Linear thinking in a non-linear world.

Imagine that you are responsible for the customer retention strategy for a large online business. Being a smart strategist, you start by segmenting your customers and find two interesting segments to pursue further — let’s call them Segment A and Segment B.

Here are some facts about the two segments:

  • Both segments currently contribute $10M each to total profits.
  • Retention Rate for Segment A is 10% and for Segment B is 40%.

Now you have a fixed budget to run activation campaigns that can either increase the retention rate of Segment A from 10% to 40% OR of Segment B from 40% to 60%. Let’s assume that it is possible to achieve this increase in both the segments and the effort and the cost required are the same.

Which segment would you choose?

Most managers will pick Segment A assuming that a 30% increase in the retention rates would deliver more value to the business compared to a 20% increase in Segment B. Plus, at only a 10% retention rate, Segment A seems to need more attention anyway. Right?

If you thought like most managers, then you would be a victim of the Linear Bias, a term used to define the bias in drawing linear relationships between variables and outputs, where no such relationship exists, and often leads to decisions that drive sub-optimal outcomes. Let me explain with the illustration below:

Let’s first calculate the impact of Retention Rate on CLV using the formula below:

Based on this formula, you can calculate the impact of investing in Segment A vs. Segment B; The results may surprise you. While going from a 10% retention to 40% for Segment A increases the total CLV by $5.6M, improving the retention for Segment B from 40% to 60%, increases the total CLV by $8.3M, almost 50% more CLV for a 33% less uplift in retention rate (when compared to Segment A). Seems counter-intuitive? (note: ignoring the discounting of future value to keep it simple)

There is an explanation: as retention rates rise, customer lifetime value (CLV) increases gradually at first and then rises steeply and thus, CLV is a non-linear function of retention rate. Because of the Linear Bias, most companies focus on customers who are likely to churn rather than customers who are more likely to stay and may just need a nudge to convert. It’s more profitable to target the latter with retention marketing strategies than to focus on the former.

In conclusion, linear thinking leads managers to prioritise opportunities that show a higher increase in the variable input (retention rates, Segment A above) but yield lower returns (CLV) when compared to those that deliver much higher yields despite a smaller increase in the variable input (retention rates, Segment B).

How can you avoid this bias as a manager? Use this three-step guide:

  1. Never Assume that there is a linear relationship between the variables and the outcome you are optimising for. Always try to estimate 3–4 data points to understand the relationship, as any fewer data points could mislead you.
  2. Visualize the relationships through a simple chart as above. Visualization not only helps you to see the kind of non-linearity at play (there are 4 types), but also to identify the tipping points where outcomes change dramatically and deliver extraordinary returns (for example, increasing the retention rate from 60% to 80% can almost triple your CLV i.e. $15M to $40M).
  3. Focus on what creates the maximum impact by choosing the strategy that delivers the highest profits. As managers, our job is to prioritize and re-prioritize our actions to focus only on those activities that deliver the maximum financial value, everything else is just a distraction.

If you wish to read more about non-linearity, then I highly recommend this HBR article, my inspiration for this post.

Originally published at on October 17, 2017.

On a mission to connect the dots amongst data, emotions & randomness. Love using tech and data to deliver joy. Currently at Stanford chasing the next big thing.