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Online advertising: mathematical formula to compute reach and frequency

How many Ad impressions should an advertiser purchase to achieve a specified reach on a website? We have investigated the problem and found a simple mathematical solution:

Online Advertising Mathematical Formula


  • Uk is the number of users visiting exactly k pages
  • P is the ratio of purchased impressions by total pages

The number of unique users who see the Ad n times is given by the formula

To make the computations, you first need to run a database query to find out the expected numbers of unique users visiting exactly k pages, for all values of k. for the campaign duration.  The formula relies on the distribution of pages per unique user during the targeted period of time. It helps determine the optimum number of ad impressions to purchase.

Tags: frequency, reach, recency

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I suspect the biggest problem with this is that the web is not a billboard, TV spot or Radio advert. These measures will inevitably be mis-used by marketing agencies more used to broadcast media.

TV adverts are interstitial - they are inserted not just between programs but within the program; the viewer is captive. Online interstitial adverts are currently mostly reviled by users, though I can identify several publishers trying to use them - and they are rare. I only know a handful of sites that I visit that offer interstitial adverts and I mostly avoid them (I either don't visit, or find the kill button as soon as I recognise what is happening).

For example, my most favoured dead-tree magazines are New Scientist, The Economist and Harvard Business Journal. I twitch every time I think about reading a New Scientist piece online because it will have a overlay advert that spoils uninterrupted reading of the article. What is my reach and frequency for these adverts? None. I only look at the advert to find the close button; I couldn't name the current advertiser(s) much less what they are showing. If the advert moves around above the text, which it does a lot now, I now kill the entire window as soon as I see motion. I can't be bothered to track down where the close button has been put, rather than have some hyperactive irrelevant advert fluttering and blinking above what I'm trying to focus on. I'll read the article offline rather than have my focus online spoiled by content-mismatched shrill jibbering by some attention starved product.

The nature of the web is fundamentally different. I don't think we have the right metrics yet. I'm pretty sure that Frequency and Reach aren't it. Why not? Lets take some specific examples:

Google AdSense (the publishing part of AdWords Content Network) allows multiple blocks per page. If any of the blocks are below the fold, then they stlll get counted as an impression. Even if the user never scrolls the block into view. It isn't a real impression unless it is in-stream. Even magazines offer a better placement strategy and recognisable metrics. Those "unviewed impressions" will be mixed in with top-of-page, below-the-headline adverts - clearly part of the visible space - but comparing user reaction to the two should be entirely different.

Jakob Nielsen (the usability guru of the Nielsen-Norman Group) has done extensive research into "banner blindness" - users don't even see site content if it has the same graphical dimensions as classical advertising slots. Users can train themselves to avoid seeing expected components and simply ignore expected advertising components.

Whereas intrusive advertising in a serial format exposes users to the advert and consequently frequency and reach are meaningful, online user behaviour is not passive but intentional, so the parallel and frequently irrelevant advertising requires that users learn to avoid seeing the adverts. A minority will even alter their online behaviour to avoid excessively intrusive advertising.

Part of the problem online is that the advertising networks have suborned the metrics and control, and tried to feed media planners the metrics they use for other media (the "your website is your online brochure" fallacy typically trotted out by print graphics guys who want to repurpose for online use). It has been next to nigh impossible to control bannering, or content match, because advertisers can't get per-user exposure figures and the publishers haven't made those details available.

But neither have they given access to the details like the position on the page, competition on the page and the other factors that would be known and recognised for broadcast media (e.g. you know that the TV spot will be surrounded by a limited number of other adverts; you may set controls on what other products you are shown with to avoid direct competition in a slot, etc).

Unless you can take meaningful management action, reach and frequency are sterile.
Could you use this formula in an example. I am very interested in determining online metrics, but I have minimal algebra experience. Thanks!


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