The goal of this paper is to propose and evaluate the hypothesis that software cost estimates based on formal estimation models are frequently expert estimation in disguise, i.e., that the cost estimates are not as mechanically derived as prescribed and assumed. We test implications of the hypothesis through discussion of related work and an empirical study of function point-based effort estimation of software projects. The actual effort estimates of the projects were compared with the effort estimates one would expect if the formal function point model was applied as prescribed. We observed several large deviations between the actual and the mechanically derived effort estimates, which we interpret as indications of a strong impact from expert judgment. Important limitations of our study are that the hypothesis is formulated vaguely, that there is not much evidence available, and, that we may have had a tendency to bias our search towards supporting evidence. More studies are therefore needed, preferably from independent researchers. If our hypothesis is correct, implementation of formal software cost estimation models should include means to avoid unwanted effects of initial beliefs and irrelevant information.