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How to Project Customer Retention for a Subscription Business August 6, 2012

Posted by seanrmoran in 2012, ltv, models, subscription.
Tags: , , ,

We’ve posted before about how to estimate lifetime value (“LTV”) for an ecommerce business and for a subscription business, and have provided a sample cohort analysis for each (ecommerce and subscription).  This is one of the most important factors in understanding unit economics.

Recently, Eric Liaw sent us a very interesting May 2006 paper entitled “How to Project Customer Retention”, authored by marketing professors Peter Fader (Wharton) and Bruce Hardie (London Business School) and published in the Journal of Interactive Marketing in 2007.  In it, the professors explain how previous attempts to project retention rates using line-fitting regression models failed, even after introducing quadratic or exponential functions.  Since we had advocated essentially using an exponential line fit for subscription LTV estimation, we figured it was worth reading.  The authors show that exponential form fitting is too conservative and underestimates actual retention rates.

Professors Fader and Hardie decide to start from scratch with a simple assumption: what if each customer has a fixed probability of renewing his or her contract at the end of each period?  So if I’m a big movie fan, let’s say I’m 80% likely to renew Netflix each month, but you’re caught up on Breaking Bad and only 30% likely to renew each month going forward.  Probability varies by customer, but each customer’s rate remains constant over time.

It turns out that, based on probability theory, this simple assumption implies that the distribution of renewal rates can be characterized by a statistical model.  Over time, the difference in each individual’s probability to renew suggests that individuals with lower renewal probabilities will generally drop out before those with higher probabilities.  Incidentally, this also explains why incremental retention may appear to improve over time, when it’s actually a likely side effect of the remaining customer mix.

After some mathematical gymnastics, the authors unveil the model they’ve derived: the shifted-beta-geometric distribution.  The authors tested the model by using the first seven years of data from a given sample to project renewal rates at the end of the final five years in the sample.  The model proved to be quite accurate, within 3% of actuals, and much better than linear or exponential form fitting.

A few quick caveats: this model is appropriate only when the data reflects a discrete renewal period, such as a defined monthly or annual cycle.  Also, the model should be reserved for projecting behavior in contractual settings, such as subscription renewals and other observable customer exit points, rather than ecommerce or other businesses where the customer can remain dormant for long periods between orders.

We’ve uploaded a spreadsheet here, along with directions for how to use it yourself.

Hope this is helpful.  We look forward to hearing from you regardless, but especially if:

1)    You use the model and have any feedback on results

2)    Your company uses any other methods to capture, analyze, and project customer retention

3)    Your innovative company achieves valuable unit economics.  As previously mentioned, we like to see LTV / Customer Acquisition Cost > 2.5 and payback periods under 12 months.

If you found this post useful, follow us @lightspeedvp on Twitter.

Forecasting ad sales for web startups April 3, 2008

Posted by jeremyliew in ad networks, advertising, business models, models, start-up, startup, startups.

Andrew Chen has a good post on how to forecast advertising for web startups:

The right way to model out inventory is a number of equations – I’ll pretend that a site has two types of inventory, their “brand” stuff and their “direct response” (aka remnant) inventory:

Brand revenue = # campaigns sold * average campaign size * brand CPM
Direct response revenue = (total impressions – brand impressions) * remnant CPM
Total revenue = Brand + remnant revenue

In an actual forecast, you could get a ton more detail in the brand revenues side, since what you really care about is the # of ad sales people you have, how many campaigns they’re selling per quarter, the size, etc. Again, think of this as an enterprise sell, and treat it as such.

Essentially, he suggests that brand advertising is a function of the size and efficiency of your direct ad sales force (and is demand constrained) while remnant advertising can go to networks and is supply constrained.

As Ed Sim notes about a direct ad sales force:

… many entrepreneurs underestimate the direct capital and management costs necessary to build such a team. In many ways, building a direct ad sales team is similar to building an enterprise sales team. These thoughts may seem quite basic to you but here they are nevertheless. First, don’t ramp up your sales team too quickly until you have a product to sell. That means if you don’t have scale or enough eyeballs you are better off using Google Adsense. If you don’t heed this advice you may quickly burn yourself out of business. Secondly, I know that many startups may not know what kind of ad units to sell but be careful of not having a standard product list or rate sheet when you go out to the market.

This advice can be difficult to follow in a new market where there are no standard product lists, which is why new forms of advertising are hard.

An excellent excel model of viral growth March 10, 2008

Posted by jeremyliew in business models, churn, models, retention, social media, viral, viral marketing.

Last week Andrew Chen wrote an excellent post about the growth and potential decay of viral apps. Rather than just focusing on the elements of viral growth, Andrew also took into account the declining likelihood of an accepted invitation as you saturate a population, and the impact of churn. He provided a useful model to social media founders who are trying to estimate their growth, and what can go wrong when a viral app “jumps the shark”:

shark fin

He notes:

* Early on, the growth of the curve is carried by the invitations
* However, over time the invitations start to slow down as you hit network saturation
* The retention coefficient affects your system by creating a “lagging indicator” on your acquisition – if you have good retention, even as your invites slow down, you won’t feel it as much
* If your retention sucks, then look out: The new invites can’t sustain the growth, and you end up with a rather dire “shark fin.”

I think this is a very useful model, but that it doesn’t quite predict what we typically see in real life. Rather than dropping to zero, failed viral apps typically hover at a steady level much lower than their peak. Since Andrew made the model available under “copyleft”, I made a small edit to his model. Rather than treating churn as a constant percentage of users in each time period, I treated it on a cohort level, with a higher churn rate in the early periods and lower churn as time goes on. This is similar to the churn profiles seen for subscriptions businesses such as AOL’s ISP business. (I was at AOL from 2002-2005 as SVP of Corporate Development, and then as GM of Netscape.) This model better matches active user graphs that we typically see for failed viral apps.

churn by cohort

If you’re interested, the model is available for download here. Viral growth assumptions are in the yellow cells on the “viral acquisition” tab and churn assumptions and output are on the “user retention” tab.