According to the recognition heuristic, people infer that an object they recognize has a higher value on a criterion of interest than an object they do not recognize. This model has been analyzed and conditions for the less-is-more effect- where recognizing fewer objects increases inferential accuracy have been derived. We extend previous studies by modelling this heuristic including the probabilistic recognition of objects and provide a number of results: First, we derive closed-form expressions for the parameters of the original model, in terms of the distributions of recognition and other cues over the objects. Second, we use the expressions to analyze the less-is-more effect. Third, we assume that the vectors of objects is random and use the expressions to calculate and compare the expected accuracy probability of success and derive the conditions under which the model equal or surpass the accuracy of random inference. Our results are general and can thus be linked to any model of recognition-based inference.