Interactive tools for my courses.
Forecasting churn and CLV: a five-part series
Work through these five tools in sequence. Each one builds on the last: why retention rises, what a cohort is worth, how the BG model's a and b shape both, two ways to compute E(CLV), and where the m / (1 + d - r) shortcut comes from.
Forecasting churn and CLV: Tool 1
A cohort of 100 customers, each a coin minted with its own chance of churning every period. Shake them out and watch the survivors look ever more loyal as heterogeneity bends the retention curve.
Why does retention rise when no customer changes?
Forecasting churn and CLV: Tool 2
The survivor curve and the CLV distribution look like separate analyses. They are not: both come straight from the rows of one table. Hover a row, or a point on either chart, and follow the same lifetime everywhere. Then watch each lifetime slide from months to dollars and see who never pays back.
How likely is each possible CLV?
Forecasting churn and CLV: Tool 3
The BG model's two parameters, a and b, are not arbitrary numbers: together they shape the whole distribution of churn probabilities. Move around the parameter plane and watch the churn distribution, survivor curve, and retention curve respond.
How do a and b change the answer?
Forecasting churn and CLV: Tool 4
Start from one survivor curve. Road 1 weights each lifetime's CLV by how many customers have that lifetime; Road 2 weights each month's discounted cash by how many customers survive. Step through the 0/1 matrix to see why they are the same sum, added up by rows or by columns.
Why do both roads give exactly the same E(CLV)?
Forecasting churn and CLV: Tool 5
One customer with a constant renewal coin. Start from the same cash-flow timeline as Two Roads, watch the infinite sum collapse to m / (1 + d - r) with the 1/(1 - x) rule, and see four contracts differ only in the first payment. Then see why the formula does not work for a group.
Where does m / (1 + d - r) come from, and when does it break?
Explore how retention, margin, discounting, and acquisition cost combine into customer lifetime value — value to date, residual value, and break-even.
Follow one cohort's revenue through the decomposition tree: six linked charts covering active customers, orders, and spend, with count/percent and calendar/tenure views. Hover any chart and every panel lights up at the same point in time.
Build discounted cash flow for one acquisition cohort step by step: cash per active customer, margin, percent active, and discounting, down to payback and ROI. Then line up every cohort on one chart to see how the economics shift.
Two customers bring in the same expected contribution each month: one pays a subscription on a regular schedule, the other buys whenever they feel like it. Build the picture one layer at a time and see what timing does to value.
The classic R Shiny app: explore the beta distribution of churn probabilities behind the beta-geometric model and what it implies for expected CLV and remaining lifetime value. Hosted on shinyapps.io, so it may take a moment to wake up.
Reference: use after the five-part series
Every piece of the BG model on one page: the churn distribution, survival and retention, survivors after n renewals, and CLV, payback, and remaining lifetime value. Nothing is built step by step here, so it works best once you have worked through Tools 1 to 5.