Sample frameDay 323·Marketing · Decay

Morning. The campaign finished three weeks ago. Whether it stopped working is a different question.

Marketing.

The Advertising Half-Life

5 min read·Apply by lunch

The question

Think about the last time you went quiet — the campaign that ended, the month the budget got frozen, the quarter you spent rebuilding the website instead — and tell me how long it took before the effect had actually run out. You can't. Almost nobody can, and it's the number that decides whether a pause is a saving or a slow write-off.

The idea

Simon Broadbent was a British advertising analyst with a mathematician's habits, who spent much of his career in media research at Leo Burnett in London and helped establish the IPA's Advertising Works series. In 1979 he published a paper in the Journal of the Market Research Society called One Way TV Advertisements Work, and gave the industry a word it still uses every day: adstock. The idea is arithmetic rather than theory. Advertising doesn't land and vanish; it leaves a residue that carries into the following week and then decays by a fixed proportion at a time. So the pressure working on your market this week is this week's advertising plus a fraction of the stock left over from last week, and once you fit that to real sales data, the fraction is a number you can estimate. Out of it falls a half-life: the time it takes the effect of a burst to fall to half its peak. Those half-lives tend to be shorter than the people who commissioned the work would like — for fast-moving goods they're usually counted in weeks rather than quarters — and they differ by brand, by category and by medium. Which makes the half-life an operational figure, not an academic one. It tells you how long you can be silent before you're starting again from nothing.

The framework

01
How fast does yours decay — and has anyone ever checked?
The rate is estimated, not assumed. Put your spend and your sales side by side, week by week, and fit the carry-over; with two clean years an econometrician will do it properly for a modest fee. Without them, run the crude version. Find the last time your spend genuinely stopped, mark the level in the final week on, and read how many weeks it took to fall halfway from there back towards your old baseline. That halfway point is your first approximation — not the week the line finally flattens, which arrives several half-lives later and will flatter you badly if you use it.
02
One blended number hides the thing you need to see.
Day 48 already sorted your budget into work that buys a response now and work that builds memory later. Take that split as given, and notice what it does to this measurement: the two halves decay at very different rates, so one blended half-life for the whole budget averages them into a figure that describes neither. Fit the carry-over separately for each kind of work you actually run. The result is usually uncomfortable — the line producing every sale you can attribute leaves almost no residue behind it, and the residue you've been quietly crediting to it is coming from somewhere else on the sheet.
03
Price the silence before you approve it.
Once you have a rate, a gap becomes arithmetic instead of instinct. A three-week half-life means twelve weeks dark leaves you at roughly a sixteenth of your peak, and the next campaign opens by rebuilding something you have already paid for once. So write down the maximum number of weeks you'll let the brand go quiet, and write it before anybody proposes a freeze — then put the rebuild cost beside the saving every single time a pause comes up. A freeze that saves a month's budget and costs a quarter's rebuild isn't a saving. It's a transfer, with interest.
04
Two clocks, running at different speeds.
Adstock measures one thing: how a sales response fades once the advertising stops. Brand memory runs on a much slower clock, and a short measured half-life isn't evidence that advertising only ever works for a few weeks — it's evidence about the response you chose to model. Read the number for what it is. Use the fast clock for what it's genuinely good at, which is scheduling activity and pricing a gap, and don't let it answer the slower annual question of whether the memory you're paying to build is accumulating at all.

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