Precision and Recall in Information Retrieval
Precision and recall are best known for their use in evaluating search engines and other information retrieval systems.
Search engines must index large numbers of documents, and display a small number of relevant results to a user on demand. It is important for the user experience to ensure that both all relevant results are identified, and that as few as possible irrelevant documents are displayed to the user. For this reason, precision and recall are the natural choice for quantifying the performance of a search engine, with some small modifications.
Over 90% of users do not look past the first page of results. This means that the results on the second and third pages are not very relevant for evaluating a search engine in practice. For this reason, rather than calculating the standard precision and recall, we often calculate the precision for the first 10 results and call this precision @ 10. This allows us to have a measure of the precision that is more relevant to the user experience, for a user who is unlikely to look past the first page. Generalizing this, the precision for the first k results is called the precision @ k.
In fact, search engine overall performance is often expressed as mean average precision, which is the average of precision @ k, for a number of k values, and for a large set of search queries. This allows an evaluation of the search precision taking into account a variety of different user queries, and the possibility of users remaining on the first results page, vs scrolling through to the subsequent results pages.