/2=0.64?！?/a>