How to Persuade with Numbers
Imagine you’re asked a question. Give the wrong answer and you’re thrown to your death. Give the right one, and you live a long, happy life filled with everything you could possibly want or need.
Sounds theoretical, but this actually happened to an astrologer in the court of France’s King Louis XI.
Here’s what happened. Several weeks before, the astrologer predicted a woman would die in 8 days. Sure enough, eight days later the woman died.
This accuracy frightened King Louis, so he decided the astrologer must die.
The king devised a plan. He told his guards at his command to take the astrologer and throw him out a castle window to his death.
But before he gave the order, King Louis decided to ask the astrologer a final question. “You claim to understand astrology and to know the fate of others, so tell me what your fate will be and how long you have to live?”
The astrologer looked at King Louis and said, “I shall die just three days before Your Majesty.”
King Louis felt a sudden change of heart. Instead of killing the astrologer, the king treated him for years with the best food and doctors in France.¹
The astrologer had followed the first rule of persuading with numbers — Always frame the number from your audience’s perspective.
At work, we often use numbers to make our point. (Or lots of numbers in small font on PowerPoints). We’re drawn to the belief the more numbers you present, the better. We get caught up in the logic of our facts and forget a key principle.
Persuasive numbers must appeal to your audience’s emotions first, then to their logic. But how do we make numbers more emotional? Here are three principles to help.
We feel loss more than we feel gain
People put a lot of faith in doctors and their judgment. We think doctors are rational and make decisions based on facts and evidence. But do doctors make different decisions based solely on the presentation of data?
Researchers asked a group of doctors to evaluate a lung cancer case and recommend either surgery or radiation treatment. The surgery’s risk was stated differently to the doctors.
Half read the surgery outcome as, “The one-month survival rate is 90%.”
The other half read, “There is a 10% mortality in the first month.”
Rationally it’s the same information. But 84% doctors who read the surgery’s “survival rate is 90%” picked surgery as the best treatment. Only 50% picked surgery when they read the “10% mortality” rate.²
Why the difference? The doctors felt more emotional impact when reading about the loss implied by the mortality rate.
We think people, not percentages
Quick test: which headline is more memorable?
“26% of Americans Think The Sun Goes Around The Earth, Survey Says.”
“1 In 4 Americans Think The Sun Goes Around The Earth, Survey Says.”³
Most people chose the second headline. It’s less abstract and more relatable. We immediately start to think, “Who do I know dumb enough to think that?” When several people quickly come to mind, we click the link to confirm what we’ve always thought about them.
By presenting it as 1 of 4, our minds easily personalized and internalized the information.
But use caution with this approach.
One study asked University of Washington students to rank which cancer was more dangerous:
Cancer with a mortality rate of “1,286 out of 10,000.”
Cancer with a mortality rate of “24.14 out of 100.”
Most picked the first cancer as more dangerous. If you stop and do the math, you’ll see the first cancer has a 12.86% mortality rate versus a 24.14% mortality rate.
These students weren’t bad at math. Intuitively it feels like “1,286 out of 10,000” is the larger number and riskier.⁴
We don’t identify with statistics
Our mind has difficulty processing abstract information. We have no frame of reference for large numbers like millions and billions unless we bring it down to the individual level. As Mother Teresa said, ‘‘If I look at the mass, I will never act. If I look at the one, I will.’’
Instead of focusing on the large number, start with one. Research into charitable giving found people more likely to give when they read:
“Any money that you donate will go to Rokia, a 7-year-old girl from Mali, Africa…”
Then when they read:
“Food shortages in Malawi are affecting more than three million children…”
When you know the story of Rokia, it’s much easier to think of three million children like her. This is called the “identifiable victim” versus the “statistical victim.”⁵
But this doesn’t just apply to numbers about people. It can also apply to any large number you can break down so it’s relatable at the individual level.
For example, at a large manufacturing company a manager had to explain the need for bulk purchasing to save money. Not a sexy topic.
But he broke it down to the individual level. He found all the different prices they paid for work gloves. Then in a conference room, he covered the table with 400 gloves all with different price tags. Managers and employees now could see the all various prices paid for the same glove.⁶
Now it was easy to understand the savings from the bulk purchasing plan. 400 gloves proved more persuasive and memorable than any spreadsheet detailing millions in savings.
Underlying all these examples is one theme. To persuade with numbers you must first appeal to emotions, and then logic. But it’s difficult at first to do this well. You’re the expert because you love the details about the topic.
But you need to prove to the rest of the world why they should care about it, too.
Remember, we feel loss more than we feel gain. We think people, not percentages. We don’t identify with statistics.
Luckily, the world is not full of people who love numbers (we’re not the best party guests). It’s helpful to have someone normal act as a sounding board. This person can be a spouse, friend, coworker, or neighbor. The key is that they’re a normal person.
Once you follow the tips above and create something you think is persuasive, run it by them. Ask how it makes them feel and how memorable it is. This feedback will improve your persuasion at work.
- Detailed in Robert Greene’s book 48 Laws of Power, page 85–86.
- Kahneman, Daniel Thinking, Fast and Slow, page 367 paperback
- NPR, “1 In 4 Americans Thinks The Sun Goes Around The Earth, Survey Says“, 2/14/2014
- Original study -Yamagishi, Kimihiko — “When a 12.86% Mortality is More Dangerous than 24.14%: Implications for Risk Communication [PDF]“, Applied Cognitive Psychology, Vol. 11, 495–506 (1997) also related in Kahneman, Daniel — Thinking, Fast and Slow, page 329 paperback edition
- Small, Debora; George Loewenstein, & Paul Slovic — “Sympathy and callousness: The impact of deliberative thought on donations to identifiable and statistical victims [PDF]“, Organizational Behavior and Human Decision Processes, 102 (2007) 143–153
- This story is described in greater detail in Chip and Dan Heath’s book, Switch: How to Change Things When Change Is Hard, pages 12–14.