The formula for engagement: source
It's been years, and I still don't quite understand the obsession with measuring site engagement at any cost.
I'm puzzled by the stuff like "engagement is an estimate of the degree and depth of visitor interaction on the site against a clearly defined set of goals." My question is why. So, you do all the calculations and come up with a number, and what do you do next? Try to increase it? Why?
To me, the two metrics that ultimately matter are:
1. How many people performed a desired action (aka "conversion rate", which often implies but doesn't have to be sales or email sign-ups -- it can be any targeted action.)
2. How many people remember what I want them to remember for a certain period of time (aka "branding"). Under the current and mercilessly simplified ad theory, recall is influenced by frequency and length of exposure as well as the message's emotional impact. Designing for and measuring the emotional effect might still be more qual than quant, but frequency and length is pretty straightforward, especially online.
One definition of engagement this model fits is Innerscope's "engagement = attention * emotion", and I'm fine with that since here engagement is an indicator of recall and not an end in itself.