The use of IR methodology in the evaluation of recommender systems has become common practice in recent years. IR metrics have been found however to be strongly biased towards rewarding algorithms that recommend popular items "the same bias that state of the art recommendation algorithms display. Recent research has confirmed and measured such biases, and proposed methods to avoid them. The fundamental question remains open though whether popularity is really a bias we should avoid or not; whether it could be a useful and reliable signal in recommendation, or it may be unfairly rewarded by the experimental biases. We address this question at a formal level by identifying and modeling the conditions that can determine the answer, in terms of dependencies between key random variables, involving item rating, discovery and relevance. We find conditions that guarantee popularity to be effective or quite the opposite, and for the measured metric values to reflect a true effectiveness, or qualitatively deviate from it. We exemplify and confirm the theoretical findings with empirical results. We build a crowdsourced dataset devoid of the usual biases displayed by common publicly available data, in which we illustrate contradictions between the accuracy that would be measured in a common biased offline experimental setting, and the actual accuracy that can be measured with unbiased observations.