The tipping point: F-score as a function of the number of retrieved items

One of the best known measures of information retrieval (IR) performance is the F-score, the harmonic mean of precision and recall. In this article we show that the curve of the F-score as a function of the number of retrieved items is always of the same shape: a fast concave increase to a maximum, followed by a slow decrease. In other words, there exists a single maximum, referred to as the tipping point, where the retrieval situation is 'ideal' in terms of the F-score. The tipping point thus indicates the optimal number of items to be retrieved, with more or less items resulting in a lower F-score. This empirical result is found in IR and link prediction experiments and can be partially explained theoretically, expanding on earlier results by Egghe. We discuss the implications and argue that, when comparing F-scores, one should compare the F-score curves' tipping points.