The Adoption Curve: How New Products Spread

An adoption curve is the S shape made by a running count of the buyers who have taken something up, plotted against time. Everett M. Rogers set out that shape and its five adopter categories in 1962. Drawing one for a real product needs a defined population of possible adopters and a date of adoption for each. Neither is available in these notes, and a single buyer with a duration beside it is not a path.

What is this curve actually a curve of?

There are two S shaped curves in these notes, and a reader holding the wrong one will be wrong about everything that follows. So start with the thing being counted. The adoption curve counts buyers who have adopted, added up as it goes, against time. The other curve counts sellers in a field, asks how fast they are arriving and which way capacity and price are moving, and is set out under The Industry Life Cycle: Emergence to Decline.

Two curves of the same shape count two different populations, one of sellers and one of buyers, and the two shapes have two different authors. The pair of populations is worth reading twice. Nothing about the drawings themselves distinguishes one from the other. Both rise slowly, then quickly, then slowly. Both are usually drawn left to right with no numbers on either axis. Placed side by side with the labels taken off, no living person could separate them.

The shape, the five positions along it and the count of what anybody would need before drawing one can all be set out without a single number. Three restraints do that work. A percentage under any of the five names, a line fitted through points, and a value read off a point sitting to the right of the last thing somebody actually observed would each add a figure that measured nothing. The three restraints are not decoration on the lesson. The restraints are the lesson, and the working that earns them follows.

What sits on each axis, and why does the line bend?

The vertical axis is a running total of the buyers who have taken the thing up. Nothing is taken back out of a running total once it has gone in, so the total only ever rises. A buyer who adopted last year is still counted this year whether or not they are still buying. The persistence is a property of the counting rather than a claim about loyalty. The horizontal axis is time, and in this guide it carries no unit at all: no year, no quarter, no month.

Now watch the bend appear out of nothing more exotic than the counting. Early on, few members of the group have taken the thing up, so there are few of them to tell anybody about it, and the total climbs slowly. In the middle, many have taken it up and many are still left, so there are plenty of people doing the telling and plenty of people to tell, and the total climbs quickly. Late on, almost nobody is left who has not already adopted, so the total climbs slowly again however hard anybody pushes.

Slow, then fast, then slow is an S, and it falls out of a running total inside a fixed group rather than out of any claim about products. Counting alone is why the shape turns up everywhere, and turning up everywhere makes it weaker rather than stronger as evidence about anything in particular.

Here is the version anybody can stand in front of. Ten shops share one small mall. A new kind of painted sign appears, and the count is how many of the ten have put one up. In the first months one shop does it, then a second. Everybody can see the first two and everybody still has a bare shopfront, so four go up in a season. Then the last two take a year between them, with only two left to convince. The count went one, two, six, eight, ten. The count rose slowly, then quickly, then slowly, and the only reason it had a top at all is that the mall carries ten shops and there is no eleventh.

With the ceiling taken away the shape changes, and this is where the missing half of the measurement lives. If there were no fixed group, the count would have nothing to run out of. The middle phase would simply carry on. Flattening at the top means running short of people left to add, and nothing can run short of an unbounded supply, so there would be no flattening at all.

The upper flattening exists only because there is a ceiling, so the number of possible adoptersEverybody who could take the thing up, counted once each, whether or not they ever do. It is the number the curve is climbing towards, and nobody here publishes it. is not a detail of the measurement but the half of the shape that makes it an S rather than a line going up. The ceiling is where everything difficult begins. The bottom half of the S needs only a count of adopters over time. The top half needs the total. And the total is the one thing nobody ever writes down.

Where does the shape come from, and whose is it?

Everett M. Rogers set the shape out, together with the five adopter categories, in Diffusion of Innovations in 1962. He was writing about how new things spread through a population, gathering studies of how ideas and practices travelled, and the curve is the picture that came out of that work. Anybody who hands over an adoption curve is handing over Rogers whether or not they know it, so the name belongs in the body rather than in a list at the bottom. Knowing whose frame the work sits inside is part of using it carefully.

Then the part that costs something. Rogers is named here for the frame and for no figure at all. A book is not a source for a number, and the figures usually printed under the five category names are figures out of a book. The figures describe what he was writing about. The figures are not a measurement of any product an analyst will ever look at, and repeating them would print a number that measured nothing. Printing a number that measures nothing is the exact failure at issue.

Borrowing a frame without borrowing its numbers is not a special caution. Two other borrowed frames sit in the same position. One is a shape drawn over a field of sellers, borrowed by name from the man who published it and used for no figure. Another is a pair of nineteenth century conventions for splitting a movement into terms, borrowed by name and used for no figure. Attribution travels with an idea; measurement does not, and the second half of that rule is the one people forget.

What are the five names, and are they types of people?

Five of them, and the order is the whole content of the classification, so they are worth naming in Rogers's own order. Innovators, the ones who took it up before there was anything to point at. Early adopters, the ones who took it up on the strength of somebody visible having done so. Early majority, the ones who waited until it had become normal. Late majority, the ones who waited until it had become settled. Laggards, the ones who moved last, or who never moved at all.

Read those five again and notice what each name is a statement about. Every one of them is a statement about when somebody bought. Not about how curious they are, not about how careful they are, not about how much money they carry. A shop that put the sign up first is a shop that put the sign up first. The five names are positions in an order of arrival, and a position in an order of arrival is a fact about a date rather than a description of a person.

No percentage sits under any of the five, and the reason is worth saying in the open rather than leaving as a gap. The percentages under the five names are the most memorised thing about this curve. The figures arrive fluently, they feel like part of the definition, and they come from a book. A figure needs a source that measured something, and a book about how ideas travel is not a measurement of the group under examination.

Consider five neighbours and one new bus route. One of them rode it in the first week, two rode it once the first one said it was quicker, one waited until the stop had a proper shelter, and one still walks. Five neighbours in that order are five positions in an order of arrival, and the order is a complete and honest description of what happened. Nobody became a different kind of person by catching a bus early, and asking all five again about something else entirely could produce a completely different order.

What is needed before one can be drawn?

Three things, and the rest of the walkthrough runs on them, so the count is worth setting out carefully.

One, a defined population of possible adopters. Somebody has to draw a boundary and say who is inside it before a single thing gets counted. Every school in one district. Every shop in one mall. Every household on one street. Without that line there is no denominator, and without a denominator there is no ceiling, and without a ceiling there is no top half to the shape.

Two, a date of adoption for each member who has adopted. Not a count of them. A date against each one. The curve is a sequence of levels with dates attached, and a level with no date on it cannot be placed anywhere along the horizontal axis.

Three, at least two observations. One level gives no direction at all. And a shape with a bend in it wants rather more than two. A straight line already needs two, and a bend has strictly more to establish than a straight line does.

The first requirement is a boundary decision and the other two are gathering jobs, so the curve stops before it starts if nobody drew the line. That ordering matters more than it looks. Gathering jobs can be attacked with effort: more phone calls, more visits, more patience. A boundary decision cannot be attacked with effort at all. No amount of working harder settles who should have been inside the line.

What do these notes actually hold?

An honest count is the only arithmetic this guide does for itself. Adoption events with a duration attached, anywhere in these notes: exactly one. The Sunrise Public School group has bought for eleven years from Anjani Stationers Private Limited, an invented stationer. Populations of possible adopters, published anywhere for either invented business or for any product: none. Second observations of any adoption count, at any date: none.

One buyer on one date is not a path. The single buyer is a hard case to accept when the one fact in hand is a good one, honestly gathered, and eleven years is a genuinely long relationship worth knowing about. The eleven years establish that a particular school group has bought for a long time. The eleven years establish nothing whatever about the order in which anybody else arrived, or whether anybody else arrived at all.

An earlier ruling on a different quantity transfers here without a single word being changed. Under the other S shape, the question was whether the price of paper had a direction. The evidence was one weighted average of Rs 210.00/- a reamThe bundle a paper mill prices and bills in. It is made up by counting sheets rather than by putting them on a scale. in one year, a level and not a direction. One point is not a path. Change the quantity from a price to an adoption date and every word of that still stands. The eleven year relationship is therefore the second quantity in these notes to fail the same test. Two quantities failing one test is a rule rather than a coincidence.

The weighted averageAn average in which the bigger contributions count for more than the smaller ones, rather than every reading counting the same. How one gets built is worked separately in these notes. is quoted here for its ruling and never as a price for anything in this guide, and the eleven years is being put to a use it has not been put to before. The eleven years have already carried three different jobs elsewhere in these notes, none of them about adoption, so the job being done here gets named every time the figure appears. The duration is the single dated adoption event these notes carry, and it is the reason the panel below opens where it opens.

Which counts in these notes look like candidates, and why does each one fail?

A reader who has followed this far will already be reaching for something to put on the vertical axis. Every candidate will occur to somebody, so work through them one at a time and skip none.

Setu Bazaar, an invented marketplace, carries 50,000 buyers. The figure is published, and it is the largest population of buyers anywhere in these notes. The figure is also a count at one moment. No date of arrival is attached to any of those buyers, and nothing anywhere states who could have joined the marketplaceA place where many sellers and many buyers meet and deal with each other, with the place itself taking a slice of what passes through rather than selling the goods. and did not. So it is a level, and no curve has ever started from one.

The same marketplace carries 2,000 merchants. The merchant count is the same problem on the selling side, and these notes have already ruled on it: a count of sellers at one moment is not a rate of entryHow many sellers arrived in one period set against how many arrived in the period before. It takes two observations, and it belongs to the other S shape in these notes rather than to this one., no matter how big that count is or how carefully somebody took it.

Anjani Stationers carries 36 accountsA named buyer on a seller's books, with its own record of what it bought and what it still owes. A count of them says how many names there are and nothing about when each arrived. that bought in the year. The 36 are a list at one year end. Exactly one of them carries a date, being 2.78 per cent of the accounts and every single one of the dated ones. And the eleven years themselves are one duration attached to that one buyer.

Size was never the missing thing and dates were, so the largest population in these notes still cannot start this curve. A reader who decides the problem is that these businesses are small will go looking for a bigger one, find a population of millions, and hit precisely the same wall. A million undated names are exactly as useless for this purpose as fifty thousand undated names.

How is this different from the other S shape in these notes?

One clause will not hold this separation, so it gets a block of its own. The other curve counts sellers in a field over time. The seller curve asks for three things: how quickly sellers are turning up, the direction capacityHow much a seller could turn out with everything running as intended, measured in units of the thing rather than in rupees. Putting more of it in is a decision taken well before anybody buys the extra. is moving, and which way the price of the thing is moving. The seller curve names four stages, and it belongs to Theodore Levitt, who wrote about it in the Harvard Business Review in 1965.

The adoption curve counts buyers who have adopted. The adoption curve asks for two things: a population and a set of dates. The five positions along it make an order of arrival, and the curve belongs to Everett M. Rogers, who wrote about it in 1962. Same shape, different population, different author, and nothing on one of them can be read off the other.

A warning is easy to nod at and forget, so make the confusion concrete instead. A field can be filling up with new sellers arriving every year while almost nobody anywhere has taken the product up: plenty of stalls and almost no customers, a real and quite common thing to be standing in front of. And a field can be down to one surviving seller while every buyer in it adopted years ago and simply carries on buying. The two curves can point in opposite directions at the same moment. Two readings that disagree are the clearest possible evidence that the curves are two different measurements rather than two views of one thing.

Why does a bend invite a formula, and what does supplying one do?

Pretending the temptation is not there teaches nobody anything, so say it plainly. A curve with a known shape and a few points on it looks like an arithmetic problem, and the arithmetic genuinely works. A shape can be run through a set of points, and once it has been, it will return a value for any date at all, including dates nobody has seen and dates that have not happened yet. Nothing breaks. No warning appears. A clean number comes out.

A shape run through points returns a clean answer for any set of points and for any date, so the answer establishes nothing about whether the points were enough. The output does not carry a record of how thin its input was. The missing record is the property to hold on to, and the panel above demonstrates it: moving the number of points shows that the region past the last one never narrows, however many are fed in.

Then the specific refusal, narrower and harder than the general caution. There are no adoption points anywhere in these notes to run a shape through. Not few. None. So nothing turns on whether a shape would be run well or badly, and nothing turns on method at all. There is nothing to run one through.

The barred constructions are worth naming in the open. No shape is drawn through any set of points. No quantity is carried that could be adjusted to make a shape sit better against anything. No share of the people who could plausibly take the thing up is worked out. Such a share needs the denominator this whole walkthrough has been about. And no sentence is written whose truth depends on a period nobody has observed.

The last of those is the test worth carrying away, a single question that can be asked of any sentence in any document. Is there a period nobody has lived through yet that this sentence needs before it can be true? A description does not. A conditional does not either. A conditional says what would follow from a movement without claiming the movement happens. A projection does, and the moment a sentence needs next year to be true, it has stopped describing and started predicting.

What is the curve worth when it cannot be drawn?

There is still a use for the shape, and it is a genuinely good one. A shape with no numbers on it still fixes the order in which to ask, and the order is the part most people get wrong.

The shape says there is an order of arrival. So ask who arrived first, and what those buyers had in common. Who arrived first is a question with an answer somebody can actually go and get, and the answer is often the most useful sentence in a note.

The shape says there is a ceiling. So ask who could adopt and has not. The ceiling question does something no figure would have done: it drags the missing boundary into the open, and nobody can answer it without saying who they take to be inside the line. A room that cannot agree on the answer has just discovered that it never had a population. Knowing that is worth more than anything anybody could have built on top of a population nobody had.

The shape says the middle is the steep part. Visibility is what the middle of the shape is made of, so ask whether anybody visible has moved. Not a rate, not a projection. Just whether the sort of buyer other buyers watch has moved yet.

Then the honest output, copying a device these notes already use rather than inventing one. The card gets written. The card carries what is known about the one buyer that can be named. The population row stays visibly blank. The dates row carries exactly one entry. A card whose denominator row stays empty and whose dates row carries one line is finished work. The finding is the empty row itself rather than something dropped into it. Somebody reading it a year later knows exactly which row to go and fill, and a confident curve would not have told them that much.

What should be asked of any adoption curve somebody presents?

Which part of any of this is local, and which part is not?

Almost none of it is local. India supplies three things in this guide and no more: the way money is written, the way digits are grouped, and the legal form Private Limited carried by one of the invented businesses. Nothing else here belongs to any country.

The mechanism is completely universal, and that is a statement about arithmetic rather than flattery. A running total inside a finite group makes an S on every continent. The three requirements are the same three requirements everywhere. The shape was set out about populations in general rather than about any one market, and there is no rule, rate, threshold or period anywhere in this guide for any authority to be the authority on.