Vague temporal adverbials, such as ”recently," "just" and ”long time ago,” describe the temporal distance between a past event and the utterance time, but leave the exact duration underspecified. In this paper, we introduce a factorized model that captures the semantics of these adverbials as probabilistic distributions. These distributions are composed with event-specific distributions to yield a contextualized meaning for an adverbial applied to a specific event. We fit the model's parameters using existing data capturing judgements of native speakers regarding the applicability of these vague temporal adverbials to events that took place a given time ago. Comparing our approach to a non-factorized model based on a single Gaussian distribution for each pair of event and temporal adverbial, we find out that, while both models have similar predictive power, our model is preferable in terms of Occam’s razor, as it is simpler and has a better extendability.