I'm fascinated by statistics, and a lot of my work has revolved around trying to analyze and visualize online activity, whether it's Twitter conversations, email behavior or Facebook friendships. These have generated a lot of interest, but it's been hard to see how to convert that into enough revenue to create a real business.
The fundamental problem is that in most cases the statistics aren't solving a painful problem for anyone. We all love to look at ourselves in the mirror, and services that analyze our online behavior satisfy that craving, but there's seldom enough to justify a subscription or purchase. There's also the problem of driving repeat visits. Many meaningful statistics are very static, so the second visit to a site will often show exactly the same information as the first, discouraging continued engagement.
As a practical example, look at Xobni. I love what they're doing, and they initially launched with a lot of in-depth statistics about your email behavior, but in subsequent releases de-emphasized those in favor of productivity enhancements to Outlook. That's been successful for them and they're expanding back into analytics again, but it shows what a problematic driver statistics can be.
There is a tried-and-tested path to building a business around analytics though. I think of it as the Feedburner model, since they're the first company I encountered using it. They offered analytics as the carrot to give users a reason to sign up to the service, and then monetized by inserting ads into the RSS feeds they now controlled. I'm addicted to my Feedburner stats, but I'd never pay for them, so this was a great way of getting revenue out of a free service.
More generally it doesn't have to be ad-based, you just need a business model that benefits from access to a large audience of engaged users. Can you up-sell premium services that appeal to the same market? Can you get permission to pass their contact information to other companies they might be interested in, and get paid for sales leads? Is building an appealing analytics package just a good marketing investment, driving traffic to your site more cheaply than conventional advertising?
If you are interested in that approach, here's a couple of tips. First, try to show users something as soon as possible. In an ideal world they arrive at your page and immediately see a graph that tells them something interesting about themselves or something they relate too. Typically this isn't achievable, but at the very least have a single step where they enter an email address, twitter name, etc and then within a few seconds get some information. You should also show an example of what they will get on the landing page. These techniques reduced my bounce rate massively, never overestimate people's patience, you constantly need to be convincing them to spend time navigating your site.
The second key is presenting your statistics in an actionable way. If you can not only tell a user something interesting, but cause them to do something based on that information, then your chances of a repeat visit shoot way up. Feedburner has an 'Optimize' tab that guides you through ways of increasing your traffic. I found that changing from just showing your most-frequently-contacted friends to sending a report of the people you used to talk to and haven't for a while ('Losing touch report') and giving them a link to email each person alongside the list turned it from an 'oh, that's nice' to a must-have.
If you're as addicted to statistics as I am, but despairing about turning it into a business, it's worth thinking laterally. Analytics are a great carrot, can you use them to super-charge another business model?