An Example: Applying A Life Table To A Problem

How often do we launch new products, brands, or services, only to realize that sales are not meeting expectations?

Expectations are a challenge, because we have to make an educated guess as to what might happen in the future.

Within a few months, we actually have enough data to make another educated guess ... we can predict the annual repurchase rate for a product, brand or channel.

In this case, our brand launched a new product. After six months, the product is not meeting expectations. Our CEO asks us to understand if the small number of customers who purchased this product are "loyal" to the product.

We ask our SAS programmers or information technology experts to run a query for us. We identify every customer who purchased our new product, to date. For each purchase, we bring along the customer_id, as well as the order date. The dataset is sorted by customer_id and order date.

Next, we re-shape the datasets, adding a column for the order date of the first purchase of merchandise from this product classification for a customer. We then scan the database. Any customer who ordered a second time has the order date for the second purchase put into another column.

If I purchased two times, my row of data looks something like this:

• Kevin .......... Date1 = 20080115 .......... Date2 = 20080507

If I purchased just one time, my row of data looks something like this:

• Kevin .......... Date1 = 20080115 .......... Date2 = NULL.

Now we need to re-shape the dataset one more time. In this case, we calculate how many months pass between the first and second purchase. If no second purchase occurred, we instead calculate the total amount of time that passed. If no second purchase occurred, we create a new variable that tells us no second purchase occurred. If I purchased two times, my row of data looks something like this:

• Kevin Months = 04 .......... Second Purchase = YES

If I purchased one time, my row of data looks something like this:

• Kevin Months = 04 .......... Second Purchase = NO

We're almost there! Now we summarize the dataset, creating one row per each unique value of months between purchases. We sum the number of customers who purchased after "x" months. We also sum the number of people who went "x" months, through today, and have yet to purchase. These customers do not get included in the analysis after "x" months pass. The resulting life table is included in the image at the start of this post!

In the six months since launching the new product, just under twenty percent of customers buying the product chose to purchase the product again.

We can extend this relationship from six months through a year. Take a peek at the modeled relationship below:


Notice the nice, smooth relationship exhibited by the data. The relationship indicates that, after twelve months, about 24% of customers will order the product again, putting the product squarely in "Acquisition Mode".

To answer the CEO's question ... it does not appear that customers are loyal to this product. It appears that if this product line is going to grow, it will grow by attracting new customers interested in a one-time purchase of this product line.

With as little as three months of purchase information, one can make a reasonably fair assessment of the anticipated annual repurchase rate of this product line.

And that, my friends, is one way that life tables can be applied to real world problems.

Startups And Life Tables

Occasionally, I am asked what to do with a startup product, brand, or channel. In other words, you launch a new product, and after four months, you want to get an idea what the annual retention rate might be for customers purchasing from this new product.

This is where you use a life table to guess at what might happen.

The life table tells you the probability of a customer purchasing again in your embryonic product line. Once you have the details, you estimate the corresponding annual rate.

Later, I'll include a case study on this topic.

Multichannel Forensics: Online/E-Commerce Startup Example For Venture Capitalists And Founders

My work is increasingly focused on internet startups, focusing on the challenge of forecasting long-term sales based on almost no customer purchase/usage history.

I try to keep things simple. Here's a business that has been in existence for less than a half year. By recency, here is the probability of a customer buying in any given month.

Recency	Custs.	Buyers	Resp.
1	1,239	88	7.1%
2	812	47	5.8%
3	522	26	5.0%
4	279	12	4.3%

Given the limited amount of information available here, let's take a wild guess at incremental response rates for twelve months of recency.

Recency	Custs.	Buyers	Resp.
1	1,239	88	7.1%
2	812	47	5.8%
3	522	26	5.0%
4	279	12	4.3%
5			3.7%
6			3.2%
7			2.8%
8			2.5%
9			2.3%
10			2.2%
11			2.1%
12			2.0%

Obviously, your guess is as good as mine. We have no idea what will really happen. But it is important to make a guess.

Given that guess, we can estimate a twelve month repurchase rate (using an extension of the life table as described in the Database Marketing book:

• 1 - ((1 - 0.071) * (1 - 0.058) * (1 - 0.050) * (1 - 0.043) * (1 - 0.037) * (1 - 0.032) * (1 - 0.028) * (1 - 0.025) * (1 - 0.023) * (1 - 0.022) * (1 - 0.021) * (1 - 0.020) = 35.5%.

An annual repurchase rate of 35.5% (and the actual rate will be lower, because we average all twelve month buyers, not just following a cohort through a twelve month period) puts this startup in "Acquisition Mode".

Now you might say, "duh, they're a startup, of course they are in Acquisition Mode". And you'd be right. But we're talking about the dynamics this business will need to deal with when it becomes mature, not what it needs to do for the next few years.

The dynamics suggest that if this business survives, its number one focus will always be to aggressively acquire new customers.

Fortunately, there's time to see how the business really evolves. And as the business evolves, these estimates are re-calibrated.

VCs like this information because it gives them tangible data about the long-term trajectory of the startup. If this startup can acquire an ever-increasing number of customers in a cost-effective manner, the startup has potential. Venture Capitalists get an early glimpse into the direction the startup is headed in.

E-Mail Marketing And Conditional Response

My all-time favorite analytical procedure is called the "life table".

I enjoy the methodology so much (in my opinion), that I devoted a whole chapter to the application of the life table in catalog marketing in my Database Marketing Book.

These days, e-mail marketing is tailor-mailed for adaptations of the life table.

In multichannel retailing and cataloging, we're told not to over-mail our customers, as we might damage our reputation with ISPs or damage our reputation with our customers. This is probably good advice. Still, the analytical side of me wants to have the customer tell me when too much is too much. Here's where a modified version of a life table, called "conditional response", can help.

Basically, we ask the question "what is the probability of a customer clicking-through an e-mail campaign to visit your website, given the fact that the customer failed to click-through the past 'x' e-mail campaigns?"

For e-mail marketers in the multichannel world, this is ultimately the core issue. Successful e-mail marketing should cause a customer to want to act (on a website, in-store, over the phone).

So we want to look at the number of times a customer fails to act when receiving e-mail marketing. If a customer failed to act after twenty consecutive e-mail campaigns, what is the likelihood of the customer acting in a positive way on the twenty-first e-mail campaign?

Take a peek at the sample table below:

E-Mail Campaign Performance By Conditional Response
	Action:	Website	Average
Campaigns	(Open Rate *	Conversion	Order	$ per	Opt-Out
Ignored	Click-Through)	Rate	Size	E-Mail	Rate
0 to 4	14.39%	2.43%	$100.39	$0.35	0.53%
5 to 9	10.07%	2.36%	$101.39	$0.24	0.61%
10 to 14	7.05%	2.29%	$102.41	$0.17	0.70%
15 to 19	4.94%	2.22%	$103.43	$0.11	0.81%
20 to 24	3.46%	2.15%	$104.47	$0.08	0.93%
25 to 29	2.42%	2.09%	$105.51	$0.05	1.07%
30 to 34	1.69%	2.02%	$106.57	$0.04	1.23%
35 to 39	1.19%	1.96%	$107.63	$0.03	1.41%
40 to 44	0.83%	1.90%	$108.71	$0.02	1.62%
45 to 49	0.58%	1.85%	$109.80	$0.01	1.86%

In this table, we observe key e-mail metrics by consecutive e-mail campaigns that the customer failed to act upon.

Notice that after saying "no" to fifteen to twenty-four consecutive e-mail campaigns, the customer becomes much less responsive (in this example). This is the stage where the e-mail marketer considers changing strategic direction, because the customer is no longer responsive --- and the table suggests that the customer will become even less responsive in the future.

Catalogers can do the same thing --- measuring how responsive online customers are after saying "no" to the past fourteen catalogs.

So give the tool a try, it's a great way to identify the point where customers "just say no" to you!!