Visual Analytics (VA) has become a paramount discipline in supporting data analysis in many scientific domains, empowering the human user with automatic capabilities while keeping the lead in the analysis. At the same time, designing an effective VA solution is not a simple task, requiring its adaptation to the problem at hand and the intended user of the system. In this scenario, the User-Centered Design (UCD) methodology provides the framework to incorporate user needs into the design of a VA solution. On the other hand, its implementation mainly relies on qualitative feedback, with the designer missing tools supporting her in quantitatively reporting the user feedback and using it to hypothesize and test the successive changes to the VA solution. To overcome this limitation, we propose TraVIS, a Visual Analytics solution allowing the loading of a web-based VA system, collecting user traces, and analyzing them with respect to the system at hand. In this process, the designer can leverage the collected traces and relate them to the tasks the VA solution supports and how those can be achieved. Using TraVIS, the designer can identify ineffective interaction paths, analyze the user traces support to task completion, hypothesize corrections to the design, and evaluate the effect of changes. We evaluated TraVIS through experimentation with 11 VA systems from literature, a use case, and user evaluation with five experts. Results show the benefits that TraVIS provides in terms of identifying design problems and efficient support for UCD.