business case

Here’s Why Your Business Case Numbers Are Falling Flat

What if I told you I had a vaccine for a potentially deadly virus. Would you take it?

Before you respond, what if I told you the vaccine carried a risk that 0.001% of people who took it will suffer a permanent disability. 

How would you feel about getting vaccinated?

Setting those feelings aside for a moment, suppose I told you that one out of every 100,000 people like you who get the vaccine will suffer a permanent disability.

Have your feelings about getting vaccinated changed?

According to Nobel Prize winner and author of the bestselling book Thinking Fast and Slow, Daniel Kahneman, they should!

While the two statistics cited in these examples are mathematically equivalent, the second one produces a vastly different emotional response because of the more vivid imagery it conveys. 

Picturing 0.001% of anything is a difficult task for our minds. As a result, we tend to underweight the impact of the associated result and the risk appears small. However, picturing one person like you becoming permanently disabled is a far easier task for your mind. As a result, the imagery, emotional impact, and perception of risk is much greater.

The psychological principle behind this phenomenon is known as denominator neglect and its incredible impact applies equally to how you present data and statistics in your business case during the sales process.

The impact of Denominator Neglect

To highlight this impact of how business case data is communicated, consider another example Kahneman shares. You have the choice of picking a marble from one of two jars that sit in front of you. If you pick a red marble from the jar you select, you win a prize. While you can’t see inside either jar, I tell you that:

Jar #1 contains 10 marbles, of which 1 is red.

Jar #2 contains 100 marbles, of which 8 are red.

Which jar would you prefer to pick a marble from?

Of course, you realize that the chances of picking a winning red marble are 10% in the case of jar #1 and 8% for jar #2. But in laboratory experiments, 30-40% of participants chose to pick from jar #2! In fact, I’ve posed the very same questions to participants in my training programs and the results have been equally surprising (or perhaps not so).  Why? Because the principle of denominator neglect tells us that those participants focused on the number of red marbles (the numerator of the probability fraction), letting visions of the number of non-red marbles (the denominator) drift into the background. 

Incredibly, the same principle of statistical bias can also work when the probabilities are reversed!

In another study, people who saw information about ”a disease that kills 1,286 people out of every 10,000” assessed its risk as being higher than “a disease that kills 24.14% of the population”, even though the first description represents a statistically lower risk of death.


Social commentary: During the pandemic, this same principle was one of the reasons why COVID-19 statistics induced so much fear. The rapid appearance of 4,000 cases in a given country certainly sounds more alarming than saying that 0.0067% of a population became infected. 


Crafting your business case for maximum impact

In the past, I’ve spoken about the critical role that connecting with your customers on an emotional level plays when it comes to converting modern buyers. I’ve also covered how using data can help produce that emotional contrast in the mind of our customers. After all, if your goal is to move someone from their position to yours, it’s important for your business case to help them understand the difference between their current state and the potential future state your solutions can help them attain.

But given what you now know about denominator neglect, consider how you might position the quantifiable value of that future state.

For example, suppose that your solution can automate a manual, time-consuming business process for your customer. In this case, you might describe the benefits of your solution as an efficiency gain. Which one of the following two value propositions feels more compelling?

  1. Our solution can increase your efficiency by 10%
  2. Our solution can save you 20 hours per month.

Assuming these two options are mathematically equivalent, both convey the value of time savings. But the second option produces more emotional contrast in our minds because we can more vividly picture what we could do with 20 hours of extra time versus a more abstract 10% gain.

Consider a more direct demonstration of denominator neglect. Suppose your solution could help produce quantifiable cost-savings for your customers. Which one of the following two value propositions feels more compelling?

  1. Our solution can save you $3,000 per week
  2. Our solution can save you $312,000 over the next two years.

In this case, there are no percentage statistics and both value propositions represent mathematically equivalent hard dollar cost savings over time. Yet, the larger saving illustrated in by second produces a more compelling emotional reaction.

To be clear, in each example, both options convey quantifiable value which means that either would be preferable to a high-level statement devoid of data such as, “our solution can save you time and money”. However, by paying mindful attention to how you represent that data, you can enhance that all-important emotional response.


So the question is, what simple tweak might you make to your solution’s value proposition or business case to make it more emotionally relevant and compelling to your customers?


BONUS VIDEO: How to AMPLIFY your business case numbers!

BONUS VIDEO: How to supercharge your pitch with data

Subscribe for Cerebral Selling content updates and tips!

We promise never to send you junk or share your email! Just helpful sales insights.

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

0 replies

Leave a Reply

Want to join the discussion?
Feel free to contribute!

Leave a Reply

Your email address will not be published. Required fields are marked *