### Multiple Presentations - Part 3

Continuing the series of analysis of the effect of multiple presentations of the same content on the likelihood of click.

## Exponential Decay

The curve of likelihood of click after the peak can be approximated by an exponential decay function. For example, the likelihood of click on the 19th presentation may be 93% the likelihood of the 18th presentation. We will model the beginning of the curve as a constant, ignoring for now the variation in particular for the first presentation. The result looks like this.

This is a very simple model that will work well in many situations. It is also technically simple as all the memory it requires is remembering the number of times the content has been presented to each specific visitor.

I believe this model will work when:

• The number of presentations of the same content tends to be high; higher than 5 on average.
• The time between presentations is not long; within the same session or at most a few hours in between presentations.
• The content is presented only in a specific channel and location

The model will not work when:

• The number of presentations for each content is small, but bigger than 1. In these cases the difference between the first presentation and subsequent ones can not be ignored.
• The time between presentations tends to be longer; a few days in between presentations for example. This time is long enough for the effect of previous presentations to wane, but not long enough for it to disappear completely.
• The content is presented in different channels or locations. For example if the visitor may be exposed to the same message in an email as well as the main banner of the home page, or different locations within the pages, or pages with significantly different other content.
• The same message is presented with similar contents, but perhaps not the same image dimensions and text

In order to cope with these shortcomings we need to use a model that will take into account the time between presentations and the impact each presentation has. The impact is affected by factors like the channel, location and visual characteristics of the content.

I like this approach. It's simple to implement, yet it seems to capture the essence of what goes on.

"In order to cope with these shortcomings we need to use a model that will take into account the time between presentations and the impact each presentation has."

You might want to apply a decay factor to the impressions themselves as well as to the effect of the number of impressions (e.g. an impression two weeks ago might only counted for half an impression in the decay function you suggest).

How should we determine which decay constant to use? This question becomes even more relevant when we start stacking these functions as I suggest, as the effect of using different decay constants becomes more pronounced.

Posted by Lukas Vermeer on January 03, 2012 at 08:12 PM PST #

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