St. Patrick’s Day Math Lesson : My Other Favorite Italian Recipe

The art of telling a good story is a skill the Irish (myself included) really appreciate. Not to be lost for ‘tradition’ either, there’s plenty of Irish, and good stories, to go around. One of our favorite stories is that of the famous Deacon’s Son, St. Patrick. Also a fine and fitting topic to begin a small literary journey to describe complexity.

Legend says that St. Patrick brought Christianity to Ireland. It also indicates with quasi-historical context that he drove out all the snakes. Most importantly, and responsible for a greater and persistent fame, is that he used the simple leaflets of the Shamrock to describe what Catholics recognize as the ‘Holy Trinity’: a single, but triple-threat, deity of God the Father, God the Son, and God, the Holy Spirit.

A simple embodiment of that concept is an island thriving sprig of clover, which makes the story tangible, and therefore available to farmers and fisherman of Ireland – as well as the whiskey drinkers. Padraig (the Older Irish variation on his name) managed to take this concept and share it so broadly that Ireland became a fiercely Catholic territory adherent to its guidelines and the Roman Catholic Church for a few hundred years short of two millennia. At times, that deep rooted allegory of salvation became the means for other groups to develop hate and cruelty. My own family line, in fact, draws its entry to the US as a result of persecution, war, and exile (and slavery in Barbados) from Ireland for their Catholic loyalties in the 17th Century.

The goal here though isn’t to indulge in our own history, or even celebrate with the verdant variety of lilt and beer that makes the holiday so agreeable with a Friday. Instead, I’ve hooked you into something far more controversial. The reason I brought you to this article was to tell you that St. Patrick was actually the son of a Roman Deacon…which meant he was Italian. (More appropriately, he was Roman by today’s understanding of naturalization of foreign nationals – a relevant topic, but one for another time). As such has led me to believe this is true based on research, I find it appropriate then, to recognize Italian contributions to the world as part of this year’s imbibing for the holiday.

As the subject of my meditation today, I choose to share with you application of the Fibonnaci Numbers. While the snakes (or at least the vendors of their oils) and the uninspired might roll their eyes and/or mock this selection (on a shared work conference digital whiteboard) of subject matter…I ask you to bear with me, and see with me, how a 13th Century Italian mathematician is still impacting the world of technology, and for my company, the complex issues of ‘Omni-Channel Attribution’ and time series value decay.

In 2007 and 2008, after growing out of CableOrganizer.com, Decision Data developed a series of important analysis concepts which we worked and iterated on for years. Web Analytics, at the time and by its methods, had exposed that marketing spend was being misrepresented by reporting due to the reliance upon a ‘last click’ or ‘first click’ default assignment of revenue. We initially called this ‘cannibalization’ of value reporting. Over time, and through a series of agencies latching on to the concept, it became the amorphous concept of Multi-Channel Attribution…and, essentially its transcendent offspring – the ‘Omni-Channel Attribution’ marketing lightning-rod.

The challenge that comes with getting ‘Attribution’ right, or at least fair, is that there’s really no basis for a fair distribution of the value of an outcome across the variant and complex landscape of spend and source classification. Multiple major software companies were competing to develop a prefabricated report which would help simplify this. In that, they could manufacture and deliver an outcome to the company analyst that dealt with how to navigate the branches and costs in the network which leads to a sale or ‘conversion’. Enter, the Liber Abaci…a text shared in 1202 by Leonardo di Bonacci.

In the Liber Abaci, Fibonacci (a portmanteau of ‘figlio di Bonacci’ or son of Bonacci) advanced a solution to express and articulate, mathematically, the way in which rabbit populations propagate. This sequence of numbers which he wrote in the margins of the illuminated text above, outlines a scalable distribution base which has inspired us for nearly a decade of dealing with complexity in attribution, recency, valuation and at least a half-dozen other applications. It is, by all accounts, simple and brilliant sequence that allows us to understand how we can account for decay over time, and still promote the value of contribution…like a centrifuge, it layers the contributors and exposes them for the sum of their role.

For those who are unfamiliar, the Fibonacci numbers simply derive the value of the current position in the array from the sum of the values of two previous positions. To provide a starter reference, the sequence is 1,1,2,3,5,8,13….etc. What is it about this that’s remarkable? Why does this matter? Where does it apply to what we’re talking about?

Well, you see, distribution is about the parts of the whole. For the sake of simplicity, let’s illustrate the number of sequential number of unique instances of engagement with a brand as 5.

As an array, this looks like:

var myShamrock = [

0=>’Paid Search’,

1=>’Email’,

2=>’Social’,

3=>’Direct’,

4=>’Email’

];

This means that the ‘key’ in our array is the sequential visit number of the visit, and the value is the dimension across which the outcome should be distributed. In order to apply the calculation, we need to first determine the applicable value which a user generated by this recipe. Here, we can use $100 with little effort to play out this example.

The next step is to determine the position-governed denominator of the simple distribution equation. To do this, we need to evaluate the keys. If the MAX key position in the sessions is 4, we understand that this is position 5 in the array and so we can work by adding up sequential positions from the array. In Fibonacci Numbers, this is sum(1+1+2+3+5). The distributive whole needs to be cut into 12 predictable parts based on this method.

So far, our attribution equation is:

$100/12  or 12 equal parts of $8.3333…

In order to distribute these, with scale, predictability, and accounting for complexity – we then reintroduce the proportions determined by Fibonnaci’s propagation solution. (This is where you learn why I included ‘Email’ twice.) We multiply the sequence position analog (the Fib Number) by the equal part to re-distribute the value of the outcome across the variable dimensions in the object.

By that math, you should arrive as I have, at the following:

Channel             Attributed Value            Default Reporting Value

Paid Search        $  8.3333                         $      0.00

Email                  $ 50.0000                        $  100.00

Social                  $ 16.666                          $       0.00

Direct                 $ 25.0000                        $       0.00

Total:                               $ 100.00                          $   100.00

Comparing these side by side reveals that the main repeating variation on the channel is rewarded with a bulk, proportionate piece of the final outcome value. While this doesn’t perfectly account for every cent down to thousandth decimals and so on, this is still, in my opinion, a very elegant and graceful solution to a complex problem. As a result, what Fibonnaci has provided is a relatively simple method to scale and predict the value of the contributions of diverse and variable dimensions in a dynamic and complex environment.

Could it be that the 13th Century Italian mathematician Leonardo di Bonacci had discovered a way to scare all the snake oil out of 21st Century ‘Omni-Channel Attribution’?

As it stands, this also serves as notice that this method is part of our DubSaaS solution which is being distributed as part of our consulting and governance services engagements to clients.  Our testing and refinements on this have been great and continue while we iterate to a final software after thorough review. Since we’re happy with the results and heavily documented in our application, it seems pointless to keep a lid on this as some sort of ‘Secret Sauce’. We find it expressly valuable in exposing and advancing conversations with budget-minded marketers looking to really get a handle on their ROI/ROAS.

We’re sharing our method here since it would help many people really look closely at how they apply ‘Attribution’ math and to help them understand better how these approaches apply. If you’re interested in more about this, please contact us to have a conversation and see if these applications make sense for your analytics implementation, or your data/journey sciences project across channels or even IRL.

Happy St. Patrick’s Day to All My Irish AND Italian Friends!
Slainte’ & Saluti!

 

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