Most of information retrieval effectiveness evaluation metrics assume that systems appending irrelevant documents at the bottom of the ranking are as effective as (or not worse than) systems that have a stopping criteria to ’truncate’ the ranking at the right position to avoid retrieving those irrelevant documents at the end. It can be argued, however, that such truncated rankings are more useful to the end user. It is thus important to understand how to measure retrieval effectiveness in this scenario. In this paper we provide both theoretical and experimental contributions. We first define formal properties to analyze how effectiveness metrics behave when evaluating truncated rankings. Our theoretical analysis shows that de-facto standard metrics do not satisfy desirable properties to evaluate truncated rankings: only Observational Information Effectiveness (OIE) – a metric based on Shannon’s information theory – satisfies them all. We then perform experiments to compare several metrics on nine TREC datasets. According to our experimental results, the most appropriate metrics for truncated rankings are OIE and a novel extension of Rank-Biased Precision that adds a user effort factor penalizing the retrieval of irrelevant documents.