This paper presents a study based on the empirical results of the average first hitting time of Estimation of Distribution Algorithms. The algorithms are applied to one example of linear, pseudo-modular, and unimax functions. By means of this study, the paper also addresses recent issues in Estimation of Distribution Algorithms: (i) the relationship between the complexity of the probabilistic model used by the algorithm and its efficiency, and (ii) the matching between this model and the relationship among the variables of the objective function. After analysing the results, we conclude that the order of convergence is not related to the complexity of the probabilistic model, and that an algorithm whose probabilistic model mimics the structure of the objective function does not guarantee a low order of convergence.