Recall-precision trade-off: A derivation

The inexact nature of document retrieval gives rise to a fundamental recall precision trade-off: generally, recall improves at the expense of precision, or precision improves at the expense of recall. This trade-off is borne out empirically and has qualitatively intuitive explanations. In this article, we explore this relationship mathematically to explain it further. We see that the recall-precision trade-off hinges on a deceleration in the proportion of relevant documents which are retrieved, successively, over time. Further, we examine several mathematical functions sharing this property and conclude that the equation that best models recall as a function of time is the logarithm of a quadratic function. Our conclusion meets the following requirements: the function we derive predicts non-decreasing recall over time until the last relevant document is retrieved (regardless of the density of relevant documents in the collection) without imposing any artificial restrictions on either what percentage of the collection would need to be examined to achieve perfect recall or what the level of precision would be at that time. Other models examined fail to meet one or more of these criteria. © 1989 John Wiley & Sons, Inc.