Average Revenue Per User: What It Reveals and What It Hides

Average revenue per user (ARPU) divides revenue by a count of people. The division is trivial. The two numbers are not. The denominator is a choice settled by no rule, so the figure moves when the counting rule moves. And an average destroys the distribution beneath it, so Rs 4,000/- fits fifty thousand people paying Rs 4,000/- each and five thousand paying Rs 40,000/- while forty-five thousand pay nothing.

Setu Bazaar, an invented marketplace, recognised Rs 20 crore of revenue for the year against 50,000 buyers. Put the first over the second and Setu Bazaar reports Rs 4,000/- a buyer. The division is the whole computation, and a reader who stops there has learnt almost nothing. The interesting work sits in deciding what the Rs 20 crore covers, in deciding which 50,000 people are in the count, and in knowing that once the division is done, the shape of what those people actually paid has been thrown away and cannot be got back. Revenue on Setu Bazaar arrives as a take rateThe slice a marketplace keeps of the money passing across it. Setu Bazaar keeps 4.00 per cent of the goods value it handles. Where the slice comes from and how it is set is covered separately under Business Fundamentals and Models. charged on the goods value crossing the platform, and that is settled separately. A take rate settles how much revenue there is. Dividing that revenue by a count of people is a separate step, and the step costs information.

What is average revenue per user?

Average revenue per user is revenue for a stated period divided by a count of the people the business served in that period. On Setu Bazaar the numerator is Rs 20,00,00,000/- of recognised revenue for the year and the denominator is 50,000 buyers, so the figure is Rs 4,000/-. Multiply back to check it. The check takes two seconds and catches a slipped decimal: 50,000 times Rs 4,000/- is Rs 20,00,00,000/-, and the year closes where it started. The arithmetic is trivial, and every difficulty here is about what the two numbers mean rather than how they are combined.

Look at the two inputs rather than the operation between them. The numerator carries a reporting periodThe stretch of time a set of figures covers, such as a quarter or a financial year. Two figures can only be compared if they cover stretches of the same length. Which periods a business must report is covered separately under Financial Statements. and an accounting choice about what counts as revenue at all. The denominator carries a rule about who counts as a person. Neither of those is handed down by the arithmetic. Both are decisions somebody made, and in most published figures neither decision is written down beside the number. The result is a measure that looks like a fact and behaves like an opinion with a decimal point attached.

What exactly goes in the denominator?

Nothing anywhere settles who counts as a user. Setu Bazaar could count everyone who has ever opened an account, everyone who bought something during the year, everyone who bought something in the last month, or everyone who logged in without buying at all. Each of those is a defensible rule and a person could argue for any of them in a meeting. The denominator is a choice settled by no rule, and the figure moves with the choice while nothing whatever about any person changes. Take Setu Bazaar's published year, with the revenue held completely still at Rs 20,00,00,000/-. On the 50,000 buyers who transacted during the year, the average is Rs 4,000/-. Suppose only 40,000 of those same people bought anything in the final month. The identical Rs 20,00,00,000/- divided by 40,000 gives Rs 5,000/-. Same year, same buyers, same rupees, and a figure a quarter higher.

Read the first row before the other two. The first row teaches something the arithmetic rows cannot. A rule can be perfectly clear and still produce no figure at all, if the count it asks for was never published. A count of registered accounts is the ordinary case: a business knows the number, and a reader outside the business does not. The three rules are not three attempts at one true answer. Each rule asks a different question about a different set of people, so each rule produces a different answer. A cohortA set of people grouped by when they arrived, so that everyone who first bought in April is followed as one set. Building and reading these is covered separately under Customers and Brands. that includes every dormantDescribing an account that still exists on the books but has shown no activity for a stated stretch of time. What counts as dormant is set by each business, and banking regulators set their own separate meaning for deposit accounts. account will always give a lower figure than one that includes only last month's active buyers, and neither is lying.

What does the average hide about the distribution beneath it?

Everything. An average is a single number standing in for a whole population, and standing in for something means replacing it. Once Setu Bazaar publishes Rs 4,000/-, the total is known and the count is known, and how that total was spread is not known at all. The household version runs like this. Ten people sit down to eat and between them they finish twenty rotis. The average is two each. An average of two is equally consistent with ten people eating two each and with one person eating twenty while nine watch. The average is correct in both, and it is the only thing in the room that cannot say which one happened.

The same average is consistent with every buyer alike and with a handful carrying all of it, and the arithmetic offers no way to tell the two apart. Setu Bazaar's Rs 4,000/- can sit above two very different populations. In the first, all 50,000 buyers bring Rs 4,000/- each. In the second, 5,000 buyers bring Rs 40,000/- each and the remaining 45,000 bring nothing at all. Both check out: 50,000 times Rs 4,000/- is Rs 20,00,00,000/-, and 5,000 times Rs 40,000/- is also Rs 20,00,00,000/-, with 45,000 times nothing adding nothing. Both total Rs 20 crore. Both divide by 50,000 to give Rs 4,000/-. A reader handed only the average cannot separate them, and the difference between them is the difference between a business with fifty thousand customers and a business with five thousand customers and a very long mailing list.

Every component of both distributions is printed above, so either one can be rebuilt from its parts. Rebuilding a total from its parts is the only defence against a total that nobody can check. The word for what separates them is skewThe lopsidedness of a set of values. A set is skewed when a small number of very large values sit far out on one side, pulling the arithmetic mean away from the middle of the pack. Measuring it formally is covered separately under Quantitative Methods., and the second distribution has a great deal of it. Setu Bazaar's real buyer list will sit somewhere between these two, as almost every real buyer list does, and the average will report the same Rs 4,000/- wherever on that range it happens to fall. Darrell Huff made the general point in How to Lie with Statistics in 1954, in a chapter on the well chosen average: the word average covers several different quantities, and choosing between them quietly is one of the oldest moves available to anybody presenting figures.

How can the figure rise while every individual stays the same?

Because a ratio has two ways to move and only one of them involves anyone spending anything. Setu Bazaar's Rs 4,000/- becomes Rs 5,000/- if the revenue climbs to Rs 25 crore on the same 50,000 buyers. The same Rs 5,000/- appears if the revenue never moves and the count drops to 40,000. The published figure is Rs 5,000/- in both cases and the two situations have nothing in common. A rising average can mean people left rather than people spent more, and mistaking the first for the second is the single most common misreading of this measure.

Follow the second case through slowly. The second case is the one that catches people. Nobody on Setu Bazaar changed a habit. Nobody bought a more expensive item. Ten thousand of the quietest buyers stopped being counted, either because they went quiet or because somebody tightened the definition of an active account. The people who left were the ones bringing the least, so the ones remaining have a higher average almost by construction. The arithmetic is that of the school class whose average height rises when the shortest child moves away. ChurnPeople leaving, expressed as a rate: the share of a starting population no longer present at the end of a stretch of time. How it is measured and what it does to a business is covered separately under Customers and Brands. among the least active buyers pushes this measure up, not down, which is the opposite of what most readers assume when they see the line move.

What is Average Order Value, and how does it differ?

Average order value divides money by a count of events rather than a count of people. On Setu Bazaar each of the 50,000 buyers places 10 orders in the year, so 5,00,000 orders cross the platform. Divide the Rs 20,00,00,000/- of revenue by those 5,00,000 orders and average order value on revenue is Rs 400/- an order. Divide the gross flowThe total value of goods and services passing across a marketplace before the marketplace takes its slice, as distinct from what the marketplace itself keeps as revenue. What belongs inside it is covered separately under Business Fundamentals and Models. of Rs 5,00,00,00,000/- by the same 5,00,000 orders and average order value on the goods value is Rs 10,000/- an order. Both are average order values, computed on the same events with two different numerators. The numerator has to be named every time the figure is quoted.

The denominator of average order value is events and not people, so it and average revenue per user are not two views of one quantity. The two measures can move in opposite directions, they answer different questions, and each misleads in a different situation. Which of them to reach for, and when each one fails, is covered separately under ARPU vs Average Order Value.

What does the figure not establish?

Three things, and each of them gets claimed on the strength of it regularly. The figure does not establish that any individual pays that amount. Under the concentrated distribution above, not a single one of Setu Bazaar's 50,000 buyers pays Rs 4,000/-: five thousand pay Rs 40,000/- and forty-five thousand pay nothing. The figure does not establish that Setu Bazaar earns anything. The whole measure sits above every cost line, and Setu Bazaar's year in fact closes at a loss of Rs 2.5 crore once its Rs 12.5 crore of fixed cost is set against Rs 10 crore of contribution. And it does not establish that a rise is good news, for the reason the previous section worked through.

An average is a summary, and a summary is a loss of information rather than a compression of it. So ask for what was lost. The first thing to ask for is the distribution itself, in slices: what the heaviest tenth brought, what the middle brought, what the lightest tenth brought. The second, and it is much easier to get, is the median. The median is the amount brought by the person standing exactly in the middle of the queue when everybody is lined up from lowest to highest, and it is a completely different quantity from the average. Run it on both distributions above. Under the flat one, the middle person brings Rs 4,000/-, the same as the average. Under the concentrated one, the middle person is somewhere among the forty-five thousand who brought nothing, so the median is Rs 0/- while the average is still Rs 4,000/-. Two numbers, identical averages, medians a whole world apart. The median is therefore the single most useful thing to ask for when only an average has been offered, and it is why the Ministry of Statistics and Programme Implementation publishes a mean and the spread beneath it together in its household consumption surveys rather than a mean alone.

What does a lender or an analyst actually do with the figure?

A lender and an analyst both refuse to read the figure until two questions have been answered, and both questions come before any look at whether the number went up. The two questions are what is in the denominator and what the distribution looks like, and neither is usually volunteered. The first question decides who the figure is even about. A lender sizing a working capital line against a marketplace wants to know whether Setu Bazaar's 50,000 is registered accounts, yearly transactors or last month's actives. The same Rs 20 crore over those three counts produces three different figures, and only one of them describes the people who will still be buying when the loan is drawn.

The second question decides how fragile the revenue is. If Setu Bazaar's Rs 20 crore comes from fifty thousand people at Rs 4,000/- each, losing any hundred of them costs Rs 4,00,000/- and nobody notices. If it comes from five thousand people at Rs 40,000/- each, losing a hundred of them costs Rs 40,00,000/- and losing the heaviest five hundred costs Rs 2 crore, a tenth of the year. The contrast is the household on one salary against the household on four part time incomes: the two can report the same monthly total, and one of them is one letter away from a very bad year. The average is identical in both cases and says nothing about which of the two a lender is lending into. An analyst who asks for a slice by slice split, and a household that knows which of its incomes is load bearing, are doing the same work.

Setu Bazaar is invented.
Educational material. Not advice on any investment, tax, budget or market position.