This post picks up where I left off on Starting the discussion: Attention, Engagement, Authority, Influence, … and is a follow on to Eric’s two parter (Measuring Engagement Online: The Next Stage and Measuring Online Engagement: Step One). Eric references me as “Mr. Carrabis” somewhere in there. Oh, he must think I’m ancient to call me “Mr.” I will be going through the rest of the comments people made to my original post and commenting on them there. It just takes me time (nobody noticed, I’m sure) because I tend to think things over a bit before responding to them.
And FYI, I’ll be posting elements of the equation’s derivation on BizMediaScience. I doubt anybody is sitting on the edge of their seat waiting to see what I integrate and if I use Tau or Gamma functions, so me thinks that’s best. I will be posting my thought process here, though, and welcome comment, suggestions and so on.
Form Follows Function
Right now the definitions of Engagement that I’m working with are Eric’s (Engagement is an estimate of the degree and depth of visitor interaction on the site against a clearly defined set of goals.), the one we use at NextStage (Engagement is the demonstration of Attention via psychomotor activity that serves to focus an individual’s Attention.) and the dictionary’s (participation, involvement, involution).
I’d love to hear anybody else’s definitions as I’ll work to incorporate them provided they adhere to the philosophy proposed in Starting the discussion: Attention, Engagement, Authority, Influence, …:
1. What do you mean when you use the words “engagement”, “attention”, and “trust” online?
2. Can you repeatedly measure what you mean by them so that there’s a reasonable surety that what you’re measuring is what you mean by the terms you’ve used?
3. Can you make these measurements through a commonly used web-enabled device?
Both Eric’s and NextStage’s definitions pass muster on item 1 above as both are declaratory statements. It’s also worth noting that both definitions contain the meanings of participation, involvement and involution in them as conceptualized in Eric Peterson’s Engagement Project and the Engagement Equation, Part 1. So far, we’re doing real good.
Item 3 above is a definer to our variable set — we are only allowed to use measurements that can be made through a commonly used web enabled device. Note that a “definer” isn’t something that sets limits. A limit would be something like “You can only use screen size and color depth”. The phrasing of item 3 is intentional. As technologies change so will the measurements that can be made through a “commonly used web enabled device”.
Item 3 is really our “looking forward” element. When web analytics started (and when NextStage started, for that matter) web enabled phones, pdas, iPhones, Smartphones, …, were unknown. Fortunately I’ve never let something’s lack of current existence deter me from anticipating it (if you’ve read our patent, you have an idea).
Item 3 covers our “extendable” and “extensable” concerns. It allows us to create a mathematical form that can alter its requirements as new capabilities and technologies come on line without sacrificing its ability to calculate and return real (business) value.
Likewise, with Items 1 and 3 covered, all that remains is to isolate a set of easily captured variables that satisfy the definitions in item 1. The equation — the mathematical form I’m using — allows for new variables and interfaces as they arrive. In other words, the final equation will be good now and way, way down the road. Again, this is something I learned from writing up NextStage’s patents; be as far thinking as possible.
There are other concerns and considerations that (by my nature) I’m putting into the mathematical form. For example, accuracy. Accuracy is a function of target size, not mathematical rigor. Accuracy of 10% with three variables active can quickly rise to 90% accuracy with as few as four or five variables active. Let me give you a “marketing” example. You’re selling to a) 53yo b) white c) males and you’re capturing 10% of that market. But what if you’re selling to a) 53 yo b) white c) males in d) NH with who e) are business travelers? Ah, well, now perhaps you’re capturing 90% of the market.
Some people aren’t aware that the opposite can also be true; it’s possible to achieve (for example) 90% accuracy with three variables and dwindle it to 10% when more variables are present. Imagine a bullseye style dartboard. You can get lots of darts in the yellow and good for you; that’s high accuracy. Then again, there are only five colors you can hit (five variables in the equation).
Now imagine a more traditional dartboard with a very small center area and lots of other areas indicating different values and multipliers. Both types of dartboards are circles, yet add or change a few variables and accuracy as a percentage of dead-centers is shot to heck.
Thus the mathematical form should allow for various degrees of accuracy based on what variables one is able to measure. This means that careful definition of the initial and possible variable sets is critical to the success of the metric as well as its accuracy.
Am I boring you yet?
Without driving you to drink, I chose to make the equation solvable by using three spaces, A, I and V. A is the set of all possible solutions of “engagement” (note that I’m not specifying “online”). I is the set of all possible interfaces that will ever exist (note that I’m not limiting this to “online” or even “machine”) and V is the set of all possible measurements that can be collected for a given interface I (note that I’m not limiting this to real-valued measurements). From here we can go through about two pages of finalized equations and whole lots more to get there.

Or I can show you the next to the last form in the derivation. The image above is important for lots of reasons. First, it’s really nothing more than a mathematical shorthand for Eric’s definition. But wait, there’s more!
It’s also a mathematical shorthand for NextStage’s definition. Also for the dictionary’s definition.
Are you excited yet? I love this stuff! And it gets better!
It’s also a mathematical shorthand for Eric’s definition blended with NextStage’s. Or for any group of definitions that follow Items 1, 2 and 3 above. If you can define the term (1) and can measure it repeatedly through a standard, commonly used interface whatever that may be now or in the future (3) then you get the formula above and it satisfies (2).
Want to know the best part? The formula above is also a mathematical form of SQL statements. You have some data hanging around somewhere and you want to create something you call “engagement” and you want to interrogate the data to create it? No probs. The formula above does the job. It doesn’t matter the size of the query result set nor the initial parameters.
Let me give you an example
Say you have some huge data set of N records and you’re really only interested in some portion of those records. That’s “N - n”. And you want to know how many visitors in this “N-n” group were “engaged” as you define it. That’s “hi(vi)” and is also where Eric’s definition, NextStage’s, Eric’s and NextStage’s, Eric’s with five parts of NextStage’s, two parts of somebody else’s, three parts of another person’s, …, goes. Now say of those “N - n” records you want some sequencing (maybe most “engaged” to least “engaged”, maybe something else). That’s “xi - ti“. And you want everything else constant, like geographic location and income level and who knows what else. That’s “D[hk(vk)]”. Not only can you hold things like geography, income, etc., constant, you can also hold other definitions of “engagement” constant while plucking out the one form you want for a given application or deliverable. And you only want “engagement” for a given interface (web as opposed to mall kiosk, etc). That’s “V” or “I” or “A”. The above basically reads as
SELECT “hi(vi)” AS “ENGAGEMENT”
FROM “N - n”
WHERE “D[hk(vk)]” = somevalue
AND “D[hj(vj)]” = someothervalue
AND …
GROUP BY “xi - ti”
ORDER BY “V” (or “I” or even “A”)
The “But”
The only caveat to the above is that each solution to A and I and V requires the interface to be monitoring a thinking being. I won’t even suggest “person”, but (there’s the “but”) you have to be evaluating “engagement” with something we can most easily define (but not limit ourselves to) as “a visitor”. This “but” has some teeth (and a good thing, too!). This means the only vi available — the measurements and metrics you use — have to be something “a visitor” would do, which means they have to be recordable by a standard interface (item 3 above).
Okay. I’m done for today. It’s taken me about two weeks to come up with a derivation (that’s all the pages I’m not showing you) that works for any definition of engagement on any interface that has any metrics that fits items 1-3 above. Soon I’ll start showing how Eric’s solution fits and what inferences can be drawn from it.
