The diverse and vibrant ecosystem of interactive visualizations on the web presents an opportunity for researchers and practitioners to observe and analyze how everyday people interact with data visualizations. However, existing metrics of visualization interaction behavior used in research do not fully reveal the breadth of peoples' open-ended explorations with visualizations. One possible way to address this challenge is to determine high-level goals for visualization interaction metrics, and infer corresponding features from user interaction data that characterize different aspects of peoples' explorations of visualizations. In this paper, we identify needs for visualization behavior measurement, and develop corresponding candidate features that can be inferred from users' interaction data. We then propose metrics that capture novel aspects of peoples' open-ended explorations, including exploration uniqueness and exploration pacing. We evaluate these metrics along with four other metrics recently proposed in visualization literature by applying them to interaction data from prior visualization studies. The results of these evaluations suggest that these new metrics 1) reveal new characteristics of peoples' use of visualizations, 2) can be used to evaluate statistical differences between visualization designs, and 3) are statistically independent of prior metrics used in visualization research. We discuss implications of these results for future studies, including the potential for applying these metrics in visualization interaction analysis, as well as emerging challenges in developing and selecting metrics depicting visualization explorations.