How To Maximize ROI with Customer Lifetime Value & Segmentation (the right way)

Data Science is bullsh*t.

I say this a lot.

And I say it despite the fact that I run my own data science lab.

And it isn’t the science per se that is the issue.

It’s the way it’s often used.

There is an overabundance of useless projects, useless ideas, and useless analysis that do not align with business goals.

You see, the thing you must understand (especially if you’re a business owner) is that data science has mostly fallen short in providing executives with something of value to grow revenue, reduce cost, improve efficiency, or maximize profit.

There is a lot of useless research, a lot of circle jerking, and a lot of wasted money and time.

I’m not here to bullshit you though.

Data Science is hard.

This goes without saying.

But a lot of scholars who work in the science of data these days have a very weird yearning to appear super intelligent, and in doing so, often sprinkle in an excessive abundance of quantification in an effort to impress the masters.

The problem with doing this is that through this inundation of numerical manifestations they actually inadvertently appear far “less intelligent” as their analysis often comes across as an ostentatious display of statistical acrobatics and numerical intricacies, full of erudition and empty of meaning.

On one hand, a display of pure mathematical brilliance, and on the other, nonsensical ramblings and chaotic numeric sequences that nobody understands.

Which strikes me as weird, because despite having studied the art of mathematics and statistics for many years, many data scientists (even on the PhD level) still fail to mathematically determine the suboptimality of this reasoning choice.

Which also begs the question: “Is it possible to become so educated that you become an idiot?”

To properly solve for this dilemma, one must first come to understand the twofold nature betwixt quant and logic — the complimentary aspect of Newtonian third.

If one decides to venture down this path, this inescapable paradox, a duality of opposing forces between quant and logic, can become a repetitive contemplation, a chatter in the skull, where the size and scope of the very analysis itself requires one to spend entire days, weeks, years, even an entire career, pondering its meaning.

And soon, despite your best efforts to contain it, it will eventually consume you, driving you mad.

This is where the reasoning path begins to grow dark.

Where you have nothing to think about except thoughts.

Where you cannot see the forest for the trees.

Where you lose touch with reality and live in the world of illusions.

And the illusions become an uninterrupted chain of disquisitions, upon the very nature and qualities of your mind and its relation to all that constitutes the future.

Here, the reasoning path is unclear.

The road is dark.

More analysis is needed.

One must dive deeper.

So, you wander aimlessly in the forest of decision, into the black.

Each step more unsure then the last.

You go left when you should go right, up when you should go down.

And you wander into the world of confusion.

A total nightmare.

To avoid this suboptimality, I believe one must (at all costs) avoid trying to showcase theoretical prowess, and instead, focus on just showing results.

The results are all that matter.

And once you have those results, the data must align and augment executive budgets, and ad-hoc tactical decisions.

There is no time for circle jerking.

Nobody cares how smart you are if you can’t make them any money.

Or worse, you just cost them money.

A negative net.

That said, today, I’m going to show you how to avoid useless analysis and discuss two critical analyses that can actually help your business make money (that nearly every business owner overlooks).

And not only do most businesses overlook them, but the ones that do try either do it improperly or fail spectacularly.

These two critical elements are Customer Lifetime Value and Customer Segmentation.

If you’re a business owner, these are two critical metrics that you need to study and understand, especially if you want to maintain a competitive advantage in today’s hyper-tech and data focused business environment.

But first, let us define what these things mean.

Customer Lifetime Value 

Customer Lifetime Value (CLV) is defined as: The present value of the expected sum of discounted cash flows of an individual customer or cohort/segment of customers.

The key variables are as follows:

• ARPU (average revenue per user)
• Avg. Cust. Lifetime, n (This is the inverse of the churn, n=1/[annual churn])
• WACC (weighted average cost of capital)
• Costs (annual costs to support the user in a given period)
• SAC (subscriber acquisition costs, sometimes referred to as CAC = customer acquisition costs)

In simpler terms, Customer Lifetime Value (CLV) is a multidimensional construct that quantifies the net present value of all future cash flows attributed to a customer throughout their entire lifecycle with a business. It serves as a key metric for understanding the long-term value a customer brings, as opposed to transactional value.

Understanding CLV allows a business to:

• Allocate marketing budgets more efficiently
• Tailor products and services to high-value customers
• Make informed decisions on customer retention strategies

It’s a symbiotic relationship where various aspects of customer behavior (e.g. acquisition, retention, and monetization) are combined into a singular value that serves as an indicator of long-term customer profitability.

We usually calculate CLV using advanced probabilistic models (our latest build is actually 25 models in 1) where stochastic elements of customer behavior is used as a pivotal variable in strategic customer relationship management (CRM), resource allocation, and firm valuation.

If you calculate it correctly, the CLV can serve as a cornerstone metric within the interdisciplinary nexus of marketing, economics, and finance, providing a quantifiable measure of customer capital.

The key LTV is predicting the future based on historical data.

This is where normal LTV models (including the generic ones typically found online in Google search) fail miserably:

The LTV model we typically use in The Lab is a Shifted Beta-Geometric Probability Model with two parameters alpha and beta.

This model is a combination of the geometric distribution and beta distribution.

This distinction is key because the geometric distribution captures the slope or rate of change of churn over time. The beta distribution captures heterogeneity/difference in churn across customer segments/cohorts.

Geometric distribution shown below:

Beta distribution shown below:

Actual vs

Below is the implementation using Python:

And also:

We typically build and code these mathematical algorithms from the ground up, run the implementation, etc.

Coding the mathematical algorithms in Python allows for scaling to millions of customers across numerous customer segments shown below:

Customer Segmentation

The next step would be segmenting customers into unique groups (aka customer segmentation).

This is a challenge for many businesses, and most fail to do it correctly.

But customer segmentation is key to producing an accurate and scalable LTV model.

So, what is customer segmentation exactly.

Customer Segmentation is the practice of dividing a customer base into groups of individuals that are similar in specific ways, such as age, spending habits, or behavioral traits.

This is a rather advanced “analytical framework” that incorporates statistical and machine learning algorithms to partition a heterogeneous customer base into homogenous subsets based on a range of variables like behavioral patterns, demographic attributes, psychographic factors, and transactional histories.

Note for advanced users: you can also run cohort analysis that segments the customer base not just based on static attributes like age or income, but on a temporal or behavioral dimension, such as the time of first purchase or engagement with a service. You can analyze cohorts as a single unit over time to assess patterns, correlations, or causal relationships within the context of longitudinal studies. By tracking these cohorts over long timescales, you can begin to see interesting customer lifecycle patterns such as retention rates, changes in behavior, and lifetime value. 

It’s worth noting that segmentation is not just a generic classification exercise.

It’s a strategic methodology.

There is a science to it.

And if you do it right, you’ll end up with optimized marketing campaigns, optimal resource allocation, and efficient product development.

But it’s often easier said than done, as segmentation analysis typically requires advanced knowledge of multidimensional scaling, cluster analysis, and predictive modeling to identify any sneaky patterns and correlations hiding deep in the data that are not readily apparent through traditional descriptive analytics.

There are three general types of segmentation: 

1. Demographic Segmentation: Age, Gender, Income
2. Behavioral Segmentation: Purchasing Habits, User Activity
3. Psychographic Segmentation: Lifestyle, Values

And we typically use three different techniques to run segmentation analysis:

1. K-means Clustering: an unsupervised machine learning algorithm that partitions a dataset into $K$ distinct, non-overlapping subsets (or clusters) based on feature similarity. The algorithm employs an iterative optimization technique to minimize the within-cluster sum of squares, effectively assigning each data point to the cluster whose centroid is nearest in the feature space. While computationally efficient, K-means assumes spherical clusters and is sensitive to the initial placement of centroids. It is widely used in various domains, including but not limited to, market segmentation, anomaly detection, and image segmentation, and serves as a foundational algorithm in vector quantization and pattern recognition.

2. Density-based Spatial Clustering (DBSCAN): an unsupervised clustering algorithm that identifies clusters as high-density regions in feature space, separated by regions of lower point density. Unlike partitioning methods like K-means, DBSCAN does not require the pre-specification of the number of clusters and can discover clusters of arbitrary shape. The algorithm operates by defining a neighborhood around each data point, and attempts to grow clusters by stacking together closely packed data points based on a distance metric and density parameters. DBSCAN is particularly effective for applications where the distribution of data is non-uniform and the cluster structure is complex.

3. Expectation-Maximization (EM) Clustering: a statistical technique that employs the Expectation-Maximization algorithm to find maximum likelihood estimates of parameters in probabilistic models, particularly Gaussian Mixture Models, where the data is assumed to be generated by a mixture of several Gaussian distributions. The algorithm iteratively performs two steps: the Expectation step (E-step), which computes the expected value of the log-likelihood function concerning the conditional distribution of latent variables given observed data and current parameter estimates, and the Maximization step (M-step), which updates the parameter estimates to maximize the expected log-likelihood found in the E-step. EM Clustering is widely used in scenarios where the data is incomplete or has missing values, and serves as a robust method for soft clustering, where each data point can belong to multiple clusters with different probabilities.

And if you want to get fancy you can use decision trees to classify customers into different segments based on decision rules.

Finding the optimal number of clusters is key.

The elbow method finds the value of the optimal number of clusters using the total within-cluster sum of square values.

This represents how spread-apart the generated clusters are from one another. In this case, the K-means algorithm is evaluated for several values of K, and the within-cluster sum of square values is calculated for each value of K.

After this, we plot the K versus the sum of square values. After analyzing this graph, the number of clusters is selected, so that adding a new cluster doesn’t change the values of the sum of square values significantly.

The area bounded by the rectangle is optimal (clusters 1-5).

Clusters 6-12 have very little variation.

Next Steps

Business analytics can be tricky, but regardless of whether you’re selling autonomous rockets or have a lemonade stand, understanding your customer is paramount.

In today’s hyper-competitive business environment, understanding your customer is not just a marketing necessity but a strategic imperative.

Customer Lifetime Value and Customer Segmentation are two critical frameworks that can help your business optimize its marketing strategy by offering deep insights into customer behavior, maximizing profitability.

That said, it’s important to note the symbiotic relationship between Customer Lifetime Value (CLV) and Customer Segmentation. These are not isolated concepts but interconnected strategies that, when employed in tandem, can significantly elevate a business’s customer-centric approach, thereby driving long-term profitability and sustainable growth.

Here are a few ways to use CLV and Segmentation:

This is a more financially nuanced approach that you’ll typically see if you conduct a general Google search for “Customer Lifetime Value Analysis”. The CLV will be calculated by considering the average revenue per user, the average customer lifetime, the weighted average cost of capital, the annual costs to support the user, and the subscriber acquisition costs.

Customer Lifetime Value (CLV) Calculation

The CLV for Deimos-One’s customers can be calculated using the following formula:

Where:

• ARPU is the average revenue per user (per period)
• Costs are the annual costs to support the user (in a given period)
• WACC is the Weighted Average Cost of Capital, which represents the opportunity cost of the funds used for financing the customer relationship
• Avg. Cust. Lifetime, n is the average customer lifetime, calculated as the inverse of the churn, n=1/[annual churn])
• SAC (subscriber acquisition costs, sometimes referred to as CAC = customer acquisition costs)

Let us import the vars into our sh*tty bathroom formula, with the following assumptions:

Let’s assume the following for Deimos-One’s customer base:

• $ARPU$ = $13,000 per month
• Annual churn rate = 10% (hence, $Avg.Cust.Lifetime,n$ = 10 years)
• $WACC$ = 8%
• $Costs$ = $2,000 per month
• $SAC$ = $30,000 per customer

Applying the Formula

Given the assumptions, we will now apply our formula from above, plug in our numbers and calculate the CLV.

Our formula will yield the net present value of the profit that Deimos-One expects to earn from an average customer over the average customer lifetime, after accounting for the costs to support the user and the costs to acquire the customer.

Interpretation

The resulting CLV will inform Deimos-One of the value an average customer brings to the company. A positive CLV indicates a profitable customer relationship, while a negative CLV would suggest that the company is losing money on its customer acquisition and support efforts.

To illustrate the CLV calculation, we can create a chart that shows the projected net cash flows from a customer over the 10-year period.

The chart would display the initial negative cash flow due to SAC, followed by positive cash flows from ARPU minus Costs, discounted by the WACC each year.

References

1. Fader, P. S., & Hardie, B. G. (2012). Customer-based corporate valuation. Journal of Marketing Research, 49(1), 40-56.
2. Gupta, S., & Lehmann, D. R. (2006). Customer lifetime value and firm valuation. Journal of Relationship Marketing, 5(2-3), 87-110.
3. Smith, A. (2018). Data-Driven Marketing. Harvard Business Review.