Model complexity is a critical consideration when evaluating a statistical model. To quantify complexity, one can examine fitting propensity (FP), or the ability of the model to fit well to diverse patterns of data. The scant foundational research on FP has focused primarily on proof of concept rather than practical application. To address this oversight, the present work joins a recently published study in examining the FP of models that are commonly applied in factor analysis. We begin with a historical account of statistical model evaluation, which refutes the notion that complexity can be fully understood by counting the number of free parameters in the model. We then present three sets of analytic examples to better understand the FP of exploratory and confirmatory factor analysis models that are widely used in applied research. We characterize our findings relative to previously disseminated claims about factor model FP. Finally, we provide some recommendations for future research on FP in latent variable modeling. [This is the online first version of an article published in "Psychological Methods" (ISSN 1082-989X).]