The Problem with Averages in the Average Lifetime Value Formulas.

We previously covered average lifetime value by looking at actual past purchase lifetimes.  There is however an alternative formulation that is widely used that doesn't look necessarily at averaging each individual lifetime value, but instead just uses the averages in customer behavior.  Let us elaborate with each formula.

The Average Order Size

The Average Order size is given by  AO = Total Revenue / Number of Orders. This treats all orders from everyone the same, as if they came from each individual equally.

The Average Frequency Of Orders

The Average Frequency of Orders is given by AF = Number of Customers / Number of Purchases.  This doesn't measure true frequency because you don't know the actual time between purchases.

The Average Lifetime

The Average Lifetime is given by AL = sum of Customer Lifetimes / Number of Customers.  However, because you can't necessarily wait 20 years to see the total customer lifetimes, it is sometimes suggested to use 1 / churn rate percentage to estimate this value.

The Average Customer Lifetime Value

The Average Customer Lifetime Value is then given by AvgCLV = AO*AF*AL.  It is just the previous formulas multiplied with each other to get the "average" in lifetime value.

Correlated Values and Problems with using the "Average"

The above formula, while simple, has a few glaring flaws that are not fixable.  Customers don't behave like the average, and the "average" lifetime value will be terribly misleading.  When you multiply the averages together, you assume that each factor AO, AF,  and AL are statistically independent.   They are not.  When the customer is a high lifetime value customer, the Average Order sizes are larger, the Average Frequency is greater, and the Average Lifetime is greater, for example.  When the customer is a low lifetime value customer, the Average Order sizes are smaller, the Average Frequency is less, and the Average Lifetime is shorter, for example.

Let's work through an example where we can see the effect of correlation on the "average" lifetime value.  For simplicity, assume the correlation is perfect, which won't be too far from the actual case.  These numbers come from a Starbucks case study.  For Starbucks, the average frequency is AF = 4.2 visits per week.  The average order size is AO = $4.05 per visit.  The estimated lifetime is 20 years, so AL = 52 weeks * 20 years.  This gives the Average Customer Lifetime Value as

AvgCLV = $4.05*4.2*52*20 = $17,690.40

We can look at the correlation effect as equivalent to adding an extra term inside the formula for Average Customer Lifetime Value

AvgCLV = (AO+x)(AF+x)(AL+x)

When a customer is high lifetime value customer, x is added to all the base values.  When a customer is a low lifetime value customer, you can think of subtracting x from all the base values.  Now let us look at what happens to the Starbucks customer when they are a high value lifetime customer by assuming it raises all the values by 20%.

HighAvgCLV = ($4.05*1.2)*(4.2*1.2)*(52*20*1.2) = $ 30,569.01

This value is almost twice the baseline. And let's look similarly at what happens when the Starbucks customer is a low value lifetime customer by lowering all the values by 20%.

LowAvgCLV = ($4.05*0.8)*(4.2*0.8)*(52*20*0.8) = $9,057.48

This value is almost half the baseline value.  High and Low value customers might not be a problem if there were an equal number of both types, but if you recall the L-Shaped distribution from the previous post on "Why The Average Customer Lifetime Value is Not Enough", the majority of customers come from the low value of the distribution with a long tail, since roughly 80% of revenue is generated by only 20% of the customers.

The real-world effect of correlation on the terms in the "average" lifetime value AvgCLV = AO*AF*AL, is to make the calculation highly biased and misleading by making the L-shaped distribution have greater extremes in the tails and making it more L-shaped.   When the true lifetime value of customers affects the profitability of your business, you cannot depend on the "average" formulas. Given that there is a cost to acquiring customers (through ads and incentives), then knowing the true lifetime values is a key piece of information that you need for your business.

We can help you with discovering what the true lifetime value is of each and every customer in your business, because we have AI software that forecasts what each individual customer's lifetime value will be, and what their stream of future purchase values will be, with high accuracy, early in their life.  Contact us for a demo.