Whale Graphs Tell: Who Are Our Star Customers?

Photo by Andrew Bain on Unsplash

Business runners may have the common sense that it is exhaustive to treat all customers exactly the same, instead, it is wise to focus on star customers. This is true, as star customers are the ones bring the biggest chunk of profit to business. Then here comes a question: who are they?

Before getting to know them, we need to know what makes a customer as a ‘star’. So first let us familiarize ourselves with the concept of ‘CLV’: Customer Lifetime Value, which serves as the ‘star classifier’. Wiki defines CLV as: ‘ customer lifetime value , is a prognostication of the net profit contributed to the whole future relationship with a customer.’

Customer lifetime value

In math languages, it translates as:

From: https://en.wikipedia.org/wiki/Customer_lifetime_value

So from the formula we can see that CLV of a customer relies on 3 elements: Margin (m), Retention Rate(r), and Discount Rate (i). And since net CLV equals to CLV minus customer acquisition cost (ac), we can calculate how much a customer can contribute to our business of a life-time with m, r, i, ac at hand.

Now with the formula, ideally we can rank our customers based on their Net CLV. However, in real-life, m, r, i, ac usually varies among customers. So, we need a tool to simulate the heterogeneous distribution of the elements:

Whale Graph with Monte-Carlo Simulation

In a recent homework, we simulated the customer CLV ranking graph (Whale Graph) with Monte- Carlo simulation. The idea is: we assume i and ac are constant and draw m and r from different distributions. And we compared the results as below:

So, from the above we learned that:

• When margins are normally distributed and retention rate is of beta distribution with mean of 0.6, top 20% customers contributed about 67% of total profit .
• When the SD is set at $20,000 instead of $4,798.06 (combo 2 ), top 20% customers contributed about 90% total profit.
• We also tried to simulate margins with pareto distribution (combo 3), where the margin distribution is highly right skewed (the margins for majority customers are low). Result tells that top 20% customers contributed about 150% total profit.
• Further, we changed the mean of retention rate to 0.3 (combo 4), then 20% customers contributed about 265% total profit.

So, we concluded that profit value concentration does depend on how margin and retention rate variables are distributed: unequal contribution appears more likely in cases where margin and retention rate are right-skewedly distributed and widely spread, while less likely true for companies with stable margin and retention rate among customers.

For business runners, it is important to analyze the customers distributions: do margins / retention varies wildly? Or do then tend to be stable? Then we could know about what percentage of customers are our star customers who deserve more time / effort investment.