How Linearity tricks us into making bad Product decisions

And how to become a non-linear thinker

photo of a spiral starewell
photo of a spiral starewell
Photo by Fabian Fauth

All of us know that most plants need water to survive. i.e. if you don’t water your plants, they die. But that inference is not exactly accurate. Here’s what really happens:

If you don’t give the plant any water, the plant dies.

With too little water, the plant grows for a little but then dies eventually

You water it just right, the plant flourishes and grows.

You Water it too often, the plant starts wilting.

Too much water, the plant dies

In fact, the relationship between watering a plant and its growth is Non-Linear. And just water isn’t enough, some amount of sun is also involved.

A non-linear plot of plant growth vs Water & Sunlight
A non-linear plot of plant growth vs Water & Sunlight

It’s the same with food and animals (or humans). In fact, it turns out that some of the most important system relationships in our lives are non-linear.

Understanding Non-Linearity

Of course, if you love gardening — you already understand this non-linear relationship. And since you understand this relationship — your decisions on when to water your plants are most likely spot on, based on simple intuition.

Translate this to Product Management. The job of a Product Manager is to identify and understand problems that are worth solving and build solutions that solve these problems. And if you are building products, understanding and recognizing non-linearities in everyday systems and human behavior renders you with the ability to make high-quality decisions.

But here is the problem, our brains are naturally wired to default to intuitive, linear thinking often called “Linearity Bias”.

Linearity Bias is the assumption that a change in one quantity produces a proportional change in another. It is a cognitive bias that arises as a result of how our brains naturally perceive the world around us.

And our affinity to expect output changes proportional to inputs can lead us to make some really poor decisions.

Here is a familiar example.

As Product Managers, we conduct customer interviews — we uncover from our customers a burning problem that they said they have. They say they’d pay for any solution that solves the problem.

Having found a burning problem to solve for our customers, we prioritize backlogs, build the product, and ship it. It’s going to sell like hotcakes.

But it doesn’t. It doesn’t take off as we expect it to.

Didn’t the representative customer set we interviewed said it was a burning problem?

So what happened?

You guessed it. It's because of the non-linearity between what people say and what they do.

To illustrate it further, consider this.

If we plot a graph of people’s privacy concerns vs personal information they share elsewhere — what do you think the graph would look like?

Our brain immediately says — the more privacy concerns that people have, the less information they must share! Its appears to be a linear relationship like the graph below.

a linear plot of privacy concerns vs information people share
a linear plot of privacy concerns vs information people share

That sounds perfectly logical — but that’s also classic linear bias in action.

In reality, when researchers surveyed people on how seriously they took privacy (0–5 point scale, 5 being very concerned), and then asked how many loyalty cards they possessed ( The card, being a proxy for personal information they are willing to share)

But researchers found that only people that were VERY concerned about privacy took actions to protect their information. Most others despite saying that they cared about privacy, didn’t take any steps to protect their information. So did they really care?

a non linear plot of privacy concerns vs loyalty cards they possess
a non linear plot of privacy concerns vs loyalty cards they possess

Imagine if you wanted to build a product that would appeal to people that really cared about privacy. Your total available market just shrunk significantly due to this non linearity. You’ll perhaps make different decisions. This is how non-linearity can have massive implications.

Avoiding Linear Bias and Spotting Non-Linear systems

1. Check your biases

The most effective way to spot non-linearities in systems is to look for them. Checking our assumptions before making an important decision is the best way to develop non-linear thinking. Start with the decisions that are most important for your product or business and get them right.

Quick Example: If you run a SAAS business with 2 different customer segments — Segment A with a lower retention rate (say 10–15%) and Segment B with a higher retention rate (50–60%).

Assuming both customer segments bring you the same profits — What are you better off focusing on?

  1. 100% improvement in customer retention for Segment A that’s struggling to retain customers?
  2. 30% improvement in the Segment B that’s doing well?

It maybe tempting to think “hey that 100% improvement definitely looks better!”

But we’d be wrong . A 30% increase in retention for Segment B is in fact is a better ROI project.

Here’s what the relationship between Customer Lifetime Value and retention rates actually looks like. Again, its a non-linear relationship.

So if you are a Product Manager with a limited budget to work with, your resources are better spent trying to improve the product experience even further for Segment B.

2. Recognize what other variables may be at play

Non-Linearities occur because there are often other variables at play than the ones we are considering.

For instance, why might somebody that cares about user privacy a lot sign up for loyalty cards and Frequent flier points? After all Loyalty programs require that you divulge a lot of personal information — the companies know who you are, where you live, what you buy, where you like to travel to etc.

Its because there are other variables such as a person’s income, age, demographics, cultural attributes at play. People might say care they about privacy — but most are also okay to trade that off for Loyalty Program discounts at their favorite grocery store or airline miles.

These variables can affect an otherwise linear relationship, and create non-linearities.

3. Broaden your perspectives & Stay away from Averages

Sometimes we are too close and too personally invested in things, and while that is generally a good thing, being too close to something can provide the illusion of linearity.

near and far perspectives of a rocket launch trajectory
near and far perspectives of a rocket launch trajectory

So when making decisions on critical projects embrace diversity. Diversity in ideas and opinions help broaden perspectives and see the things from different view points. It helps uncover non-linearity in systems.

As you build experience and expertise, your cognitive horizons are broadened. the downside of this is that it takes time. For new Managers, a great way to accelerate learnings is to develop critical thinking and reasoning skills. Ask a lot of questions, and then ask some more.

Finally, train your mind to not make decisions based on Averages. Averages smoothen out kinks in the data, and while they are helpful to make broad statements — they must not be used to make critical decisions. Learn to embrace the details, because that’s where all the truth is.

Common, but Counterintuitive

As you build products or even a business, it worth knowing some common scenarios that seem easy but are actually counterintuitive. Knowing these right off the bat will help you make much better decisions. I’ll share two of my favorite ones.

1. Growing Profits

Assume your business produces 100,000 widgets. Fixed costs are $50K, and the variable cost to produce each widget is 50 cents. Say you sell each widget at $2.00. Your profits on each widget then is $1.00

Do the math and you’ll see that if you double your units to 200,000 your profits on each unit increase to $1.25.

At this point you might think, why stop there? Why not produce even more units, spread your fixed costs over more units, and grow profits?

Do the math again — and you’ll find that while you make 25 cents more when you double production from 100,00 to 200,000, but if you increase production from 200,000 to 400,000 you are only making 12 cents more in profits. Double production to 800,000 and you are making only about 6 cents more.

Bottom line? As you increase production — the growth in profit per unit is actually slowing down.

The point here is that linear bias will tempt us to see increasing production as a way to increase profits — and it does increase profits, albeit inefficiently. On the other hand, pricing increases may be a much more efficient way to increase profits.

non linear graph of profits / unit slowing down as units produced increases
non linear graph of profits / unit slowing down as units produced increases

2. Customer Satisfaction

Assume you operate in a hyper-competitive market, where customers are very price sensitive and there is little to no product differentiation. Your company’s customer satisfaction scores are similar to your competitors. Would you invest in further increasing your customer satisfaction scores to drive loyalty towards your brand?

Most managers would estimate that there is little to no ROI on spending money to increase customer satisfaction scores, as there is very little loyalty. There is a general consensus that it does not pay to make additional investments to try to satisfy customers in a hyper-competitive market.

But this very interesting research shows that in highly competitive industries, customer loyalty increases slowly at first, but then climbs up exponentially. This means once a customer is completely satisfied — they become super loyal to your product.

Non- linearity tricked us again!

It turns out that the more competitive an industry is — there is in fact tremendous value in investing in programs to totally and completely satisfy customers — it turns them into your die-hard loyalists.

To summarize, Understanding and acknowledging non-linearities in systems is fundamental to making better decisions and creating value where others see none. Making higher quality decisions has tremendous upsides, both professionally as well as personally. So embrace it as best as you can.

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