Data can help us understand the world around us. Equally, numbers can be forgettable or simply too hard to relate to - even for those who love math and/or have the training and patience to look deeper.
Stanford Graduate School of Business professor Chip Heath and writer Karla Starr's book Making Numbers Count is a guide to making numbers relatable and sticky.
From presenting data in a way that makes people care about it to scaling numbers to human size and pegging them to examples, Heath and Starr share scenarios to explain ways to make numbers memorable.
To be sure, we have come across some of these solutions before. For example, we've all read descriptions of the size of a festival arena in terms of the number of football fields it might fit.
Heath and Starr push these comparisons and examples further. In this email interview, for example, they start by explaining how rewinding a billion seconds would take us to the beginning of Sachin Tendulkar's cricket career. A million-second rewind, by comparison? Well, that wouldn't even take us to the beginning of this month. Here is the full interview:
In ‘Making Numbers Count’, you indicate that nobody’s a natural with numbers. Could you give an example to explain this, please?
If you read the news, you see things measured in millions and billions every day, but our brains aren’t designed to process numbers that are bigger than what we can count on our fingers. How long is a million seconds? Be honest, do you have any idea? Now how long is a billion seconds?
It turns out a million seconds is 12 days. A billion seconds is… 32 years. If you get a letter in India from the USA by regular mail, it was sent about a million seconds ago. But a billion seconds ago, Sachin Tendulkar had just made his cricket debut.
Outside their own domains of expertise, even people very practiced with numbers can struggle with “millions” and “billions”. Almost no one gets the million/billion seconds comparison right, not even accountants, scientists, engineers, physicists, or that formidable math teacher you had when you were 10.
What would you say is the most common mistake that people (analysts, journalists, etc.) make while reporting numbers-based stories?
Too many numbers, too few comparisons. Numbers stick best when we think about them in the context of a known comparison - Turkey’s population of 70 million is about “twice as large as Canada’s”. Researchers at Microsoft found that when people were given a comparison, they remembered about twice as many facts as people who were given numerical facts alone.
Imagine you are a B2B salesperson and you are able to double a potential client’s memory for the key numbers in your sales presentation with a small amount of additional effort. Would you be willing to invest time developing some comparisons?
In the book you mention that your love of numbers started with the Guinness Book of World Records – would you say that we respond to the records the way we do because they are naturally at a human scale? For example, when I read that the record holder for longest nails has 358 inches of nails on the fingers of one hand, I can instantly compare that that's a lot more than mine.
Yes, the nice thing about the Guinness records is that they’re remarkable but still understandable within our human experience. The record for the most somersaults in one minute is 75 by Richard Cobbing of Lightwater, Surrey. As a kid I could have done at least 7 and there I was, one-tenth of the way toward a world record.
I don’t remember too many numbers from my Guinness Book of World Records, but I remember the heaviest man. He weighed 1,400 pounds, a figure I never learned. But I will always remember that to move him, they had to break apart his house and lift him out by construction crane. Our brains will remember that image more than any number, so if you can show a concrete implication of your numbers, you’re way ahead.
Even Guinness records can become better with some translating. What’s 358 inches of fingernails? Well, if you divide it evenly between the five fingers of one hand, each nail is about 5’2” which is almost the height of the average woman. Now those nails suddenly seem more than a little high maintenance. Good luck getting in and out of a car.
How important is this scaling to human size in terms of understanding numbers in, say, business or public health?
Oh, it’s essential. Both fields are susceptible to what we call the “curse of knowledge”. Someone spends decades around fellow experts in a field like medicine that takes half a lifetime to learn. By the time they master their field, they are cursed because they can’t imagine how little the rest of us understand about their field. But their jobs force constant communication with people who are less expert. Public health people need to communicate with, of course, the public. And business brings together clients, customers, and suppliers.
In the book we describe the remarkable insights of Florence Nightingale, who not only revolutionized nursing and statistics, but she was way ahead of her time in developing communication techniques that made non-experts understand her findings. In her time “non-expert” meant “almost everyone except Florence Nightingale.” She would tell people, “We’re killing more of our boys in our hospitals through unsterile practices than the enemy is killing on the battlefields with guns. In fact, for every one killed by the enemy, we’re killing eight. Our military hospitals are worse than the Black Death.” Those number translations motivated a complete overhaul of the military hospital system. That’s analysis that matters.
All through the Covid-19 pandemic, we’ve been bombarded with numbers and data – from R naught to active cases, extra deaths and vaccine efficacy. Could you give an example each of the best and worst explanations for any one of these that you’ve come across, please?
Yes! It’s a great example of how experts had to translate breaking findings to a general public in real time. So R naught, for example, is something a non-statistician has no hope of understanding, but “each person infects three people on average” is intuitive, and shocking. Especially if you ask, “who would you infect?” - if you think of them as real people, which they are, you’ll stay isolated until you test negative.
For vaccine efficacy, we liked the stats that broke it down by how outcomes would change for, say, 100 people. “95% effective” doesn’t mean much by itself, other than it’s not perfect. So it would have helped to be more concrete but going from X ICU visits and Y deaths to a different number, that was easy to visualize.
What advice would you give to traders and financial analysts and writers, to make numbers more accessible without losing any of their specificity?
Finance whizzes here should borrow a practice from the other great domain of limitless statistics: sports. Sports reports often provide a scorecard for the fans who are experts on the statistics and can add their own comparisons to put them in context. So the writers should aim to tell “what’s happening,” and “why does this matter,” the questions that only they can answer.One example is Tesla, which in October of last year reached (momentarily), a market capitalization of $1 trillion. That made it worth more than the next 10 car companies combined - including Toyota, Daimler, GM, Honda, and VW. That comparison helps us make sense of what that $1 trillion market cap means. You might not believe that Tesla is really worth that much and that would cause you to bet against Tesla in the market. (You would have made big dollars on that short.) Or if you do believe that Tesla might be that valuable, then it might suggest some other assets that are undervalued for the future: Lithium mines, anyone? In a world dominated by electric cars, what happens to the locations currently occupied by gas stations? The right number translation can not only help you communicate, it can help you think.