The Logic of Numbers

How Numbers Mislead

Numbers feel objective, but they can be just as misleading as words. Every number comes with context that determines its meaning, and that context is often omitted.

Base rate neglect: 'Crime increased by 50% in our district.' If the district had 2 crimes last year and 3 this year, the 50% increase is statistically meaningless. Percentages without base numbers can make tiny changes sound dramatic.

Cherry-picked timeframes: 'The stock market has risen 30% since I took office.' The starting point matters enormously. If the market crashed right before you took office, a 30% recovery might still be below where it was three years ago. Always ask: why did they choose this starting date?

Absolute vs. relative risk: 'This drug doubles your risk of disease X.' If the baseline risk is 1 in 10,000, doubling it to 2 in 10,000 is very different from doubling a baseline risk of 1 in 10. Relative risk (doubled!) sounds scary. Absolute risk (from 0.01% to 0.02%) reveals the actual impact.

Five Questions for Every Number

1. What is the source? Government statistical agencies, peer-reviewed research, and reputable organizations have quality controls. Advocacy groups and campaigns may select numbers that support their message.

2. What is the denominator? '10,000 people signed the petition' means something very different in a city of 50,000 (20%) than in a country of 50 million (0.02%).

3. What is the comparison? A number only means something in context. 'Our GDP grew 2%' is good or bad depending on what other countries achieved and what was expected.

4. What is excluded? Unemployment figures exclude discouraged workers who stopped looking. GDP excludes unpaid work. Crime statistics exclude unreported crimes. Every metric has blind spots.

5. What is the trend? A single data point tells you almost nothing. Is this number going up, going down, or fluctuating randomly?

Worked Example: Decoding a Scary Headline

Headline: 'New supplement cuts heart attack risk by 40%!' Run the number through the checklist.

Relative vs. absolute. '40% reduction' is a relative figure. Suppose the baseline risk over five years is 5 in 100 (5%). A 40% relative cut lowers it to 3 in 100 (3%) — an absolute reduction of just 2 percentage points. The same 40% applied to a baseline of 5 in 10,000 would move the needle almost imperceptibly.

Denominator and source. Was this measured in 80 people or 8,000? Funded by the supplement maker or an independent body?

Comparison and trend. Compared to a placebo, or to an existing cheaper drug that cuts risk by 50%?

The table shows how each framing of the same underlying effect lands differently:

All three describe an identical result. Reporters and marketers reach for the relative figure precisely because it is the most dramatic. Converting to absolute risk, or to 'number needed to treat,' is the single fastest way to see what a health statistic actually means.