Reach and frequency: the trade-off inside every media budget

Reach and frequency describe how a campaign’s impressions are spread across people: reach is how many unique people in your audience saw the ad at least once, and frequency is how many times, on average, each of those people saw it. Multiply them and you get impressions, which means that on a fixed budget every extra exposure you give one person is an exposure you didn’t give someone new.

That trade-off sits inside every media plan, whether anyone names it or not. From running a growth agency that spent over $10 million a year on Facebook ads, I’d say frequency is one of the first numbers worth checking on a tired campaign, because it rises quietly as an audience gets used up. The more interesting question, and the one a marketing mix model can help with, is whether the next million impressions would do more good on the people you’ve already reached or on people you haven’t. I’ll start with the arithmetic and where the three-exposure rule came from, then show how to work out the frequency that maximizes total response.

Reach, frequency and impressions: the arithmetic

The relationship is simple when everyone agrees on the definitions:

One million impressions can be 500,000 people seeing the ad twice, or 100,000 people seeing it ten times. TV planners have long expressed the same thing in gross rating points (GRPs), where reach is a percentage of the target audience and GRPs are reach percentage times average frequency, so a schedule of 300 GRPs might be 60 percent reach at an average frequency of five. Digital platforms report reach and frequency per campaign, usually over a chosen date range.

There are two traps in those numbers. Reach reported separately by each platform isn’t deduplicated: someone who saw your YouTube ad and your Meta ad is counted once in each, so adding platform reach figures together overstates how many people you reached. And average frequency hides the distribution. A campaign with an average frequency of four almost never means everyone saw it four times; some people saw it once and a few saw it fifteen times, and the widget below shows how wide that spread is even when delivery is random.

Where effective frequency came from

The idea that there’s a minimum number of exposures before an ad works is usually traced to Herbert Krugman, a researcher at General Electric, who argued in a 1972 talk at an Association of National Advertisers (ANA) workshop that three exposures might be the basic minimum; the written version is usually cited as “Why Three Exposures May Be Enough”, in the Journal of Advertising Research the same year. His reasoning was psychological rather than statistical. The first exposure prompts a “what is it?” reaction, the second a more personal “what of it?” evaluation, and the third works as a reminder, with later exposures behaving like repeats of the third. Krugman later reinterpreted some of that data himself in a 2000 paper in the same journal.

The idea became industry doctrine through Michael Naples, director of marketing research at Lever Brothers, whose 1979 book Effective Frequency reviewed the studies available for the ANA. Its conclusions are more nuanced than the “three hits” rule they’re remembered for:

• One exposure within a purchase cycle has little or no effect in all but a minority of circumstances.
• Two exposures within a purchase cycle is an effective level, and it was often hard to distinguish the response at two exposures from three.
• Three exposures within a purchase cycle (or a four-week period) is the lowest level that can offer peak response.
• Beyond three, increasing frequency continues to build effectiveness at a decreasing rate, with no evidence of a decline.
• Wear-out is mainly a copy or campaign problem rather than a function of frequency itself, although too much frequency can be inefficient.
• Large, dominant brands respond differently to frequency from smaller brands, and each brand needs its own experimentation to find the right answer.

That last point tends to get lost. The book was explicit that these were generalizations about the average brand in the studies it covered, mostly TV-era packaged goods, and that research could answer the question for any specific brand. That’s still the right attitude: it’s better to treat “three” as a hypothesis about your own per-person response curve, which modern tools let you estimate rather than inherit.

Reach curves: why the next impression reaches fewer new people

As a campaign buys more impressions, reach grows more slowly than impressions because more of the new impressions land on people who’ve already seen the ad. That relationship is the reach curve, and it’s itself a saturation curve. Jin et al. (2017), in Google’s paper on Bayesian MMM, cite an earlier Google formulation by Jin, Shobowale, Koehler and Case (2012) that describes reach $R$ as a function of GRPs $G$:

That’s the same shape as a Michaelis-Menten curve, which you’ll recognize from the saturation curves page. A simpler approximation, and the one the widget below uses, assumes impressions land at random across the people you target. If $\lambda$ is the number of impressions per targeted person, the share reached at least once is $1 - e^{-\lambda}$ and the average frequency among those reached is $\lambda / (1 - e^{-\lambda})$. Real delivery is lumpier than random (heavy users of a platform see more ads), which is why planners often use a negative binomial distribution instead, but the Poisson version gets the direction right and keeps the arithmetic transparent.

The practical consequence is that a broad audience has a minimum achievable frequency. If you buy two impressions per person in your audience, random delivery reaches about 86 percent of them at an average frequency of about 2.3; you can’t buy two impressions per person and have everyone see exactly two. To push frequency lower you’d need more audience, and to push it higher you need to concentrate delivery on fewer people, with tighter targeting, a smaller audience or a longer flight on the same group.

Finding the frequency that maximizes total response

For a budget decision, the trade-off works like this. Extra exposures may make each reached person more likely to respond, but with a fixed number of impressions, higher average frequency means fewer people reached. The course lesson on reach and frequency puts it in a phrase I like: a person-level gain can hide a campaign-level loss. Total response depends on both terms, so you need a per-person response curve and a reach calculation together to see which way it goes.

The widget lets you set a budget and CPM, which fixes impressions, then choose an average frequency and a per-person response curve. It works out reach from the impressions, the share of reached people at each exposure count, and the total responses, and then scans frequencies from 1 to 20 to find the peak.

With the default S-shaped curve (half the maximum response at four exposures), the peak lands around three to four. That follows from the default curve I typed in, so it says nothing about whether Krugman was right, and the course lesson is careful to say the same about its own invented curve. Drag the shape below 1 and the curve becomes concave from the first exposure, and the best plan becomes maximum reach at the lowest frequency the audience allows. Raise the half-response point and the peak moves right. The answer is only as good as the per-person curve, which is exactly the part most media plans assume rather than measure.

Frequency caps and what they protect

A frequency cap limits how many times one person can be served an ad in a period, for example three times a week, and most programmatic, video and social platforms let you set one. In the terms of the widget, a cap trims the long tail of the exposure distribution, which protects reach (the impressions that would have gone to the fifteenth exposure go to someone new instead) and reduces the share of budget spent on people who are past the flat part of their response curve.

The cost is that a tight cap can stop a campaign from spending its budget, or push the platform into more expensive inventory to find new people, which shows up as a higher CPM. It can also hold everyone below an effective level if your product genuinely needs several exposures. In my experience the useful way to set a cap is the same as for any other parameter: start from a hypothesis about the per-person curve, then test two caps against each other in an incrementality test or a conversion lift study rather than picking the number that looks tidiest.

How Meridian models reach and frequency

Most MMMs only see a channel’s spend or impressions, which treats a million impressions as a million impressions no matter how they were spread. Google’s Meridian can do better for channels where you provide reach and average frequency for each geo and time period (YouTube data is available through Google’s MMM data platform). Reach here is the number of unique people exposed within each period, not cumulative reach, and frequency is impressions divided by that reach. For those channels the media effect is:

In words, Meridian puts frequency through a Hill curve, multiplies by reach and then applies adstock for carryover. The Hill curve on frequency is what allows response per person to be S-shaped, so that there can be an optimal frequency, with too little frequency failing to build recall and too much causing ad fatigue. Reach, by contrast, is assumed to have a linear effect at a fixed frequency, so each additional person reached adds the same amount. The documentation notes that this is a reasonable approximation as long as the channel isn’t reaching people well beyond its target audience, and warns against extrapolating that linear effect far outside the reach values observed in the data.

Meridian then solves for an optimal frequency for each reach and frequency channel, constrained to one value across all geos and time periods (since a frequency that changes by region and week isn’t practical to buy), and by default uses it in budget optimization; you can switch to historical frequency instead with the use_optimal_frequency setting. One consequence worth knowing is that a channel’s reported ROI reflects the frequency it actually ran at, while the optimizer assumes future campaigns run at the optimal frequency, so the two can disagree, especially when historical frequency was far from optimal. If your buying team can’t actually deliver the optimal frequency for a channel, it’s worth running the optimizer on historical frequency for that channel instead.

What to ask before you trust a frequency recommendation

A frequency recommendation is a claim about a per-person response curve and about the reach you’ll give up, so both halves need evidence. These are the questions I’d ask:

• Is reach deduplicated across platforms, or are platform reach figures being added together?
• What does the exposure distribution look like, not just the average frequency?
• Where does the per-person response curve come from: a model, a test, or an assumption like 'three'?
• Does the recommended frequency hold the impression total fixed, and how much reach does it give up?
• Is the recommendation inside the range of reach and frequency the channel has actually run at?
• Can the buying team deliver that frequency, and what happens to CPM if they cap or narrow the audience?
• Has a test compared two frequencies (or two caps) at the same spend?

Reach and frequency also feeds straight into budget allocation: a channel’s response curve to spend is, underneath, a reach curve combined with a frequency response, which is part of why returns diminish. The Vexpower MMM course has a lab on this trade-off in its invented Northstar case, using its own S-shaped frequency curve, if you want to practise reading it alongside the rest of a model.