Why Impressions from the Ad Server Don't Match to C3?

C3 compares differently on display impressions to an Ad Server: it is apples and oranges.

Your ad server and network/DSP impressions are a metric of sell-side impressions.  A sell-side impression is when a call is made from a publisher to an Ad Serverfor an ad to be delivered.
Remember that the publisher's page is essentially on a server, and the consumer is at a location at work or at home.
The ad is "called" to be delivered...almost as if you called Domino's pizza by phone and ordered the pizza.  The pizza order is equivalent to the "impression."  It is simply the sell-side order.  The consumer hasn't yet gotten their pizza, and hasn't yet been delivered their ad.
C3 Metics, however, measures consumer-side impressions.  Very different from sell-side impressions which are simple "calls".  C3 Metrics is only concerned with the consumer side...and C3's impressions are deemed impressions when the ad fully loads in the consumer's browser.
Typically there is a 30% difference between the two...sometimes less (excluding Facebook).
The difference between a 30% difference between the two and a 10% difference is dependent on four things:  publisher page speed, the connection speed of the consumer, the consumer's behavior (how fast she clicks to a different page before the ad loads), and the speed and nature of the technology stack from the particular exchange the display unit was bought from (think about the old Right Media exchange versus a modern, fast PulsePoint exchange).
This is just the impressions--C3 obviously goes even deeper with is viewability technology.  The precursor to this is obviously the ad has to load in the consumer's browser first.

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