Many visual representations, such as volume-rendered images and metro maps, feature a noticeable amount of information loss. At a glance, there seem to be numerous opportunities for viewers to misinterpret the data being visualized, hence undermining the benefits of these visual representations. In practice, there is little doubt that these visual representations are useful. The recently-proposed information-theoretic measure for analyzing the cost-benefit ratio of visualization processes can explain such usefulness experienced in practice, and postulate that the viewers' knowledge can reduce the potential distortion (e.g., misinterpretation) due to information loss. This suggests that viewers' knowledge can be estimated by comparing the potential distortion without any knowledge and the actual distortion with some knowledge. In this paper, we describe several case studies for collecting instances that can (i) support the evaluation of several candidate measures for estimating the potential distortion distortion in visualization, and (ii) demonstrate their applicability in practical scenarios. Because the theoretical discourse on choosing an appropriate bounded measure for estimating the potential distortion is yet conclusive, it is the real world data about visualization further informs the selection of a bounded measure, providing practical evidence to aid a theoretical conclusion. Meanwhile, once we can measure the potential distortion in a bounded manner, we can interpret the numerical values characterizing the benefit of visualization more intuitively.