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When an advertiser uses (say) 5 versions of an ad for a same landing page and same Adwords keyword group (keywords purchased on Google), how frequently should each of the 5 ads show up?

From Google's perspective, the optimum is achieved by the ad providing the highest revenue per impression, whether or not the advertiser is charged by impression (CPM model) or by the click (pay-per-click). For the advertiser, the ad commanding the lowest CPC is sometimes the optimum one, although it might generate too few clicks.

However, Google can not just simply show 100% of the time, the ad with the highest revenue per impression: this metric varies over time, and in two weeks the optimum ad could change, as users get bored seing the same ad all the time, or new keywords are purchased. So Google will show the 5 ads, semi-randomly: the optimum ad is displayed much more frequently, and the worst one very rarely.

But how do you define "much more frequently" and "very rarely"? Of course it depends on the impression to click ratio, multiplied by the CPC. Interestingly, it seems that Google has chosen a logarithm relationship between how frequently an ad is displayed, and its CTR (impression to click ratio). The CPC (cost per click) is ignored in Google's model, at least in this example.

What do you think about Google's choice of a logarithmic distribution?

Is it

  • arbitrary, 
  • coincidental (more tests would show that the relation I found is wrong and just happened by chance for this specific ad campaign), 
  • or the result of deep investigations by Google data scientists?

And why is the CPC decoupled? To avoid fraud and manipulations?

Anyway, here are my results, based on a sample ad campaign used to promote Data Science Central:

My test campaign, with 5 versions of a same ad. Source: Google Analytics.

Ad served proportionally to log(CTR). The Y axis is CTR

In the above chart (Y axis is CTR), the optimum ad is served 76.29% of the time, the second best one only 10.36% of the time, despite having both a similar CTR and similar CPC. The CPC is not taken into account, just the CTR: models involving CTR have a worse R^2 (goodness of fit). Models other than logarithmic have a worst R^2 than logarithmic.

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