"Doubles your risk" of almost nothing is still almost nothing.

“Eating bacon raises your risk of bowel cancer by 18%.” “This drug cuts heart attacks by a third.” “The new pill doubles the danger of a clot.” Every one of these is a relative statement — a change measured against a starting point that the sentence carefully declines to mention. And without the starting point, the number is unreadable. An 18% increase on a one-in-a-million risk is a rounding error; an 18% increase on a one-in-three risk is a catastrophe. The same words, two different universes.

The translator above lets you feel the gap. Hold the headline change fixed and slide the baseline: the scary percentage never moves, but the actual number of affected people — the thing you presumably care about — swings from invisible to enormous. Relative risk tells you how the needle moved; absolute risk tells you how big the needle was to begin with. Only the second one tells you whether to worry.

In October 1995 the UK's Committee on Safety of Medicines issued an urgent warning: a newer, third-generation contraceptive pill roughly doubled the risk of venous blood clots compared with older pills. “Doubled” is a relative statement, and it landed like a bomb. What the warning struggled to convey was the baseline. The risk it doubled was tiny — on the order of one extra case per 7,000 women a year.

Frightened women across Britain stopped taking the pill. The result, by the following year, was an estimated thirteen thousand additional abortions in England and Wales and a sharp rise in unintended pregnancies, with the effects falling hardest on teenagers. The bitter irony is that pregnancy itself carries a substantially higher risk of exactly the clots the warning was about. A relative number, reported without its baseline, did real and measurable harm — the cleanest case on this site of a presentation choice with a body count.

The deep reason a bare relative risk is uninformative is that it deliberately discards the one quantity that fixes its meaning. “+50%” is compatible with one extra case in ten thousand people and with a thousand extra cases in the same ten thousand — a difference of three orders of magnitude, all wearing the identical label.

This is why relative risk is the framing of choice for anyone with something to sell or scare. A drug company quotes the relative reduction because it is the bigger-sounding number; a newspaper quotes the relative increase in some everyday pleasure for the same reason. Neither is lying. Both are counting on you not to ask “of what?”

The cure isn't to distrust all percentages — it's to insist on seeing the same fact in more than one frame, because the frames that get hidden are the revealing ones. Any change in risk can be stated at least four ways, and a trustworthy source gives you enough of them to reconstruct the rest.

The last of the four, number needed to treat, deserves special love because it answers the question a patient actually has: how many people like me have to take this for one of us to benefit? “Treat 100 people for one to be spared” is sobering in a way that “cuts risk by half” never is, and it is the same fact. Risk-communication researchers, Gerd Gigerenzer foremost among them, have shown for decades that natural frequencies and absolute differences let ordinary people — and their doctors — reason correctly where bare relative percentages reliably mislead.

The bacon headlines. When the World Health Organization's cancer agency classified processed meat as carcinogenic in 2015, the figure that travelled was “50g a day raises bowel-cancer risk by 18%.” True — and the absolute version is that a lifetime risk of roughly 6% rises to roughly 7%. Worth knowing, hardly the apocalypse the relative number implied, and reported almost everywhere without the baseline.

Screening benefits. Cancer-screening leaflets have a long habit of quoting the relative reduction in dying from a specific cancer (large and encouraging) while omitting the absolute reduction (small) and the harms of over-diagnosis entirely. The same asymmetry, pointed the other way: relative framing to sell the benefit, silence on the base rate.

The asymmetry is the tell. Notice the pattern across all these cases: the relative frame is wheeled out when someone wants a number to feel big, and the absolute frame appears when they want it to feel small. A source that consistently shows you only the flattering frame is telling you something — just not about the risk.

Demand the baseline, ask for the natural frequencies — “so many in a thousand, before and after” — and the spell breaks every time. This is a close relative of the truncated-axis trick: both leave every individual number true while quietly removing the reference point that would let you judge it. Strip the baseline from a risk, or the zero from an axis, and honest data does the misleading for you. The rest of the compendium is full of the same move in other costumes.