MODELING LIFETIME VALUE

PREDICTIVE LIFETIME VALUE

(A more detailed and technical version of this article was first published in Applied Marketing Analytics, summer 2015)

Life-Time Value (LTV) is typically done as just a calculation, using past (historical) data. That is, it’s only descriptive. 

While there are many versions of LTV (depending on data, industry, interest, etc.) the following is conceptually applied to all. LTV, via descriptive analysis:

1) Uses historical data to sum up each customer’s total revenue.

2) This sum then has subtracted from it some costs: typically cost to serve, cost to market, maybe cost of goods sold, etc. 

3) This net revenue is then converted into an annual average amount and depicted as a cash flow. 

4) These cash flows are assumed to continue into the future and diminish over time (depending on durability, sales cycle, etc.) often decreasing arbitrarily by say 10% each year until they are effectively zero. 

5) These (future, diminished) cash flows are then summed up and discounted (usually by Weighted Average Cost of Capital) to get their net present value. 

6) This NPV is called LTV. This calculation is applied to each customer.

Thus each customer has an associated value. The typical use is for marketers to find the “high valued” customers (based on past purchases). These high valued customers get most of the communications, promotions / discounts, marketing efforts, etc. Descriptive analysis is merely about targeting those already (on average) engaged, much like RFM. 

This seems to be a good starting point but, as is usual with descriptive analysis, contributes nothing about WHY. Why is one customer more valuable, will they continue to be? Is it possible to extract additional value, but at what cost? Is it possible to garner more revenue from a lower valued customer because they are more loyal or cost less to serve? What part of the marketing mix is each customer most sensitive to? LTV (as described above) gives no implications for strategy. The only strategy is to offer and promote to the high valued customers.

SURVIVAL MODELING: AN INTRODUCTION

Survival modeling came from bio-statistics in the early 1970s where the subject studied was an event, death. Survival analysis is about modeling the time until an event. In bio-statistics the event is typically death but in marketing the event can be response, purchase, churn, etc. 

    Due to the nature of survival analysis, there are a couple of characteristics that are endemic to this technique. First, the dependent variable is time-until-an-event, so time is built into the analysis. Second, survival analysis accounts for censored observations. A censored observation is either an observation that has not had the event or an observation wherein there is no knowledge of having the event or not--but we do know at some point in time that observation has not had the event.

    In marketing it’s common for the event to be a purchase. Imagine scoring a database of customers with time-until-purchase. That is far more actionable than, from logistic regression, probability of purchase. Thus, survival modeling takes into account time until the event and includes information about those that have not had the event (yet).

PREDICTIVE LIFETIME VALUE (USING SURVIVAL MODELING)

How would LTV change using predictive analysis instead of descriptive analysis? First note that while LTV is a future-oriented metric, descriptive analysis uses historical (past) data and the entire metric is built on assumptions about the future applied unilaterally to every customer. 

Prediction will specifically thrust LTV into the future (where it belongs) by using independent variables to estimate the next time until purchase. Since the major customer behavior driving LTV is timing--and secondly, the amount and number of purchases--a statistical technique needs to be used that predicts time until an event. (Ordinary regression predicting the LTV amount ignores timing.)

Survival analysis is a technique designed specifically to study time until event problems. This removes much of the arbitrariness of typical (descriptive) LTV calculations.

So, what about using survival analysis to see which independent variables, say, bring in a purchase? This decreasing time until purchase tends to increase LTV. While survival analysis can predict the next time until purchase, the strategic value of survival analysis is in using the independent variables to CHANGE the timing of purchases. That is, descriptive analysis shows what happened; predictive analysis gives a glimpse of what might CHANGE the future.

Strategy using LTV dictates understanding the causes of customer value: why a customer purchases, what increases / decreases the time until purchase, probability of purchasing at future times, etc. Then when these insights are learned, marketing levers (shown as independent variables) are exploited to extract additional value from each customer. This means knowing that one customer is say sensitive to price and that offering a discount will tend to decrease their time until purchase. That is, they will purchase sooner (maybe purchase larger total amounts and maybe purchase more often) with a discount. Another customer prefers say product X and product Y bundled together to increase the probability of purchase and this bundling decreases their time until purchase. This insight allows different strategies for different customer needs and sensitivities, etc. Survival analysis applied to each customer yields insights to understand and incent changes in behavior. 

This means just assuming the past behavior will continue into the future (as descriptive analysis does) with no idea why, is no longer necessary. It’s possible for descriptive and predictive analysis to give contradictory answers.  Which is why “crawling” might be detrimental to “walking”. 

If a firm can get a customer to purchase sooner, there is an increased chance of adding purchases--depending on the product. But even if the number of purchases is not increased, the firm getting revenue sooner will add to their financial value (time is money).

Also a business case can be created by showing the trade-off in giving up say margin but obtaining revenue faster. This means strategy can revolve around maximization of cost balanced against customer value.

The idea is to model next time until purchase, the baseline, and see how to improve that. How is this carried out? A behaviorally-based method would be to segment the customers (based on behavior, transactions, responses to marcom, etc.) and apply a survival model to EACH segment and score each individual customer.

Using this technique gives two incredible strategic insights. 1) Each customer’s next (and all subsequent) purchases can be predicted. That is, the database can be scored with time until the purchase event. 2) Because this is a regression equation it can be discovered (using the coefficients on the independent variables) what makes a purchase happen sooner, that is, a customer’s LTV can be changed! 

As a simple example, say a segment is sensitive to price. The coefficient on net price in a survival model is 0.256 and a particular customer purchases on average every 55 days. This means as the price increases, the time until purchases goes out, that is, happens later (the coefficient is positive). This is very lucrative information. If you want to increase this customer’s value (and you do) you can make their average time until purchase decrease, that is, the customer purchases sooner. In this example, if price is lowered by $1 (say from $10) the time until purchase goes from 55 days to 38.95 days. (e^0.256 – 1 = .29175 and that times 55 is 16.046 and 55 – 16.046 = 38.95days.) So given a discount of 10% (from 410 to $9) the time until purchase decreases by 29.175%, and the amount of the purchase can be used to calculate ROI.

CONCLUSION

While it took some time for survival analysis to move from bio-statistics into marketing, it has now become an important tool in marketing analytics. Much of this is because WHEN an event happens is typically more important to marketers than the PROBABILITY of an event happening. Marketing is about choice and that choice happens in time.