A Reach/Frequency Model You Can Implement Yourself

A Reach/Frequency Model You Can Implement Yourself

Enquiring media planners might not happily accept reach/frequency (R/F) calculations without question and may be a little distrustful of arcane mathematical models.  So this paper explains and provides a set of easily understood equations that can be implemented in a spreadsheet program by anyone who wishes to better understand the inner workings of R/F models.

Some definitions are required because in my view the term Reach is widely misused.  In some media (e.g. Print, Radio, TV) it means people with one or more OPPORTUNITIES to see or hear your ad, while in other media (e.g. Out-Of-Home, where Probability of Seeing is applied) it means one or more IMPRESSIONS.  The word ‘reach’ clearly implies actual contact, so I think the latter definition makes more sense.

Terminology Definition


1+ Opportunities To See (OTS)

1+ Impressions (IMP)

In my terminology, Coverage is that part of a target population having one or more OTS over the time period under consideration, whereas Reach is that part having one or more Impressions.

This distinction between Coverage and Reach is important because we wish to know how many or what percentage of a target population we are actually delivering advertising messages to. Reach is calculated from Coverage, as we shall see.  But before getting to that, I set out a model of Coverage that can be implemented by proficient spreadsheet users.

As far as I’m aware, this is the first time this model has been documented as such.  But it isn’t really a different model in terms of the Coverages is produces because it exactly mirrors standard models for single media vehicles (given the same inputs, of course).  Multi-vehicle R/F will be discussed in a separate paper.


We start with measured Coverage, in particular the Coverage of 1 unit (C1) and the Coverage of 2 units (C2).  E.g. in the case of Print media, C1 is the measured average issue readership, while C2 is the unduplicated readership of 2 average issues.

For most other media, C1 and C2 are based on people with one or more OTS over whatever the measurement time unit may be.  Time units differ between media and between measurement systems around the world.  For TV it’s typically the average minute, while for Out-Of-Home it might be an average day.

From C1 and C2 we determine the rate at which Coverage increases as further units (i.e. ad insertions or time-periods) are put into the same media vehicle.  We are all familiar with the curve of diminishing returns, so of course we expect the new Coverage added by each successive unit to be less than that added by the previous one.  But how much less?

Suppose for a moment that everyone in a target population had the same OTS probability – i.e. there were no groups of light, medium and heavy consumers of the media vehicle.  In this unusual ‘independent’ case, the population probability of being covered by neither of 2 average units (i.e. 1 – C2) is equal to (1 – C1) squared.

Non-coverage of 2 units :

Transposing …

∴ Coverage added by 2nd unit …


Rearranging …

1 – C2 = (1 – C1)²

C2 = 1 – (1 – C1)²

C2 – C1

= 1 – (1 – C1)² – C1

= (1 – C1) – (1 – C1)²