When you implement a new process, tool, environment, etc. you generally want to know that you are making things better. How you measure success can be complicated and many times inaccurate. The success of a web self service site is largely impacted by the success of the search engine you choose to deploy.
Hopefully your main driver for building a web self help site was to provide faster more accurate and consistent solutions to your customers' issues. A side benefit of a good wed self help site is that many calls are deflected from the contact center agents. Although it may be obvious that case deflection is occurring, putting an exact number on deflection can be difficult and dangerous.
The below white paper gives you some insight as to how to measure the success of your search engine and how that relates to case deflection, if there is any relationship at all.
Measuring Search Success and Understanding Its Relationship to Call Deflection