The Unit of Demand

A field that measures everything and defines nothing cannot tell a real number from a nonsensical one.

I once watched two people argue for twenty minutes about a conversion rate before realizing they were talking about two different quantities that happened to share a name. One of them meant the fraction of leads that eventually became customers, a pure number between zero and one, the kind of thing you would write as a percentage. The other meant the number of conversions the team produced per week, a flow, a count of events over a stretch of time. Both of them called it the conversion rate, both of them were certain the other was confused, and both were right about that, because the word rate was quietly carrying two incompatible meanings and nobody had noticed. When they finally saw it, the argument did not resolve so much as evaporate, because there had never been a disagreement about the world, only a collision between two quantities wearing the same label.

That small confusion is a tiny instance of something the whole field does constantly, and it points at a gap that sounds too basic to matter and turns out to be foundational. Go-to-market measures everything. It is drowning in metrics, dashboards, rates, ratios, scores, and velocities. And it has never defined what it is measuring, in the precise sense that the physical sciences define what they measure, which is to say it has no base quantities and no units, no agreed account of the fundamental thing a number in go-to-market is a number of. A field can survive this for a long time, the way go-to-market has, by relying on context and good faith to paper over the ambiguities. It cannot become a discipline this way, because a discipline needs to be able to tell a coherent quantity from an incoherent one, and you cannot do that without units.

What a unit actually buys you

It is easy to underrate units, because by the time most of us meet them they are already settled and invisible. A meter is a meter, a second is a second, and the immense intellectual labor that went into defining those things, and the power that the definitions confer, has faded into the background. So it is worth recovering what a unit is actually for.

A unit is a fixed, agreed reference for a quantity, and its first job is to make measurements comparable, so that a length measured here and a length measured there can be meaningfully combined. That much is obvious. The deeper job is less obvious and more important. Once you have units, every quantity carries with it a dimension, a statement of what kind of thing it is, and the dimension lets you check whether an expression makes sense before you ever put numbers in it. A speed has the dimension of length divided by time. An area has the dimension of length squared. You cannot add a speed to an area, and you do not need to know the numbers to be sure of that, because the dimensions alone tell you the operation is meaningless. The unit is what gives a quantity a dimension, and the dimension is what lets you catch nonsense early.

It is worth remembering how hard-won these references are, because their solidity makes them look inevitable when they were anything but. The meter was once a physical bar kept in a vault, then a multiple of a wavelength of light, and is now defined by fixing the speed of light and letting the meter follow from it. The kilogram was a literal lump of metal in a French vault until a recent redefinition tied it to a fundamental constant. Each of these definitions was a serious scientific undertaking, pursued precisely because a measurement is only as good as the stability of the unit underneath it, and a field that wants its numbers to mean anything has to do this work or inherit it from someone who did. Go-to-market has neither done it nor inherited it, which is why its quantities float free of any fixed reference and its arguments about them have nowhere solid to land.

This is the part go-to-market is missing, and the cost of missing it is exactly the twenty-minute argument about conversion rates, multiplied across every metric the field uses. Without defined quantities and units, there is no dimension attached to a go-to-market number, and without a dimension there is no way to check whether a calculation is coherent, so the field performs operations on its numbers that would be caught instantly as nonsense in any field that had done the basic work of defining its quantities. It adds things that should never be added, divides things whose ratio means nothing, and compares quantities that are not the same kind of thing, and it has no mechanism to notice, because the mechanism that would notice is dimensional analysis, and dimensional analysis requires units the field has never established.

The cheapest error check ever invented

Dimensional analysis is one of the great bargains in all of science, a way of catching a large class of errors for almost no effort, and it works entirely on the dimensions of quantities without touching their numerical values. The rule at its heart is the principle of dimensional homogeneity, which says that any equation describing something real must have the same dimensions on both sides. If you have written an equation in which the left side has the dimension of a length and the right side has the dimension of a length divided by a time, you have made an error, and you know this before measuring anything, because a true equation cannot equate two different kinds of quantity. Physicists and engineers use this constantly, often unconsciously, as a first check on any expression, because an equation that is not dimensionally homogeneous is wrong with certainty, and finding that out by checking dimensions is far cheaper than finding it out by experiment.

A quick illustration shows how mechanical the check is. Suppose someone proposes to measure the health of a go-to-market system by adding the number of new leads this month to the average deal size in dollars. Set the numbers aside and look only at the dimensions. A count of new leads has the dimension of demand. An average deal size has the dimension of currency. The sum of a demand and a currency has no dimension at all, because the two terms are different kinds of thing, and the principle of homogeneity tells you the expression is meaningless before you have computed a single value. You did not need the data to know the metric was broken. You needed only to ask what kind of thing each term was, which is the entire move, and which costs nothing.

The power of taking dimensions seriously is not a small or academic thing, and the cost of ignoring them is not hypothetical. A spacecraft sent to Mars was lost, after a journey of hundreds of millions of kilometers, because one team supplied a quantity in one set of units and another team read it as though it were in a different set, and the mismatch, which a dimensional check at the boundary would have caught, instead expressed itself as a navigation error that destroyed the mission. The lesson that the engineering world took from this is the lesson go-to-market has never learned, that units are part of the meaning of a quantity rather than mere bookkeeping, and that a number without a clear and carried unit is a numeral with no guaranteed connection to anything, not yet a measurement.

Dimensional analysis can do more than catch errors, which is part of why it is so prized. Through a result known as the Buckingham pi theorem, it can take the list of quantities that matter in a problem and tell you how many independent dimensionless combinations of them there are, which constrains the form any true relationship among them can take, sometimes narrowing the possibilities dramatically before any data is collected. The details of that result are more than this essay needs. What matters here is the posture, the habit of asking, of any quantity and any equation, what kind of thing is this, what are its dimensions, and does this expression respect them. That habit is the cheapest source of rigor available to any quantitative field, and go-to-market cannot practice it, because it has never named the dimensions its habit would check.

Proposing a base quantity

So let me propose the thing the field has never had, a base quantity for go-to-market, and then build the small system of derived quantities that follows from it. I am going to propose it as a hypothesis, in the proper sense, a definite claim offered so that it can be tested, refined, and if necessary discarded, because the worst thing I could do here is offer something vague enough that it could never be wrong.

The proposal is that go-to-market has a base dimension of its own, which I will call demand and write as $[D]$, in the same way that mechanics has the base dimensions of mass, length, and time, written $[M]$, $[L]$, and $[T]$.

There is good precedent for adding a base dimension rather than straining to reduce a new domain to old ones. When physics had to account for electricity, it did not force charge and current into the existing dimensions of mass, length, and time. It admitted a new base dimension for electric current, with its own base unit, the ampere, because electricity was a truly new kind of quantity and pretending otherwise would have produced exactly the dimensional confusion we are trying to avoid here. Demand has the same claim. It resists reduction to counts of people or sums of money, behaving instead like its own kind of quantity, and the honest move is to grant it the status of one rather than to keep measuring it through proxies borrowed from other dimensions. To make demand a base dimension is to claim that there is a fundamental measurable quantity underneath all the field’s counting, a quantity that the leads and the opportunities and the customers are all imperfect attempts to measure. The base unit of this dimension, the single quantum of demand, I will write as $q$. One $q$ is one unit of genuine, realized demand, and the hard work, which I will come back to, is saying precisely what that is.

Hold the difficulty of the definition for a moment and notice what the proposal immediately gives you. Once demand is a base dimension, the quantities the field uses every day acquire dimensions, and the dimensions let you check them. The accumulated demand a business has at a moment in time, the installed base of realized want, is a stock, and I will write it $Q(t)$, with the dimension of demand, $[D]$. The speed at which new demand arrives is a flow, the derivative of the stock with respect to time,

$$\lambda(t) = \frac{dQ}{dt}, \qquad \text{with dimension } [D]/[T].$$

This $\lambda$ is a genuine rate, demand per unit time, and its dimension is demand divided by time, exactly as a velocity is length divided by time. A conversion, by contrast, is a ratio of two demand quantities, how much demand made it from one stage to the next, and a ratio of two quantities with the same dimension is dimensionless,

$$c = \frac{Q_{\text{out}}}{Q_{\text{in}}}, \qquad \text{with dimension } [D]/[D] = 1.$$

This $c$ is a pure number between zero and one, with no units at all, the kind of thing you can legitimately call a fraction or a probability.

Now return to the two people arguing about the conversion rate, and watch the confusion resolve into something you can see. One of them meant $c$, a dimensionless ratio of stocks. The other meant $\lambda$, a flow with dimension $[D]/[T]$. These are not two opinions about one quantity. They are two different quantities, with two different dimensions, and the word rate was being asked to name both. The moment you carry dimensions, the collision is visible immediately, because $c$ and $\lambda$ cannot be the same thing, their dimensions do not match, and no amount of arguing could ever have reconciled a pure number with a flow. The twenty minutes were spent doing by frustration what one glance at the dimensions does for free.

Running the test on real metrics

The proposal earns its keep only if it does useful work on the metrics the field actually uses, so let me run the dimensional check on a few of them, in the spirit of the check rather than with false precision.

Some common metrics survive the test cleanly, and it is worth saying so, because the point is not that go-to-market’s numbers are all nonsense. The ratio of the lifetime value of a customer to the cost of acquiring one is a ratio of two quantities measured in the same currency, so it is dimensionless and coherent, a pure number, and comparing it across businesses is meaningful in the way comparing two pure numbers is meaningful. A conversion fraction between two defined stages is coherent, a clean $c$. Demand arriving per week is coherent, a clean $\lambda$. The field is not incapable of well-formed quantities. It simply produces them by luck rather than by discipline, with no way to tell the well-formed ones from the rest.

A worked version of the rate confusion makes the stakes concrete. Imagine one team reports that its conversion rate rose from 0.10 to 0.15 over a quarter, and a second team reports its conversion rate rose from 40 to 55. The first team is reporting a dimensionless fraction $c$, the share of demand that converts. The second is reporting a flow $\lambda$, conversions per week. If a manager, seeing both on one dashboard under one column headed conversion rate, concludes that the second team improved more because fifteen points beats five, the manager has compared a fraction to a flow, which is the dimensional equivalent of concluding that a speed of fifty miles per hour is longer than a trip of ten miles. The quantities are not comparable, because they are not the same kind of thing, and the only reason the error is available at all is that the dimensions were stripped off and a single word was laid over both.

Other metrics fail the test, and they fail in instructive ways. The word velocity is attached to several go-to-market quantities, and it is usually used loosely enough that you cannot tell whether it means a flow, a dimensionless ratio, or a flow divided by yet another quantity, which means that two people using it are often computing different things and combining them as though they were the same. Worse are the composite scores, the single numbers built by adding or multiplying quantities of different dimensions, a lead score that sums a count and a probability and a currency amount into one figure, which is dimensionally exactly the error of adding a length to an area, a number that cannot mean anything because it was assembled from incompatible parts. The field produces these constantly and treats them as information, because nothing in its practice flags the incoherence, and nothing flags it because the dimensions that would do the flagging were never assigned.

The most pervasive failure is the quiet one, the one in the opening, where a single word like rate is used for both a dimensionless ratio and a flow, so that quantities of different dimensions get compared, trended against each other, and reasoned about as though they were the same kind of thing. This is not a rare slip. It is the normal condition of a field that has no dimensions to keep its quantities apart, and once you start looking for it, you find it everywhere, in the way targets are set, in the way performance is compared, in the way one number is divided by another to make a third that no one has checked for meaning.

None of this requires new data or new tooling, which is part of why the omission is striking. Dimensional discipline is pure thought, a habit of asking what kind of thing each quantity is before combining it with another, and it pays for itself at once by deleting the meaningless metrics and dissolving the arguments that were never about the world. A field that adopted it would lose nothing worth keeping and would stop shipping numbers that cannot mean what they claim. The resistance to it, where there is any, tends to be that it feels pedantic, a fussing over definitions while the real work waits. The lost spacecraft is the standing rebuttal to that feeling. The definitions are the real work, or at least the floor beneath it, and skipping them does not save time so much as defer a cost to the moment the incoherent number is finally trusted and acted on.

The hypothesis, stated so it can be wrong

Let me state the claim of this essay as a hypothesis sharp enough to be tested and, if it is false, to be shown false.

The hypothesis has two parts. The first is that the well-formed quantities of go-to-market are dimensionally homogeneous, that the metrics which actually carry meaning are exactly the ones whose dimensions are coherent, expressible cleanly in terms of a base demand dimension $[D]$, time $[T]$, and currency. The second, the empirical and more provocative part, is that a large fraction of the metrics in everyday use are not dimensionally well formed, that they conflate stocks, flows, and ratios, or combine quantities of different dimensions into composites that cannot mean what they claim to mean. This is a claim about the world, and it is testable. Take a sample of real go-to-market dashboards, write down the dimension of every quantity on them, and check each metric and each calculation for homogeneity. The hypothesis predicts that the incoherence will be common rather than rare, concentrated in the composite scores and the loosely named rates, and detectable mechanically by anyone willing to track dimensions. If you ran that audit and found the field’s metrics overwhelmingly coherent, the hypothesis would be wrong, and I would want to know, because it would mean the discipline of units is already present in practice even though it is absent in theory.

I am fairly confident of which way the audit would come out, because the twenty-minute argument is the field’s normal weather rather than an unusual event, and you do not get weather like that in a field whose quantities are dimensionally sound.

The hard part, which I will not pretend is solved

Honesty requires me to come back to the thing I set aside, which is the definition of the demand quantum itself, the single $q$. It is easy to declare that demand is a base dimension. It is hard to say exactly what one unit of demand is, and I do not think the field has a settled answer, or that I can hand you one in a paragraph.

The difficulty is real and worth naming precisely. A lead is not a unit of demand, because most leads carry almost no genuine intent and a few carry a great deal, so counting leads is like measuring mass by counting objects regardless of how heavy each one is. A customer is closer, but customers vary enormously in the depth and durability of the demand they represent, so a raw customer count is a coarse and lossy measure of the underlying quantity. The true quantum, the thing the field is always trying to measure through these proxies, is something like a unit of realized, durable intent, and defining it well enough to measure is a genuine research problem, the kind of problem that took metrology decades, in some cases centuries, to solve for quantities we now take for granted. The definition of the second was refined for centuries. There is no reason to expect the definition of the demand quantum to be easy, and a field serious about becoming a discipline would treat pinning it down as foundational work rather than a detail.

A candidate definition, offered mainly to be shot at, is to anchor the demand quantum to a unit of sustained behavior rather than to a moment of intent. One $q$ might be defined as a single customer relationship of some reference duration and depth, so that a fleeting purchase that never repeats counts as a fraction of a quantum and a deep, durable relationship counts as several, with the reference case calibrated to a standard the field agrees on. This is surely not the final answer, and its problems are easy to see, the reference duration is arbitrary, depth is hard to observe directly, and different businesses would calibrate it differently. It is the right kind of answer even so, an operational definition that ties an abstract quantity to something measurable, which is how every base unit was eventually pinned down, and offering a flawed version of it does more for the field than gesturing at the difficulty and walking away.

What I want to claim is narrower and, I think, secure. Even before the quantum is perfectly defined, treating demand as a base dimension and tracking the dimensions of every quantity built on it is a discipline available right now, and it would catch most of the incoherence the field currently ships, because most of that incoherence is at the level of dimensions, not at the level of the precise unit. You do not need to have perfectly defined the unit of length to know that you cannot add a length to an area. You only need to know which quantities are lengths and which are areas. Go-to-market could have that much tomorrow, and having it would change what counts as a sayable sentence in the field.

Once quantities have dimensions, a new question becomes askable, the question every engineering discipline asks of its quantities once it can measure them. It is no longer enough to know that demand is a stock that flows and converts. You begin to want to know how the system that carries this demand behaves when you push it, how much of the flow it can take before something gives, which is the question of load and capacity, and that question cannot even be posed until the quantities are defined well enough to say what is being loaded and in what units it is being measured.

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References

• On dimensional analysis and the principle of dimensional homogeneity, and the Buckingham pi theorem, see standard treatments in the methodology of the physical sciences and engineering.
• On the role of units and the definition of base quantities, see the literature on metrology and the history of the International System of Units (SI).
• The loss of the Mars Climate Orbiter (1999) to a pound-force-seconds versus newton-seconds units mismatch is documented in NASA’s Mars Climate Orbiter Mishap Investigation Board, Phase I Report (1999).