The Customer Lifetime Value Formula is Flawed

If you’ve been to business school, this equation should look familiar:

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It is the formula for calculating customer lifetime value (LTV or CLV). It fits nicely on the back-of-the-envelope for simple math. It is also wrong. We have proclaimed that LTV is the foundational metric of customer centricity, and for something that important, we marketers must do better than this.

Let’s focus on the three most wrong parts of this formula:

  1. It’s a summation rather than an integral. This makes the math easier, but it implicitly assumes contractual transactions with discrete purchase opportunities. However, most retail environments are non-contractual and continuous in nature. I can shop at Target any time I’d like, several times a day or not at all: non-contractual and continuous.
  2. The range from t=0 to T represents a finite customer lifetime. Customers do not all have the same lifetime, which should be accounted for somehow, but for a true lifetime value, an infinite time horizon should be used. Oh, the math is starting to make my head hurt!
  3. rt is the retention rate. However, it represents a highly unrealistic survival curve. In fact, in reality, r itself is often a function of t. As the multiplier in this summation formula, that can make a huge difference in the resulting value. The orange line below represents what is typically observed with survival curves; a steep initial drop, followed by a leveling off. The gray line below is what rt would represent instead:
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There are more reasons this classroom formula is suboptimal. Mostly, it has been made simple for convenience in the days before big data science roamed the Earth. In today’s modern marketing world of real-time interactions and data-informed decisions, relying on the simple LTV calculations of yesterday can be costly and inefficient.

This classic method also leaves no room for prediction of future value. How do Excel jockeys like to solve for projections? Regression. The problem with regression is that it is notoriously bad at predicting the future.

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Citation: Fader, Peter S., Bruce G.S. Hardie. “How to Project Customer Retention.” Journal of Interactive Marketing 21.1 (2007): 76–90. Print.

Regression models often have a decent in-sample fit to the data, but deviate quickly when looking forward. Analysts that sell regression models for prediction show you the left-side of the survival graph above, along with some convincing R-squared stats, but then just look at how little predictive value these models demonstrate on the forward-looking side of the vertical line above.

Here’s a better formula from professors Peter Fader (The Wharton School) and Bruce Hardie (London Business School):

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It is the integral over continuous opportunities for purchase of a customer’s expected monetary value, times the probability that an individual is still within his/her customer lifetime, times a discount factor that accounts for the time value of money. It is very mathy, but there are cloud computing methods that now bring this type of accuracy within reach.

If you believe that the future of marketing is customer centric, and we do, then you must make sure you have the most accurate view of LTV, the fundamental metric of customer centricity, for each customer.

Originally published at crookedchimney.com on July 20, 2015.

Product Exec with a Code Habit, Founder

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