RBF metamodels, which are commonly used in expensive optimization problems, rely on a hyperparameter which affects their prediction. The optimal hyperparameter value is typically unknown and hence needs to be estimated by additional procedures. As such this study examines if this overhead is justified from an overall search effectiveness perspective, namely, if changes in the hyperparameter yield significant performance differences. Analysis based on extensive numerical experiments shows that changes are significant in functions with low to moderate multimodality but are less significant in functions with highly multimodality.