Analytics Strategist

March 10, 2009

fairness is not the principle for optimization

In my other post, what you want may not be what you need, I wrote about the principle of optimization. Some follow up questions I got from people made me realize that I had not done a good job in explaining the point. I’d like to try again.

Correct attribution provides business a way to implement accountability. In marketing, correct attribution of sales and/or conversions presumably help us optimize the marketing spend. But how?  Here’s an example of what many people have in mind:  

    Suppose you have the following sale attributions to your four marketing channels:
             40% direct mail
             30% TV
             20% Paid Search
             10% Online Display
    then, you should allocate future budget to the four channels in proportion to the percentage they got.

This is intuitive, and perhaps what the fairness principle would do:  award according to contribution.  However, this is not the principle of optimization. Why?

Optimization is about maximization under constraints.  In case of budget optimization, you ask the question of how to distribute the last (or marginal) dollar more efficiently.  Your last dollar should be allocated to the channel with the highest marginal ROI.  In fact, this principle dictates that as long as there is difference in marginal ROI across channels you can always improve by moving dollars around.  Thus with true optimal allocation, the marginal ROI should be equalized across channels.

The 40% sale/conversion attribution to Direct Mail is used to calculate the average ROI.  In most DM programs, the early part of the dollar goes to the better names in the list, which tends to contribute to higher ROI; on the other hand, the fixed cost such as cost incurred for model development effort etc. will lower the ROI for the early part of the budget.  ROI and marginal ROI are variable functions of budget, and the marginal ROI in general is not equal to the average ROI.  There are different reasons for every channel with similar conclusion.  This is why those attribution percentages do not automatically tell us how to optimize. 

You may ask that, assuming all the marginal ROI are proportional to the average ROI, are we then justified to use of attribution percentages for budget allocations?  The answer is no.  If your assumption is right you should give all your dollars to one channel with the highest ROI, but not to all channels in proportion to the percentages.

This is an example of macro attribution. The same thinking applies to micro attribution as well.  Attribution is seen as linked to accountability and further more to operation and/or budget optimization.

We used an example of macro attribution to illustrate our point; same thinking applies to micro attribution as well.  Contrary to commonsense that regards attribution as the foundation for accountability and operation optimization, attribution percentages should not be used directly in optimization. The proportional rule or the principle of fairness is not the principle for optimization.

Advertisements

1 Comment »

  1. […] micro and macro attribution problems; there is also no discussion of the relationship between attribution and  optimization which has confused many researchers as well as […]

    Pingback by Media Mix Modeling, the new challenges « Analytics Strategist — March 16, 2009 @ 4:36 am


RSS feed for comments on this post. TrackBack URI

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Create a free website or blog at WordPress.com.

%d bloggers like this: