Explaining Hard Things: Numbers, Risk, and Bad News

Numbers, risk, and bad news are where communication most often fails, and usually not because the audience is unintelligent but because the format fights comprehension. A "30% increased risk" sounds alarming yet tells you almost nothing without the baseline. People make real medical, financial, and personal decisions on the strength of such phrases.

Honesty and clarity are not in tension here; the task is to be both truthful and understood. That means choosing formats the human mind handles well, stating uncertainty plainly rather than laundering it into false confidence, and delivering hard news with enough structure and warmth that the person can actually take it in.

Natural frequencies beat percentages

Conditional probabilities and bare percentages overwhelm most people, including trained experts. Expressing the same facts as natural frequencies, "10 out of 1,000" rather than "1%," makes the arithmetic visible and the risk graspable. The key is to keep a single reference class, such as "out of 1,000 people like you," so the numbers can be added and compared directly.

Relative versus absolute risk

"Cuts your risk by 50%" (relative) can describe a fall from 2 in 10,000 to 1 in 10,000 (absolute), a tiny change dressed up as large. Always give the absolute numbers and the baseline. Relative figures presented without a base rate are among the most common ways statistics mislead, often without anyone intending to deceive.

Uncertainty and bad news, stated plainly

Do not launder uncertainty into false confidence or vague hedging. Say what is known, what is not, and how likely the outcomes are. For bad news, structure helps: a brief warning that hard news is coming, the facts in plain words, a pause, then support, a pattern clinicians formalise in protocols such as SPIKES.

A screening test is described two ways. "This test is 90% accurate" tells a worried patient little. Reframed: "Out of 1,000 people like you, about 10 have the condition. Of those 10, about 9 will test positive. But of the 990 who are healthy, about 70 will also test positive. So among everyone who tests positive, fewer than 1 in 8 actually has the condition." The facts are identical; the second version lets the patient reason for themselves.

Clarity is not the same as sugar-coating. "Simplifying" bad news into euphemism, saying "the numbers are not quite where we would like" instead of "the treatment did not work," is a failure of honesty, not a kindness. Equally, dropping the uncertainty to sound authoritative, "this will definitely work," is clearer but false. The aim is understandable truth, never comfortable fiction.

Psychologist Gerd Gigerenzer and Ulrich Hoffrage showed, in a 1995 paper in Psychological Review, that people reason far better about probability when information is given as natural frequencies rather than conditional probabilities. In a widely repeated demonstration, doctors were asked to estimate the chance that a woman with a positive mammogram actually has breast cancer, given a low base rate, a high detection rate, and a modest false-positive rate. Presented as percentages, most physicians were badly wrong, with estimates ranging wildly. Presented as natural frequencies, so many out of 1,000, far more doctors reached the correct figure of roughly 8 to 10%. Gigerenzer has argued for years, including through the Harding Center for Risk Literacy, that much apparent innumeracy is really a problem of poor representation, and that simply changing the format improves how both doctors and patients understand medical risk.

• "Percentages are the precise, professional way to state risk." They are precise but often poorly understood; natural frequencies are usually clearer.
• "A 50% risk reduction is always a big deal." Not without the baseline; it may represent a tiny absolute change.
• "Being clear means sounding certain." Honest communication states uncertainty rather than hiding it.
• "Kindness means softening the facts." Euphemism that obscures the truth is not kind; clear, warm honesty is.

Take any "X% risk" claim from the news. Rewrite it as a natural frequency with a fixed reference class, then find and add the baseline it was compared against. Notice how much the story changes once the absolute numbers are in view.

Think Like a Maester: Change the format before you conclude the audience cannot handle the number.

1. Why do natural frequencies tend to be understood better than conditional probabilities?
2. Explain the difference between relative and absolute risk with an example.
3. What role does a fixed reference class play in stating a frequency?
4. What did Gigerenzer and Hoffrage demonstrate about doctors and mammography risk?
5. Why is euphemism a failure rather than a kindness when delivering bad news?

Hard content fails when its format fights comprehension. Natural frequencies such as "10 out of 1,000" make probability graspable; absolute risks and baselines stop relative figures from misleading; plainly stated uncertainty keeps you honest. Deliver bad news with structure and care but without euphemism. Gigerenzer's work on medical risk shows that changing the representation, rather than the audience, is often what finally makes a difficult number clear.

• Visual and Data Communication
• Becoming a Great Explainer