Calculating Behaviors on your site

I recently came across a press release from Revenue Science claiming that they now reach 1 Billion behaviors per day. http://www.revenuescience.com/site/media/press-releases/2006/20061107.asp. So what is this all about? In my opinion Behavioral Targeting (or any kind of targeting) is about reaching users/visitors /customers not behaviors.
Anyway, even if they are reporting their reach in terms of numbers of behaviors, then how are they counting behaviors? The way I think of behaviors, Revenue Science is underreporting reporting the number of behaviors they reach everyday, it has to be way more than 1 Billion. Let me show you how a single visitor can exhibit over a Billion behaviors.

What is an online behavior?

Every single action that a user takes on the site determines user’s behavior. Following are some of the different elements that determine the behaviors of users online

1. Every page view
2. Number of minutes on a page
3. Path taken
4. Links/Ads clicked
5. Scrolling on the page
6. Referring Sites
7. Each second in the visit
8. Each visit
9. Total Visits
10. Total Page views
11. each Product viewed
12. Each cart abandoned
13. Each step of the funnel completed/abandoned
and the list goes on…...

Let’s take a site with 30 pages. A single user visits all 30 pages. So how many behaviors has this user exhibited? According to my calculation, way over 1 Billion.

How do you calculate online behaviors? (I am only going to count pages viewed to count behaviors)

Each page view by itself is a unique behavior; so this user has exhibited 30 behaviors by viewing all 30 pages.
Combination of pages 1 and 2 is a unique behavior too, that is one more behavior, so total is now 31.
Every combination of these 30 pages will be a unique behavior exhibited by this user.
So how many combinations of 30 pages exist? I am not going to go into details of calculus but show you the formulas here

ⁿC_k = The number of combinations of n things taken k at a time
The sum of all the combinations of n distinct things is 2ⁿ.
ⁿC₀ + ⁿC₁ + ⁿC₂ + . . . + ⁿC_n = 2ⁿ


We won’t count any combination with 0 page views (i.e. the user never showed up on the site) so in our example above
ⁿC₁ + ⁿC₂ + . . . + ⁿC_n = 2ⁿ - ⁿC₀
i.e.ⁿC₁ + ⁿC₂ + . . . + ⁿC_n = 2ⁿ - 1

So, combinations of 30 different page views (behaviors) = 2³⁰ - 1
That comes to 1, 073, 741, 823 Behaviors. That comes to 1, 073, 741, 823 Behaviors. (http://www.google.com/search?hl=en&lr=&q=2**30+-1&btnG=Search)

Yes over a billion behaviors exhibited by 1 user viewing 30 pages.

If I take various other elements that define behavior (see above) than you don’t even need 30 pages to reach 1 Billion behaviors.

Conclusion
Behaviors motivate but people read your content and buy your products. In my opinion, it is not about how many behaviors a BT vendor can reach, it is about how many customers they can reach.