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From Business Intelligence to Bathtub Insights

So you’ve built a website and are doing on-site analytics. You split-test pages to maximize conversions and are getting measurable results from your search engine and social media marketing efforts. You’re able to tell whether an uptick in sales for a particular product is a seasonal change seen every year or perhaps the start of a new growth trend.

The question then becomes: What do you do with that power?

One possibility is to look beyond the goal of collecting conversions and ask, “What larger insights can we get from our online data? What can we learn about our market?” These are the sorts of questions that fall under the domain of “business intelligence“, a term search marketers are likely to hear with increasing frequency. But going from ‘data’ to ‘insight’ requires an understanding of the mechanics driving your business. Without that, it is easy to get lost in the numbers.

Consider that your company runs a subscription-based service, like a dating website or online magazine, and wants to increase the proportion of its subscriber base that are new customers. Subscribership has been steady about 10,000 people (call that number ‘P’) for the past few months. The average subscriber hangs around for 20 months, so you lose 5% of your customer base each month, but you’ve also been gaining 500 new customers per month, so overall your business is neither growing nor shrinking.

But now that the economy seems to be turning around, your boss wants to see some growth and fresh faces at the site. Your current proportion of customers who signed up in the past month is 5%, but your boss would like to raise that to 10% and keep it there, so she increases your advertising budget and tells you to make it happen. Immediately you plow that money into search engine advertising and quickly double your customer acquisition rate.

Now you’re bringing in 1000 new customers per month instead of 500, so that should increase the fraction of customers who are new, right? You had 10,000 subscribers at the beginning of the month, lost 500 as you normally do, and brought in 1000 new ones. So the population of subscribers is 10,500, of whom 1000 are new. The ‘new customer fraction’ (NC_frac) is 1000 / 10500, or 9.5%. Your boss is elated and promises you a bonus if you actually hit and maintain your target. But how likely is that to happen?

Well, let’s say that you do keep pulling in new customers at that elevated rate, 1000 per month. You keep a close eye on your marketing dashboard which shows the NC_frac actually falling from 9.5% in the first month to 9.1% in the second. It goes down to 8.7% in the 3rd month and to 8.4% by the 4th. Your bonus is quickly slipping away. What’s going wrong here?

In month 5 you pull out all the stops. You email former subscribers and offer a special deal to win them back again. Your new efforts are only half as successful as the old ones (diminishing returns and all), bringing in an additional 250 subscribers a month, for a total of 1250 per month. But again you watch the fraction of subscribers who are new customers (NC_frac) go from 9.8% to 9.3% to 8.8% over the next few months. What in the world do you need to do to hit and maintain your 10% goal?

Think of your existing subscriber base as a bathtub full of people (And what an exciting bathtub that would be!). Every month, some number of new customers flows in (I) and some proportion of your existing customers flows out (nP). The difference between those two numbers (I-nP) determines how much the number of people in the bathtub rises or falls over time. This relationship is represented both mathematically and visually below:


(In fact, MIT Sloan professor John Sterman playfully refers to this branch of management science as “bathtub dynamics”, though it’s more commonly called “System Dynamics” or “business dynamics”.)

The population of subscribers will remain constant (i.e., ΔP/Δt will be 0) when nP = I, or P = I / n. The proportion of subscribers who are new customers (NC_frac) is simply the past 30 days’ worth of ‘I’ divided by P and we can see from nP = I that this value will tend toward n, your average monthly customer loss fraction.

The fundamental reason you are drifting away from that 10% target is that the proportion of customers who are new depends, in the long run, on the customer loss rate, not the customer acquisition rate. Generating more new customers only temporarily raises the fraction of customers who are new.

Only by reducing the average lifetime of a customer to just 10 months (something that might not be desirable at all) can you sustainably increase the percentage of subscribers who are new to 10%. Trying to hit that target when your customer loss rate is 5% is simply fighting the physics of your business. (This might not be obvious from staring at a spreadsheet of metrics each week, but hopefully it is clear from examining the ‘bathtub dynamics’ above – either visually or mathematically – without even needing to see any specific data.)

In this example, I’ve only considered your existing customer base, but the concept can easily be extended to the entire conversion funnel by adding a bathtub ‘people actively shopping’ for a dating site / online magazine upstream (or even the bathtub of ‘former customers’ downstream). Perhaps mapping out the entire network of ‘bathtubs’ in your business, and the pipes between them, will help you readily turn online marketing data into business intelligence and insights.

About Bradd Libby

Bradd easily becomes obsessed with small details. He can barely make it through a conversation without drawing a graph of something. He lives in the woods on the side of a hill in Norway. Bradd doesn't willingly wear shoes. He makes maps of places that don't exist. He picks up small shiny things he finds on the ground. He devolves into violent shouting matches with himself. He takes things apart to find out how they work but then can't figure out how to put them back together again. He also writes at Search Engine Land [7], Search Engine Journal [8] and his personal blog [9].