In 2010 Byron Sharp published buying-panel data that embarrassed half the marketing canon. This chapter is the physics lesson — what decades of purchase records say brands can and cannot do.
Here's the whole chapter in one line: brands grow by being easy to think of and easy to buy, for as many category buyers as possible — mostly the ones who barely think of you at all. Everything below is that sentence, backed by fifty years of purchase records.
For its first century, marketing ran on anecdote. Award reels, gut feel, the highest-paid person's favorite campaign story. Everyone had a theory about why brands grew; nobody had run the numbers, because there were no numbers to run.
Then came consumer panels: tens of thousands of households recording every purchase, week after week, for years. Andrew Ehrenberg — a statistician, not an ad man — got hold of them in the 1950s and did the unglamorous thing: he fit distributions. Panel data is the profiler you finally ran on marketing's hot loop. For decades everyone argued about where the time went. Now there was a flame graph.
What the profiler showed was offensive in its boredom. Buying behavior follows regularities — the same mathematical shape (a model called the NBD-Dirichlet) fits category after category, country after country, decade after decade. Colas, banks, detergents, gasoline: different products, same curves. These are laws in the physicist's sense — not deep truths about the soul, just patterns that keep showing up no matter who's looking.
Ehrenberg published for forty years and adland mostly shrugged. Then in 2010 Byron Sharp of the Ehrenberg-Bass Institute compressed the whole program into How Brands Grow — same math, ruthless prose — and it landed on the CMO shelf. Its sequel with Jenni Romaniuk extended the evidence to emerging markets, services, and luxury. P&G and Unilever rebuilt their media plans around it. The shrug became doctrine.
The first law out of the panels is the one with the courtroom name. Small brands get hit twice: fewer buyers, and those buyers are slightly less loyal — that's the whole scandal of double jeopardy. Not less loyal because small brands are worse. Less loyal because they're small.
Plot every brand in a category — penetration on one axis, loyalty (say, purchases per buyer per year) on the other — and the dots don't scatter. They hug a single rising curve. The big brand gets more buyers and a little more frequency; the small brand gets fewer of both. Every category reproduces the same picture.
The uncomfortable translation: loyalty is mostly a computed column, not an input. It's derived from size. Marketing departments keep hiring people to turn a dial that isn't wired to anything — you can't hold penetration fixed and crank loyalty, any more than you can raise a cache's hit rate while refusing to give it more entries.
Below is the scatter every category keeps reproducing. Try to build the brand every founder pitches — tiny but beloved — and watch where the data lets you actually stand.
Every marketing plan eventually rediscovers the same seductive idea: find your best customers and get more out of them. The 80/20 rule says 20% of buyers drive 80% of revenue — so aim everything at the 20%. There are two problems, and the panels expose both.
First, Pareto is real but mild. In actual purchase data the top 20% of a brand's buyers deliver around 50–60% of volume — not 80%. Which means the bottom 80% — the people who buy you once or twice a year and couldn't pick your logo out of a lineup — deliver the other half of your revenue. The customers you never think about are half your business.
Second, heavy buyers are already maxed out. Someone buying you every week has nowhere to go. Worse, this year's heavies are partly this year's lucky draws — next year they regress to the mean and buy less, through no failure of your marketing. Building a growth plan on heavy buyers is optimizing a function that's already at its ceiling while ignoring the enormous flat tail where all the headroom lives.
Here's the tail. Hover the bars, then try both strategies and watch where three years of effort actually compounds.
Put the two previous laws together and the arithmetic of growth only has one direction left. If loyalty is chained to size, and the heavies are at their ceiling, then brands grow by recruiting more buyers — overwhelmingly light ones — not by squeezing more out of the buyers they already have.
The panels confirm it with brutal consistency. Compare growing brands to shrinking ones and nearly the entire difference is how many people bought them at all. Purchase frequency barely moves. When a brand doubles, it doesn't have buyers buying twice as often; it has roughly twice as many buyers, most of them occasional. Growth looks like a wider, shallower pool — never a deeper puddle.
Which reframes two decades of loyalty-industrial complex. A loyalty program mostly pays people for behavior that was already going to happen: your heaviest buyers sign up first, collect points on purchases they'd have made anyway, and the incremental purchases are a rounding error. That can still be rational — as a pricing instrument, a selective discount to your base. It just isn't where growth comes from, and the budget line should say so.
One more law, and it's the one that quietly kills the tribal fantasy. The duplication of purchase law: your customers buy competing brands roughly in proportion to those competitors' market shares. Coke's buyers also buy Pepsi — a lot of them. Pepsi's buyers also buy Coke — even more of them, because Coke is bigger. Nobody's base is a walled garden.
Put differently: "Coke buyers" are mostly "cola buyers who buy Coke a bit more often." The brand doesn't own a tribe; it owns a slightly larger slice of everyone's repertoire. People keep a handful of acceptable brands per category and rotate through them with the enthusiasm of someone picking a parking spot.
Programmer's version: your customer base isn't a private table. It's a view over the whole category, weighted by share. Query "our customers" and "their customers" and you get almost the same rows with different weights. Any strategy that assumes your rows are a different species — different values, different psychology, a different "tribe" — is doing analytics on a join artifact.
So growth means recruiting light buyers you don't control, can't identify in advance, and who think about you almost never. What could possibly move that? The evidence keeps loading onto exactly two levers.
Mental availability: the probability you come to mind in a buying situation. This is Chapter 1's ladder, operationalized — not one rung in one list, but wiring to many situations. Thirst, road trip, guests coming over, 3pm slump: each cue is a separate retrieval path, and the brand that's linked to more of them gets "thought of" more often without anyone feeling persuaded.
Physical availability: the probability you can actually be bought when the situation fires. Distribution, shelf space, delivery coverage — and their digital descendants: search rank, app-store placement, being in stock, a checkout that doesn't fight back. Every step between impulse and receipt is physical availability, whether it happens in a store aisle or a tap target.
The crucial fact is that they multiply, not add. An occasion where you're remembered but not findable is lost. An occasion where you're stocked but unthought-of is lost. Nearly everything in marketing that measurably works — advertising, packaging, distribution deals, SEO — works because it loads one of these two levers. Slide them and watch the arithmetic.
Every doctrine deserves its stress test, and this one has real boundary conditions. Here's where it bends.
Subscriptions. The laws were minted on repertoire categories — many small, low-stakes purchases. A subscription is one decision that then repeats by default, so churn math gets real weight: a lost subscriber is a lost annuity, and retention work has direct, computable value. Penetration still rules acquisition, but the leaky bucket is no longer a footnote — it's a term in the equation.
Luxury. When scarcity is the product, mass penetration can dilute what you're selling. Yet even here the doctrine half-survives: luxury houses advertise far beyond the people who will ever buy, because a Birkin only works if the millions who can't afford one know exactly what it is. The audience is broad even when the customer list is short.
Durables and tiny B2B universes. Cars and CRMs sell on decade-long cycles to buyers who enter the market rarely — panels thin out, and when your total addressable market is 94 procurement teams, "penetration" needs air quotes. But the logic survives translation: reach everyone in the universe, stay remembered across the long silent gap.
And notice what the critics concede. Reach beats precision-targeting surprisingly often, even in performance-marketing's own attribution data. Distinctiveness compounds where clever repositioning decays. Going dark hurts on a lag. The boundary conditions adjust the coefficients; they haven't overturned a law yet.
The satisfying thing about laws is that they compile down to a to-do list. If the panel data is right, Monday looks like this:
One thread is left hanging. Mental availability means being retrieved from memory — but retrieved as what? Not as a positioning statement; nobody's brain stores your value proposition. What the mind actually keeps is embarrassingly concrete: a shade of orange, a bottle silhouette, three notes of a jingle, a lizard with an accent. Those assets are how reach becomes memory — and they're where we go next.