The best way to do that is to have some sort of survey that asks the question around whether they got what they needed, and what they would have done had they not gotten their question answered.
Without that data, you're mostly guessing. You could take a small percentage of page views and extrapolate them into cases deflected, but it's not going to be as accurate as a survey.
First you have to have the data, which generally comes from the Value Analytics survey (Admin > Features > Value Analytics). Then the formula is:
# respondents that indicated in Q1 that the nature of their visit was support
# respondents that answered Q2 as Yes (found what they needed)
# respondents that answered Q4 as "Contact Customer Support" would've been their next stop had they not found what they were looking for
Total Visits for the period you're measuring
= # cases deflected
So, it may look something like:
0.43% Seeking Support X 0.65% Resolution Rate X 0.09 Deflection Rate X 100,000 Visits in July = 2,515 Support Cases Deflected in July
I also recommend getting from your support team the number of cases that they handled in the period and creating a percentage of "Community-Solved Support". When you prepare reports or go to meetings you can say something along the lines of "Community is responsible for servicing 65% of our overall support volume." It's an easy message for most people to understand and drives home the value of community to the organization.
Obviously these numbers are an extrapolation based on a small data set, so be careful how you message it. It's a directional estimate.
Hope that helps 🙂
ROI is very subjective and there are other factors to consider that are dependent upon your community. For example, if your community is private to customers only, the examples so far are great. If it is a public community or private with a mix of customers and other users, things get more complicated. With a mix of users you hopefully have a way to identify who is a customer or not (assigned role for example) so you can narrow your reporting down to this group.
ROI formulas also vary based on who is providing them. Some like to include all community activity regardless of if it is a customer or not. Some include search activity as well as accepted solutions and solution views. Some give up to 30% or 40% weight to certain views while others drop as low as 10%. It is very subjective.
I tend to be more conservative and look at lower percentages of customer solution views, searches with results and TKB views while putting more weight on solutions accepted by a customer.
If you speak with your Khoros success manager, they should be able to provide some suggested formulas for calculating ROI that they have been well received by customers in their experience.