CLV Contracts

Contrasting the two fundamental approaches to valuing customers: Contractual (Subscription) vs. Non-Contractual (Retail).

Customer Profile

Current Tenure (Months)

New CustomerLoyal

12 months

This is "s" in P(T > t+s | T > s)

Monthly Revenue ($)

$50

Baseline Churn Risk

StickyHigh Risk

3.0% / mo

The "Reset" Logic

In the Telco model, if a customer has already survived 12 months, we reset the clock. We only care about the probability of them surviving future months given they are here today.

Survival Probabilities (Exponential)

Discounted Expected Value (Accumulated)

Formula: CLV = ∑ [ S(t + s | T > s) × $M × (1+d)^-t ]

BG/NBD Model — P(Alive) and E[Tx] use the closed-form BG/NBD equations from Fader, Hardie & Lee (2005). Hyperparameters (r, α, a, b) are assumed known; in production these would be estimated via maximum likelihood on your transaction log.

RFM Inputs

Customer Age (T)

Weeks since first purchase

52 weeks

Recency (Last Purchase)

Weeks since first purchase

40 weeks

Warning: High gap!

Frequency

Total repeat purchases

5 purchases

The "Ghost" Logic

We don't know if they left. The BG/NBD model combines Recency, Frequency, and T with population-level hyperparameters to compute the posterior probability that a customer is still active.

Advanced: BG/NBD Hyperparameters

In production, these are estimated via MLE on your full transaction log. Here you can set them manually to explore model behavior.

r (purchase rate shape)

0.25

α (purchase rate scale)

4.00

a (dropout shape 1)

0.80

b (dropout shape 2)

2.50

Customer Timeline (Buy 'Til You Die)

P(Alive)

Prob. active right now
(BG/NBD closed-form)

Est. Future Tx

0.00

over next 12 weeks
(BG/NBD conditional expectation)

Avg Spend ($)

User-defined input

BG/NBD Formulas (Fader, Hardie & Lee 2005):
P(Alive | x, t_x, T) = 1 / (1 + δ) where δ = (a / (b + x − 1)) × (α + T)^r+x / (α + t_x)^r+x
E[X(t) | alive] = (r + x) / (α + T) × t | CLV = P(Alive) × E[Tx] × AvgSpend