Best Practices for Communicating Probabilities

Persuading Decision Makers of Future Probabilities Works Better when You Embed Numbers in Narratives

Behavioral economics research into how people make decisions under risk compellingly demonstrates that the human mind is not naturally good at thinking about probability rationally and clearly. Our minds much prefer to think in simplifying stories that ring true than to tease out the analytical truth conveyed in numbers. But for historical reasons, modern people also tend to be highly trusting of numbers; they seem more “true” and straightforward than narratives.

 But this disconnect between narrative and numbers didn’t always exist, according to Roberto Franzosi in From Words to Numbers.  Consider:

…the etymological roots of the words “count” (numbers) and “recount,” as in narrative or tell a story (words). The word “recount” was imported into English from the French reconter in the fifteenth centry. In French, the verb reconter, a close proxy of conter, hasd been adopted in the twelfth century from the Latin computare (meaning reckon and calculate). And computare (meaning reckon and calculate). And numbers, telling and measuring, counting and recounting, were once simply intellectual activities, involved thinking, or, more appropriately, enumerating or going through a sequential list.

Perhaps then, it is not surprising to learn that the most powrful and persuasive way to communicate probabilities is to embed numbers and statistical information in narratives. Ultimately, numbers don’t actually speak for themselves. Rather, they speak most eloquently and persuasively when they are in context.

Here is a short list of practical ways to bridge the historical divide, and reunite narrative and number.

Here then, a short list of ways to bridge the historical divide, and reunite narrative and number.

1. Frameworks Institute:  “Don’t fight the narrative with numbers”

According to Frameworks, which helps institutions shape discourse around social issues, numbers and facts are not persuasive to people, if the cited numbers counter strongly held worldviews.

The fact is that many Americans find it hard to digest data and interpret it; mathematical literacy is a major hurdle. But, that aside, the psyche is often resistant to data that erode a comfortable view of the world. Quite often, the numbers are reinterpreted to substantiate an entirely different conclusion. From the social science roots of framing research we learn this maxim: If the facts don’t fit the frame, the facts get rejected not the frame.

New numbers won’t fix an outworn frame, is the message. If your audience has a worldview that your numbers don’t support, the numbers will not change their minds.

3. Harvard Business Review:  “Use numbers to season the points you serve — they’re not the main dish”

HBR extracted some basic pointers from investor Warren Buffet’s yearly letter to Hathaway stockholders for using numbers effectively. Buffet’s story is in the numbers themselves, but he helps others to understand it by explaining related terminology

Buffett doesn’t just report on the underwriting gains of their insurance businesses and let the numbers stand for themselves; he explains the terminology, what the numbers mean, and how he and Charlie Munger, his business partner, view them. Case in point: “Our $58.5 billion of insurance “float” — money that doesn’t belong to us but that we hold and invest for our own benefit — cost us less than zero. In fact, we were paid $2.8 billion to hold our float during 2008. Charlie and I find this enjoyable.”

3.  Straight Statistics: Use numerical frames consistently

We laypeople may think we understand medical information that uses numerical bases to explain the benefits and harms of particular treatments, but we probably don’t because they are presented so unevenly, according to Straight Statistics:

Typically, benefits [of a medical procedure or drug] are presented as a percentage improvement, while the  harms are given in absolute terms. This makes the benefits look much bigger and the harms much smaller – even to clinicians who might be expected to know better.

Take the following example:

A common way of presenting benefits is as a percentage increase in survival. This looks mightily impressive. But it tells us nothing about the baseline risk. If that is small, even a 50 per cent reduction will be small, too. Compare the statement: “Mammography screening reduces the risk of dying from breast cancer by about 20 per cent” with the statement: “Mammography screening reduces the risk of dying from breast cancer by about one in a thousand – from 5 in 1,000 to about 4 in 1,000”. Both represent the same data, but the first looks like a huge benefit, the second rather a small one.

Presenting benefits and harms in consistent terms is the answer to this skewed story that medical and health claims often tell. The advice is equally useful in any other domain in which you are seeking to share probabilities.

4. Journal of Behavioral Decision Making: Use small scale frequencies if you want to be understood (and don’t, if you don’t)

Despite the difficulty people have grappling with statistical information, we can reach accurate conclusions to problems when we are presented with of statistical information that aligns with our other perceptions of the world.

We are at our best, reasoning-wise, when presented with “natural frequencies,” (the number of people or things impacted from an entire population), especially when the total population size is small enough for us to imagine.  With large populations—like the size of the U.S. defense budget, or the number of stars in a summer sky—we are less good at drawing meaning from frequencies.  And no wonder, who can picture $700 billion (give or take a few)?  Kansas State psychology professor Gary Brase explains how to make this information useful in Which Statistical Formats Facilitate What Decisions? The Perception and Influence of Different Statistical Information Formats:

When the goal is to promote fast and easy understanding of the numbers, one should use smallscale (simple frequency) and percentage (relative frequency) formats. This guideline can be used in presenting information to legal juries, in designing advertisements, in presenting health and environmental risk information, in more effectively educating students, and other areas. Supplementing such information with absolute frequency (or at least absolute reference class) information should tend to produce understanding that is both clear and accurate.

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