The balanced F measure (a. k.a. F1) is defined as the harmonic mean of precision and recall. What is the advantage of using the harmonic mean rather than "averaging" (using the arithmetic mean)?

Because the value derived from harmonic mean reflects the credible result of search engine

Explanation:

Given that the value of arithmetic mean tends to be closer to the highest value between Precision and Recall, while the value of the harmonic mean, is the lowest value between Precision and Recall, in a situation where all documents relevant to a query are returned, where R = 1 and P is closer to 0, the arithmetic mean will be greater than 0.5 and will not reflects the credible result of search engine

However, if the harmonic mean is utilized, the value will be closer to the low Precision value, hence it closely reflects the credible result of search engine