TP INFINITY LAB

A river, and the thing it couldn't see

Most CRM can tell you what a customer is right now. Almost none can tell you which way they're moving. The tool to see the difference has existed since 2008, and a 1982 book already wrote down the gap. Scroll.

DANIEL WEI · COO, TP INFINITY

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THE METAPHOREvery customer is a chip drifting on a river. Its speed is its purchase rate, how often it buys, and that speed runs below the surface where you can't see it. What you see is the moment a chip breaks the surface: a purchase, a sign-up, any visible action. Between those moments it's underwater, and the customer is invisible to you.

1959 · 1982Ehrenberg gives the statistics; Greene gives the river. The math describes the spread of speeds across your whole base. Hand it one customer's history and it tells you, with real skill, fast chip or slow. For the plain question, who are my heavy buyers, that is still most of what a brand needs. Those differences between people are roughly fixed. Call them fate.

1987Schmittlein adds a darker possibility. Some chips don't just slow down; they sink for good. A customer can leave silently, with no cancellation and no goodbye, and you can estimate the odds they are already gone.

2008Netzer's breakthrough. A single chip can change its own speed, and a hidden Markov model can compute when. The within-person change Greene's model could not detect becomes the thing you watch for. Call it fortune.

2018+Sequence models read the whole order of what someone did, not just how often. The path itself starts to carry the signal.

A COUNTER-TRACKSharp pushes back. In mass markets the speeds converge, the river narrows, and the differences nearly vanish. There, reach beats segmentation. Which world you are in depends on the category.

SIXTY-SEVEN YEARSEach generation widened the reality we can see. The river was always moving. We just kept building better instruments for watching it.

1982 · CHAPTER TEN

In a chapter most readers skip, Greene wrote down what his own model could not do.

The book is a 1982 popularization, The River of Time, written by Jerome Greene for marketers who did not want to read statistics. Not famous. In his own words, the model cannot detect trends in a person's rate: a shift inside the window you study is "completely overlooked and lost," it does not show up anywhere. He named the floor of his own work, in a book meant to sell that work. I find that more honest than the field usually is about its blind spots. Then, with no tool to do better, it moved on for twenty-six years.

THE SAME STORY, AS A LEDGEREhrenberg and Greene. The model sees the differences between people, fast chips and slow. It cannot see one person change.

1987 · 2005Schmittlein's Pareto/NBD, then Fader and Hardie's BG/NBD in 2005, made it cheap enough to run at scale, the quiet engine inside a lot of "customer lifetime value." (Fader's company Zodiac was bought by Nike in 2018.) Now the ledger can mark a customer who has left for good. It still can't see them change while they stay.

2008Hidden Markov models. For the first time the ledger gets a column for within-person change. The rate can move, and the model can read the move from the order of what happened.

2018+Sequence models add the full path, not just the counts. The newest column.

THE OTHER TRACKIn low-differentiation categories, the within-person columns matter less. There, penetration and reach do the work.

Read the matrix down its right edge. Most of what a modern CRM actually runs still lives in the 1980s columns.

2018 · A LIMITAscarza adds an unwelcome finding. A large share of the customers any model flags as about to churn will not respond to anything you do. Seeing the turn and reversing it are different problems, and the rescue budget aimed at the unmovable ones is mostly spent for nothing.

THE 2008 MODEL

A hidden Markov model assumes the customer is in one of a few hidden states at any time, each with its own purchase rate, and moves between them month to month. Two matrices define it.

Show the math

Transition matrix A · probability of moving from one state to another in a month (row = state you are in, column = state you move to):

	→ Dormant	→ Transitioning	→ Active
Dormant	0.92	0.07	0.01
Transitioning	0.18	0.52	0.30
Active	0.04	0.16	0.80

Emission matrix B · probability of what you observe in a month given the state (no purchase, a core purchase, or a purchase in a new category):

	no purchase	core	new category
Dormant	0.80	0.19	0.01
Transitioning	0.50	0.32	0.18
Active	0.30	0.50	0.20

Feed in a customer’s purchase sequence and run the forward algorithm, and you get the belief over states at each month: the probability the customer is dormant, transitioning, or active right now. That running belief is what the Customer 847 chart further down plots. The dormant state is sticky (0.92 stays dormant), so a lone purchase barely moves it; a new-category purchase, rare for a dormant customer, moves it sharply.

And yet.

Open the CRM at most brands and ask a plain question: which of my customers is changing direction right now? It can name the tier. It cannot answer. The instruments exist; adoption is decades behind. Most systems are parked, more or less, in 1987.

THE SERENITY PRAYER

the serenity to accept the things I cannot change,
the courage to change the things I can,
and the wisdom to know the difference.

Accept what you can't change: the difference between people. Fate.

Change what you can: the movement inside one person. Fortune.

The wisdom is the hard part, telling which is which. The same rising number can mean "this person was always valuable and we missed it" or "this person is having a good quarter and will drift back." Read it as fate and you pour budget into someone already turning back down. Read it as fortune and you watch the direction first. Same number, opposite move.

CUSTOMER 847Two years on the books. Four purchases a year. Filed under low value, and the label hasn't moved in twenty-three months.

MONTH 14He buys something outside his usual pattern. The snapshot doesn't blink; one odd purchase barely moves a twelve-month average.

But the trajectory model already sees it. Its belief tips: this customer is changing state, while RFM still reads "stable, low value."

MONTH 18Only now, after the new rhythm has stacked up in its window, does the snapshot reclassify him as active.

Four months between the turn and the label. Long enough to meet him where he was heading, or to keep chasing where he used to be.

No model, however large, changes fate. A naturally low-rate customer stays low.

What the new tools buy you is speed and resolution on fortune. They see the state change sooner. They can estimate how much of a campaign's revenue was coming anyway. The value isn't a smarter answer. It's finally being able to ask the question Greene couldn't.

When you call someone a high-value customer, do you know whether that's fate or fortune?

Pull the time series. Flat is one, bumpy is the other. Most people have never looked.

SOURCES

Ehrenberg, A. S. C. (1959). “The Pattern of Consumer Purchases.” Applied Statistics 8(1), 26-41.
Greene, Jerome D. (1982). Consumer Behavior Models for Non-Statisticians: The River of Time. New York: Praeger.
Schmittlein, D. C., Morrison, D. G., & Colombo, R. (1987). “Counting Your Customers: Who Are They and What Will They Do Next?” Management Science 33(1), 1-24.
Fader, P. S., Hardie, B. G. S., & Lee, K. L. (2005). “‘Counting Your Customers’ the Easy Way: An Alternative to the Pareto/NBD Model.” Marketing Science 24(2), 275-284.
Netzer, O., Lattin, J. M., & Srinivasan, V. (2008). “A Hidden Markov Model of Customer Relationship Dynamics.” Marketing Science 27(2), 185-204.
Sharp, Byron (2010). How Brands Grow: What Marketers Don’t Know. Oxford University Press.
Ascarza, Eva (2018). “Retention Futility: Targeting High-Risk Customers Might Be Ineffective.” Journal of Marketing Research 55(1), 80-98.