I don't know of any modules that build this functionality inside Drupal itself. However, there are several tools out there, for which there are Drupal modules, that allow you to visualize the arc that you speak of. Two of my favorites are:
MixPanel: Mixpanel can allow you to create funnels that will help you see how the user is progressing through your website. For example, how many logged in users clicked on a product, how many of those went on to the payment page, and how many of those actually ending up paying. Mixpanel also has a Drupal module for easy integration. Or you could easily integrate this using a custom Mixpanel module with minimal effort. This is how a funnel in MixPanel would look like:
Google Analytics: It has a fantastic Visitors flow functionality that will allow you set flows, goals, and track against those too. Again, Google Analytics has a readymade Drupal module. Here's what a flow in GA would look like:
