Impressions, Reach and Frequency Are Three Numbers, and You Need All Three

One identity, and everything else follows from it

Frequency is not measured. It is calculated: frequency equals impressions divided by reach. That is a definition, not a finding, and it means the three numbers carry only two independent pieces of information. Give me impressions and reach and I can tell you the frequency without asking anyone anything. Give me impressions alone and I can tell you nothing at all about who saw the campaign or how often.

Two consequences fall out immediately. First, frequency can never be below 1 in a campaign that reached anybody, because every reached person received at least one impression — a reported average frequency of 0.8 is a measurement fault, not a thin campaign. Second, reach can never exceed impressions. If a platform reports more people reached than impressions served, the two numbers came from different measurement systems and should not be divided.

The identity also fixes what you are allowed to buy. You cannot independently order 1,000,000 people and an average frequency of 6 on 1,200,000 impressions; that arithmetic asks for 6,000,000 impressions. Media plans that state all three numbers should be checked with a division before anything else, because a plan that fails its own identity is a plan nobody costed.

One budget, five completely different campaigns

Fix the budget and let the identity do the work. Buy 1,200,000 impressions at an $8 CPM and you have spent $9,600 — that part is settled before any targeting decision. Now suppose the addressable audience is 1,200,000 people. Reach 1,000,000 of them and the average frequency is 1.20; reach 600,000 and it is 2.00; reach 400,000 and it is 3.00; reach 240,000 and it is 5.00; reach 100,000 and it is 12.00. Every one of those campaigns costs exactly $9,600 and delivers exactly 1,200,000 impressions.

The first of those is a launch: almost everyone who could see it sees it, most of them once. The last is a retargeting pool: one person in twelve of the audience, hit twelve times in the period. Anyone reporting only the impression total has reported the one number that is identical across all five. If a dashboard shows you impressions without reach, it has told you what you spent and nothing about what you bought.

The three-exposure rule is a 1970s heuristic, and it is contested

The rule has a source, which is more than most media folklore can say. Herbert Krugman, then at General Electric, published "Why Three Exposures May Be Enough" in the Journal of Advertising Research in 1972. His argument was psychological rather than statistical: the first exposure asks what this is, the second asks what of it, the third is where the viewer decides, and further exposures merely repeat the third. Michael Naples' 1979 monograph for the Advertising Research Foundation reviewed the literature around it and is the reason the idea entered media planning as a threshold.

What happened next is the part the rule's users tend to skip. From the mid-1990s a body of work argued the reverse: that response is strongest at the first exposure, that the planner's job is to be present near the purchase decision rather than to accumulate contacts, and that the same budget therefore buys more by maximising weekly reach at a frequency near one. Erwin Ephron's recency planning is the standard reference for that position, also published in the Journal of Advertising Research. Both camps have been arguing in the same journal for fifty years. Treating three exposures as settled fact misrepresents the state of the evidence.

Two response curves, two opposite plans, same money

The argument is settleable on paper, and doing so shows why it never settles in practice. Take the same 1,200,000 impressions and stipulate that every exposure is independent and converts a person with probability 0.25, so the chance of responding after f exposures is 1 minus 0.75 to the power f. At one exposure to 1,200,000 people, 0.250000 of them respond: 300,000 responses. At two exposures to 600,000 people, 0.437500 respond: 262,500. At three to 400,000, 0.578125: 231,250. At four to 300,000, 0.683594: 205,078. At six to 200,000, 0.822021: 164,404. Breadth wins every single time, and the widest possible plan wins outright.

Now stipulate the opposite shape — a threshold, where a single exposure does nothing at all and response only starts to build from the second. Put the response at 0 at one exposure, 0.15 at two, 0.35 at three, 0.45 at four and 0.55 at six. The same five plans now yield 0, then 90,000, then 140,000, then 135,000, then 110,000 responses. The optimum is three, and it is three because the curve was drawn with a threshold in it. Neither of these curves is data; both are assumptions I made up to make the arithmetic visible. The lesson is that the answer to "what frequency should I buy" is entirely determined by the response shape, which means it is an empirical question about your own campaign and cannot be imported from a monograph.

What a frequency cap actually does to your delivery

A cap does not reduce frequency for free. It converts frequency into reach, and it can only do that while there is unreached audience left to convert it into. When there is not, the cap converts your budget into undelivered impressions instead.

Change the audience to something narrower — a 250,000-person business segment — and keep the same 1,200,000-impression plan. Uncapped, you reach 200,000 of them at a frequency of 6.00 and spend the full $9,600. Set a cap of 6 and nothing changes; the cap is exactly non-binding. Set a cap of 4 and the segment can absorb at most 250,000 times 4 equals 1,000,000 impressions: 200,000 impressions, or 16.67% of the plan, have nowhere to go, and $1,600 goes unspent. A cap of 3 leaves 750,000 deliverable and strands 450,000 impressions, 37.50% of the plan and $3,600. A cap of 2 leaves 500,000 and strands 58.33%. A cap of 1 leaves 250,000 and strands 79.17% — $7,600 of a $9,600 budget with nowhere to spend it.

In practice the money does not sit still; the buying system spends it somewhere, which usually means widening the targeting or paying a higher price for scarcer inventory. Either way the cap has quietly rewritten the campaign. Before you set one, divide the impression plan by the cap and check that the result is smaller than the audience you actually have.

Reach is deduplicated inside a platform, never across them

Every platform tells you how many distinct people it reached, and every platform means distinct people it can identify. It has no idea whether the person it counted is the same person another platform counted. So reach numbers from two systems must never be added, and the error is not small.

Suppose platform A delivers 1,200,000 impressions to 400,000 people, a frequency of 3.00, and platform B delivers 600,000 impressions to 300,000 people, a frequency of 2.00, inside a shared universe of 1,000,000 people. If the two audiences are statistically independent, the expected overlap is 400,000 times 300,000 divided by 1,000,000, which is 120,000 people. The true combined reach is 400,000 plus 300,000 minus 120,000 equals 580,000, not 700,000. The naive sum overstates reach by 20.69%. And because frequency is impressions over reach, the true combined frequency is 1,800,000 divided by 580,000 equals 3.10, against the naive 2.57 — you are hitting a smaller group harder than the plan says.

Independence is the optimistic case. Audiences bought on the same interest signals correlate, and correlation makes the overlap larger. Push the overlap to 250,000 and the combined reach falls to 450,000 with a combined frequency of 4.00 — a third above the naive figure. If you need a real cross-platform reach number, it has to come from a single measurement system that sees both, such as a panel or a clean-room match, not from adding two dashboards.

Viewability changes what the word impression means

An impression as a billing event means the ad was served. An impression as a viewable impression means it had a chance to be seen. The Media Rating Council's guidelines define the second: for display advertising, at least 50% of the ad's pixels in the viewport for at least one continuous second; for video, at least 50% of pixels for at least two continuous seconds; and for large display units of 242,500 pixels or more, at least 30% of pixels for one continuous second. Those thresholds are deliberately low — they measure opportunity to see, not seeing.

The arithmetic consequence is that a viewable rate silently rewrites both of your other numbers. Suppose the measured viewable rate on the 1,200,000-impression plan is 62%. Then 744,000 impressions met the standard, and the $9,600 you spent works out at $12.90 per thousand viewable impressions rather than the $8.00 you thought you were paying — a 61.3% increase in the real price. Frequency moves too: at a reach of 200,000, the viewable frequency is 744,000 divided by 200,000, which is 3.72, not 6.00. If you were capping to control frequency, you were capping the wrong quantity.

Frequently asked questions

Can average frequency ever be less than 1?

No. Every person counted in reach received at least one impression, so impressions divided by reach is at least 1 by construction. A reported figure below 1 means the two numbers came from different measurement systems, different date ranges or different definitions of a person — for instance reach measured on logged-in users and impressions counted on all deliveries. Find the mismatch before you act on either number.

So should I target a frequency of 3 or not?

There is no answer that holds across campaigns, and anyone who gives you one without asking about your response curve is quoting a 1972 paper. Krugman's three-exposure argument and the Advertising Research Foundation's 1979 review are real sources, but so is the recency-planning literature that argues for maximising weekly reach at a frequency near one. Run the split yourself: hold the impression budget fixed, vary the reach, and measure the response. That is the only version of the question your own campaign can answer.

Can I add reach across two ad platforms?

No, because each platform deduplicates only the people it can identify itself. In the worked example — 400,000 reached on one platform, 300,000 on another, inside a universe of 1,000,000 — statistical independence already gives 120,000 people in both, so the true combined reach is 580,000 and the naive sum of 700,000 overstates it by 20.69%. Correlated targeting makes the overlap larger still. A cross-platform reach figure has to come from one system that observes both.

What does a cap of 3 per week cost me at a fixed budget?

Nothing, if your audience is at least as big as the impression plan divided by 3. Something, otherwise. A 1,200,000-impression plan capped at 3 needs 400,000 people to absorb it; against a 250,000-person segment only 750,000 impressions can be delivered, so 37.50% of the plan and $3,600 of a $9,600 budget have nowhere to go. At a cap of 2 that rises to 58.33%, and at a cap of 1 to 79.17%. Do the division before you set the cap.

Should I plan on served impressions or viewable ones?

Plan on whichever you are billed for, and report both. The Media Rating Council's threshold for display is 50% of pixels for one continuous second, which is an opportunity to see rather than a view. If a 1,200,000-impression plan costing $9,600 measures 62% viewable, the real price is $12.90 per thousand viewable impressions instead of $8.00, and the viewable frequency at a reach of 200,000 is 3.72 rather than 6.00. Both numbers describe the same campaign; only one of them describes ads that had a chance.