Privacy Policy Retention Rate, why is important and why is a convergent sequence - Andrea Ciufo

Retention Rate, why is important and why is a convergent sequence

Last month I was explaining to a client the importance of (Customer) Retention.

In my opinion, after Profits and Gross Margins,  Retention is the most important KPI in business. 

What is Retention? 

Customer Retention measures how much customers liked your product/service and would buy or use it again. If I like your product I will use it, if I don’t I will not use or buy it again. 

Customer Retention is a percentage and expresses how many customers are retained over a specific time period.

Quoting Alex Schultz, former VP for Growth At Facebook: 

Retention is the single most important thing for growth.

This quote is from his presentation at Stanford. Honestly, I have seen it on Youtube at least 4 times and always It makes me think. 

How Retention Affects Your business? 

I found an interesting Bain’s Research, it highlights that increasing customer retention rates by 5% increases profits by 25% to 95%. 

The impact is huge! 

How to measure it? 

The formula is very easy.

Customer Retention Rate (CRR) = ((# Customers End Period # New Customers )/Customers Start Period)) X 100

How could it impact your business?

To give you an idea I created a business case with three scenarios. 

You can imagine a book e-commerce, where each month on average each customer spends 30£.

I am going to analyze 13 months, from 0 to 12 (I start counting from zero, here prof.dr. Dijkstra explains why), and the time window frequency is 1 month. 

Below the starting hypothesis: 

  • Customer Acquisition Cost 10£
  • Monthly Marketing Budget 10.000£
  • New Monthly Customers 1000 (Monthly Marketing Budget / Customer Acquisition = 10.000/10)
  • Three Retention Rate Scenarios:
    • 30%
    • 40%
    • 50%
  • Starting from Month 0 we invest 10.000£ every month for 12 Months
  • Monthly Revenue at Month 0 = 30.000£
  • Customer Monthly Value = 30£

Extra, I will attach at the end of the article three tables with:

  • Total Customers 
  • Total Monthly Revenues 
  • Total Cumulated Revenues

What is important to know is that a the end of the analysis period:

  • If the input variables are stable through the time, then the succession it’s convergent. And this means that when the curve is asymptotic “you have a viable business and you have a product-market fit for some subset of the market.”
  • 39% More customers at the end of the 12 months with a 50% retention rate compared with 30% retention rate  
  • 39% More Revenues on a Monthly basis, at the end of the 12 months with a 50% retention rate compared with a 30% retention rate 
  • 33% Difference in Total Revenues at the end of the 12 months between 50% retention rate compared with 30% retention rate 

How can I make a graph and evaluate different Retention Rate Scenarios? 

It’s important to plot and have a visual representation of what is going on. That’s why I created, thanks also to Marco Pietrosanto (yes, an Innlaber), a Colab Notebook where you can create with matplot a chart that automatically annotates the difference between different scenarios. 

You can change the retention rate in the Notebook and see how the difference between the scenarios changes. 

If you are interested to see the code you can find here the Codelab

Monthly revenues based on customer retation rate
Customer Retention Rate Plot

Some Ideas for a Retention Strategy

Retention is not only related to “how much your customers love your products”, but also the marketing, the experience and how you feed the relationship between your customers and your company. 

On this point think about how many company are switching to a subscription business model (Amazon Prime, now also Walmart

Here two ideas that I recently evaluated to increase retetion rate: 

  1. Increasing retention through referral links. Referral Link, also known as an affiliate one, is the URL that allows a company to promote their products or web content. It contains the affiliate ID that tracks how visitors arrive at a website. It is generated when a visitor is converted into a customer by submitting a form or buying a product. Then the affiliate site is rewarded a commission
  1. Increasing retention through a Digital Loyalty Programme (I am doing some research on this point until now I didn’t find any  API or White Label Service)

Point 1 could be declined through two interesting companies that I found

New Retention Strategy Opportunities for Small Restaurant Related to COVID 

This point is tricky, and for privacy reasons, you can’t implement if you don’t have your customer’s explicit consensus

Basically for contact tracing in Italy, UK and other European Country restaurants are taking a huge amount of personal data, Name, Mobile Phone, therefore putting in an excel file and see how often a customer is going to come again it’s quite easy to implement and monitor.

Based on that a merchant can implement a different set of strategies to increase frequency and retention through better service and other marketing strategies. 

Why Retention Rate is a convergent sequence?

This last point of my post is quite mathematical. I noticed empirically that Retention Rate was a convergent sequence, but I could not demonstrate why. 

So I asked on Mathematics Stack Exchange, a question-answer site-specific for Mathematical problems, and I received a very interesting reply. 

Here part of my question and the rigorous demonstration: 

Retention Rate is a ratio that defines how many customers will shop again after the first purchase in a fixed period of time.

The starting conditions are:

  • 100 customers at t0
  • Retention Rate is =0.4
  • New customers at time t1=10 and this value is a constant for t2,…tn

So we have this series:





Why customer retention rate is a convergent series?
I really love it, It is so elegant and harmonious
Customer Acquisition Customer Value Retention RateMonthly Marketing Budget 

In conclusion, you must keep in mind:

  • What is your retention rate
  • How to improve it

Thank you for reading the article!

If you liked or you think is useful feel free to share. 

With just a tweet or a like on LinkedIn new opportunities might arise.

# Customers 
0 month I monthII monthIII monthIV monthV monthVI month VII month VIII month IX month X month XI month XII month
0 month I monthII monthIII monthIV monthV monthVI month VII month VIII month IX month X month XI month XII month
Cumulated Revenue
0 month I monthII monthIII monthIV monthV monthVI month VII month VIII month IX month X month XI month XII month

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