Day 2
What a customer is worth
What is a customer worth, in money, with uncertainty?
The day’s modules
09:15–11:15
Module 4
Add a Gamma-Gamma spend model after checking that spend is independent of purchase frequency, compute discounted CLV with its uncertainty, test how it moves with horizon and discount rate, and handle the contractual case with the shifted-beta-geometric model.
11:30–12:25 · 13:25–14:30
Module 5
Turn posterior CLV into decisions: the most we can pay to acquire a customer in each channel, segment value with credible intervals, the break-even effect of a retention campaign and scores written to a warehouse table, with the numbers for a one-page CFO memo that you write in the afternoon clinic.
Warm-up: what carried over from Day 1 (15 minutes)
Answer alone on paper for 5 minutes, notes closed. Compare with a neighbor for 4 minutes. The facilitator takes the most-missed questions for 5 minutes, then says in one minute where today starts.
W1. Two customers each made 4 repeat purchases in a 52-week calibration period. A’s last purchase was in week 50, B’s in week 20. Which has the higher P(alive) at week 52, and why?
Answer
A. Both bought at the same rate while active, but B has been silent for 32 weeks, which would be unusual for someone buying about once every 10 weeks. The longer the silence relative to a customer’s own rate, the more likely they have left. P(alive) depends on frequency and recency together.
W2. “Recency” means two different things on Day 1. What are they, and which direction is “good” in each?
Answer
In marketing RFM segments, recency is the time since the last purchase: smaller is better. In BTYD models (buy-till-you-die models such as BG/NBD), recency is the customer’s age at the last purchase, measured from their first purchase: for a given age T, larger is better, because the customer was seen buying more recently. Mixing the two silently reverses a model’s input.
W3. Why were the BTYD model and the gradient-boosting model both scored on a holdout period, and what would make the machine-learning comparison unfair?
Answer
A forecast is only tested on data it has not seen: both models are fitted on the calibration period and scored on purchases in the holdout period, with the same metric. The comparison is unfair if any feature for the machine-learning model uses data from the holdout period (leakage), or if the two are scored on different customers or metrics.
W4. In Lab 3, the customers of one acquisition channel have a positive coefficient on the purchase process. Can you conclude that moving acquisition budget to that channel will bring in more frequent buyers?
Answer
Not from this alone. The coefficient says that channel’s customers bought more often than the reference channel’s customers, holding the model’s other inputs fixed. They may differ for reasons the channel did not cause (who the channel reaches), and more budget may bring in different, marginal customers. A budget decision also needs each channel’s acquisition cost, which Module 5 brings in.
Why today. Today’s question is What is a customer worth, in money, with uncertainty? Module 4 adds money to the purchase forecasts: spend per transaction, discounting and the horizon. Module 5 turns customer value into decisions (how much to pay to acquire a customer, when retention pays) and the afternoon clinic starts by writing them into a one-page memo for a finance review.
CFO memo clinic (60 minutes)
Goal. Make your Module 5 decision memo survive a finance review: one clear recommendation, in money, with its uncertainty and the assumptions that would change it.
What you bring. The memo template that Lab 5’s Decision section printed with your numbers. You write the memo here, in the first part of the clinic: at most one page (about 250 words), headed by a one-sentence recommendation.
Format. Groups of three. Each round, one person is the Author, one the CFO and one the Analyst; roles rotate, so everyone plays each role once and every memo is reviewed. In a group of four, the fourth person is a second Analyst; in a pair, the CFO also uses the Analyst’s checklist.
| Minutes | What happens |
|---|---|
| 0–3 | The facilitator explains the two roles, hands out the CFO card and the Analyst checklist below, and forms groups. |
| 3–15 | Write. Everyone writes their memo from the template Lab 5 printed: the recommendation first, then the numbers with their intervals, the assumptions, and what would change your mind. |
| 15–51 | Three rounds of 12 minutes, one memo each: 2 minutes for the CFO and Analyst to read in silence; 4 for the CFO’s questions; 3 for the Analyst’s checklist; 2 for the Author to note what to change (no defending); 1 to rotate. |
| 51–57 | Revise. Each Author rewrites the headline sentence and the “what would change my mind” sentence. |
| 57–60 | The room. Two volunteers read their headline before and after. The facilitator names the most common gap they heard. |
The CFO’s card. Ask up to four, and only from this card. The Author answers briefly; no slides, no notebook.
- What exactly are you asking me to approve, in dollars, and for how long?
- What is the range, and what kind of range is it?
- Is that revenue or margin? Over what horizon, and at what discount rate?
- If the true value is at the low end of your range, do we lose money?
- What did you assume that you did not test?
- What result would make you change the recommendation?
The Analyst’s checklist. Tick each line that the memo meets; say which lines it misses.
Roles of the facilitators. One keeps time and calls each change of step aloud. The others circulate, listen, and write down the gaps they hear for the wrap-up. They do not fix anyone’s numbers.
Deliverable. The revised memo with the Analyst’s checklist ticked, pasted into a Markdown cell at the end of your Lab 5 notebook (or your own notes). You will reuse it for slide 2 of the capstone brief on Day 5.
Wrap-up: fixed and left open (20 minutes)
1. Fixed and left open (6 minutes: 3 in pairs, 3 with the room).
- Module 4 put a dollar value on each customer: spend per transaction, discounted over a horizon, with an interval, and a separate model for subscription customers.
- Module 5 turned that value into decisions: acquisition cost caps, the value of segments with intervals, when a retention offer breaks even, and a memo a finance team can act on.
- Left open for Day 3: every decision today assumed we know what marketing does. The retention offer’s lift and the channels’ effects were assumed, not measured. Did the marketing cause the sales?
2. The running results table (8 minutes). Add today’s rows to the table from Day 1, with interval type and probability, run mode and, on synthetic data, the truth.
| Lab | Quantity | Your number | Interval (type, probability) | Truth (synthetic data) | Run (FULL or QUICK; yours or reference) |
|---|---|---|---|---|---|
| 4 | Average spend per transaction (Gamma-Gamma) against the truth | ||||
| 4 | Average discounted customer value (margin) | ||||
| 4 | The same at another discount rate or horizon | ||||
| 5 | Acquisition cost cap per channel | ||||
| 5 | Retention offer: break-even lift in retention | ||||
| Clinic | Your memo’s headline sentence, revised |
3. One decision claim (6 minutes: 3 writing, 3 with the room). Write one sentence in the form number → rule → recommendation: “Based on [number and interval from Lab N], I would [action], because [rule, with its cost or margin], unless [the assumption that would change it].” Today’s is probably your memo’s headline. Two or three people read theirs; the room asks each: what would change your mind?
Run sheet
Times are on the schedule. Every lab opens from the notebooks page too.