Summary
Summary Customer Analytics
- Course
- Institution
Summary of Module 1 - Module 5 of Customer Analytics 2023/2024 of the lecture slides, theory in the labs and some additional explanations.
[Show more]
Seller
Followlisaholling1
Reviews received
Content preview
ContentsModule 1 - CLV in Contractual Settings 1
Geometric Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Calculating CLV with the BG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Calculating RLV with the BG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Ruse of heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
CAC and ROI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Shifted Beta Geometric Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Calculating CLV with the sBG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Calculating RLV with the sBG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Module 1 - CLV in Contractual Settings
Definition: CLV is the PV of future profits of one particular customer
We look at specific cohorts that started at t = 0
Survival function (prob that a customer is still active, thus compared to t = 0)
=
S(t) = P (T > t)
Retention rate (prob that a customer who was active in t − 1 it still active at the end of t, thus compared
to the last period)
=
S(t)
r(t) = P (T > t|T > t − 1) =
S(t − 1)
Geometric Model
Coin-flipping
Probability that a customer leaves (i.e. T ) at period t
P (T = t) = pt−1 (1 − p)
Thus, S(t) = pt
r(t) = p
Calculating CLV with the BG
2 3
E[CLV ] = m + (1+d)
mp
1 + (1+d)2 + (1+d)3 + . . .
mp mp
= m(1+d)
1+d−p
with: retention rate (p) , margin (m) , discount rate (d)
1
,Calculating RLV with the BG
CLV looks at new customers, but RLV looks at customers that did start before t = 0
RLV = already acquired customers = they tend to have lower churn rates than new customers
i.e. for customers with an age > 0 at t = 0
RLV right before renewal:
mp2 mp(1+d)
E[RLV ] = mp + (1+d) + ... = 1+d−p
RLV right after renewal:
You have to discount with one additional /(1 + d) , so it goes away in the upper term
E[RLV ] = mp
1+d−p
Ruse of heterogeneity
In a given cohort, the retention rate increases over time due to heterogeneity = sorting effect
CAC and ROI
Customer Acquisition Cost: to be profitable CAC < CLV =
marketing expenditures
CAC =
customers acquired
Return on Investment = ROI = prof it
cost = CLV −CAC
CAC
Shifted Beta Geometric Model
Model with a distribution of retention rates across customers; we have to write the survival function
in terms of θ
S(t|θ) = pt = (1 − θ)t
With the distribution of θ between 0 and 1 with parameters a and b
Beta Distribution:
θa−1 (1 − θ)b−1
f (θ|a, b) =
B(a, b)
With mean = a
a+b and variance = ab
(a+b)2 (a+b+1)
This gives the new survival function and retention rate:
B(a, b + t) b+t−1
S(t|a, b) = r(t|a, b) =
B(a, b) a+b+t−1
r(t) increases over time, depending on a and b
• small a and b: retention rate rises quickly but levels off quickly
• medium a and b: rate of increase in retention slows down
• large a and b: hardly any increase; almost a constant retention rate
• a and b relatively equal in value: symmetric beta distribution
2
, • b > a: skewed to the right; values are closer to 1
• a > b: skewed to the left; values are closer to 0
In this model, you can estimate using the maximum likelihood function
Calculating CLV with the sBG
Each term contributes less to CLV, because of discounting and the diminishing survival function
You need a suitably large T, to estimate the same E[CLV ] function as before (you can ignore the latest
terms because they are so small)
mS(1) mS(2) mS(3) mT
E[CLV ] = m + + + + ... +
(1 + d)1 (1 + d)2 (1 + d)3 (1 + d)T
3
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller lisaholling1. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $6.26. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
73314 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now