TRADECRAFT: The Denominator Blindspot

The Concept

You can tell a lie without ever saying a false number. All you have to do is pick the right Denominator.

• The Numerator is the thing you are counting (Deaths, Crimes, Dollars).

• The Denominator is the context (Per Year? Per Person? Per Mile?).

If you want to make a problem look huge, use Total Numbers. If you want to make a problem look tiny, use Per Capita or Percentages.

CASE STUDY 1: The “Safest” Way to Travel

How to use math to prove that Hot Air Balloons are safer than Cars.

The Data: | Transport Mode | Total Deaths (Annual) | Deaths Per Million Miles | | :— | :— | :— | | Cars | 1,350,000 | 0.45 | | Hot Air Balloons | 20 | 40.0 |

The Spin:

• The Lobbyist: “Hot Air Balloons are the safest transport on earth! Only 20 people died last year, compared to 1.35 MILLION in cars. Cars are mass murderers!”

  • Trick: Uses Total Numbers (ignoring that billions of people drive, and almost nobody flies balloons).

• The Safety Inspector: “Hot Air Balloons are a death trap! For every mile you travel, you are 88 times more likely to die in a balloon than in a car.”

  • Trick: Uses Per Mile (highlighting the technical danger).

The Verdict: Always ask “Compared to what?”

CASE STUDY 2: The “Murder Capital” Trick

How politicians manipulate crime stats.

The Data:

• City A (Metropolis): 500 Murders. Population: 10 Million.

• City B (Small Town): 10 Murders. Population: 10,000.

The Spin:

• Headline 1: “METROPOLIS IS A WARZONE! 500 Dead! 50x more killings than Small Town!”

  • Reality: In Metropolis, your chance of being killed is 1 in 20,000.

• Headline 2: “SMALL TOWN MURDER EPIDEMIC! Residents are 20x more likely to die here than in Metropolis!”

  • Reality: In Small Town, your chance of being killed is 1 in 1,000.

The Verdict: Totals measure impact (how busy the morgue is). Rates measure risk (how safe you are).

CASE STUDY 3: The “Bacon Panic” (Relative vs. Absolute)

How health news scares you for clicks.

The Scenario: A study shows bacon causes cancer.

• Non-Bacon Risk: 5 people in 100 get cancer (5%).

• Bacon Risk: 6 people in 100 get cancer (6%).

The Spin:

• The Clickbait: “Bacon increases cancer risk by 20%!”

  • (True: 6 is 20% higher than 5).

• The Doctor: “Bacon increases your risk by 1 percentage point.”

  • (True: 5% to 6% is a +1 difference).

The Verdict: Whenever you see a “Percentage Increase” (Relative Risk), ask for the Absolute Numbers. A “50% increase” in a 1-in-a-billion risk is still irrelevant.

LAB EXERCISE: The “Headline Audit”

Task: Find a scary headline today involving a number.

1. Identify the Denominator: Is it a Total Number? (e.g., “$50 Billion lost!”).

2. Flip It: Calculate the other statistic.

   • If it says “$50 Billion,” ask: “What percentage of the budget is that?” (Often it’s 0.1%).

   • If it says “Crime up 100%,” ask: “Did it go from 1 crime to 2?”

3. The Result: If the flipped number isn’t scary, you are being manipulated.