I use Google Analytics a fair bit at work, and have been mulling over the question of how we can really define user engagement for ages. Today I found a rather good answer on Quora, funnily enough by one of their own Product Designers. My own answer typically is time spent on site, but I realise that isn’t good enough because you can have a page open and not really be interacting with it much; indeed you may be looking at another open tab. Whereas if you see multiple visits over a sustained period of time, that’s a much better indication of whether someone is really motivated to visit your site or not, and therefore engaged with it, even if he or she does not leave comments and so on.
If I had to live with just one user engagement metric, it would be Visitor Recency.
Visitor Recency measure how frequently your visitors return to your site. Specifically in Google Analytics, it looks at what percentage of your visitors come back each day, every other day, each week, etc. The reason I like this metric is that it’s crucial for building a meaningful web product, and it’s almost always a positive signal. If someone comes back to your site regularly each week, or even better each day, it means you’re becoming a regular and important part of their life. The problem with any other single metric is they can be the result of positive or negatives changes to your product:
Visits & pageviews are susceptible to all sorts of external factors, like SEO, SEM, press, seasonal traffic swings, etc. Bounce rate is dependent on the type of traffic you recruit, going up with things like SEO/SEM and down with directed traffic. Time On Site and Pages/Visit are good, but will oscillate with design changes, e.g. paginating long text articles will increase Pages/Visit without being any better for your site.
Ultimately the best indicator I’ve found of creating a truly great experience is whether people want to do it again. And again. And again and again as part of their daily routine. Visitor Recency is the best way to measure that.
*A number of caveats: Of course, to get a full idea of a site’s engagement you need a battery of metrics, not just one; My answer is for sites that don’t sell products, so I’m ignoring anything like “Conversion to Purchase”; I’ve restricted my set of choices to those available in Google Analytics, so as not to give some crazy, derived, business-specific metric, though that may be right for you…
As Joel Lewenstein points out, I’m not saying this one measure in Google Analytics is sufficient to track user engagement, but without getting into a complex equation, I think this is a good solution. I’m not the biggest fan of quantifying user engagement in terms of page views and unique visits due to the potential to skew results with SEO and the like, and this to me is a suitable middle path.
One Size Fits One 
Really like the point you’re making here. As you say, it’s often a mix of metrics that gives a properly rounded picture but I agree with the point being made here about visitor recency – too often in my experience the measures that are applied to understand ‘engagement’ (which is often poorly defined in itself) are blunt and one dimensional. Good post
Thanks for your comment Neil. After ages of agonising over how ‘engagement’ can really be measured, I think this really helps sort a bit of it. It’s always a mix of metrics that can give a comprehensive view, quite right!