Reading the result

Two health stories run on the same day. The first: “New pill cuts your risk of a heart attack by 50%.” The second: “New pill cuts your risk of a heart attack by 1 in 100.” Read fast, and the first sounds like a breakthrough and the second sounds like nothing. Here is the catch — they can be the exact same pill, the exact same study, the exact same result. One headline is dressed up. The other is honest. Learning to see that they are the same number is the single most useful skill for reading any medical claim.

”Halves the risk” is meaningless on its own

A drug doesn’t lower your risk by a fixed amount. It lowers it by some fraction of where you started. So the first question is always: started from what?

Two numbers describe the same drop, and they are not the same.

Relative risk reduction is the drop as a percentage of the starting risk. “Cuts risk by 50%” means whatever your risk was, it’s now half that. It’s the percentage that sells.

Absolute risk reduction is the actual change in your chances — starting risk minus ending risk, in plain percentage points. It’s the number that tells you what you’d feel.

Here’s the worked example. Suppose, without the drug, 2 in 100 people like you have a heart attack over five years — a 2% risk. The drug cuts that relative risk by 50%. Half of 2% is 1%. So with the drug, 1 in 100 has the heart attack.

• Relative: down 50%. (From 2% to 1% — half.)
• Absolute: down 1 percentage point. (2% minus 1% = 1%. One fewer person in 100.)

Both are true. “50%” is the honest relative number. “1 in 100” is the honest absolute number. The headline picks “50%” because it’s the bigger word — but the thing you actually get is: out of 100 people who take this pill for five years, one of them avoids a heart attack who otherwise wouldn’t have. The other 99 get no change in outcome. That’s the real shape of a “50% reduction” when the baseline is small.

The same 50% on a different baseline

Now slide the starting risk up. Suppose you’re in a high-risk group where 40 in 100 would have a heart attack — a 40% baseline. Same drug, same 50% relative cut. Half of 40% is 20%.

• Relative: down 50% — the same headline as before.
• Absolute: down 20 percentage points. (40% to 20% — twenty fewer people per 100.)

Same “50%,” wildly different gift. In the low-risk group it spared 1 person in 100. In the high-risk group it spared 20. The relative number hid that completely. This is why “cuts risk by half” tells you almost nothing until you ask “half of what?” — the relative percentage is the same whether the real benefit is tiny or enormous.

A small study is mostly noise

There’s a second trap, and it lives in the size of the study. A result from a tiny trial proves very little, because chance alone swings small numbers hard.

Flip a fair coin 20 times and you might get 13 heads — 65%. That doesn’t mean the coin is bent. Flip it 20,000 times and you’ll land very close to 50%, every time. Big samples average out luck; small ones don’t.

A drug trial is the same. Imagine a disease where 30% of people recover on their own. Test a useless sugar pill on 20 people, and just by luck you might see 9 of 20 recover — 45%. Looks like the pill works. Run the same useless pill on 20,000 people and you’ll see almost exactly 30% — the truth. The tiny trial’s exciting number was a coin landing 13 heads. It wasn’t a finding. So when a claim rests on “in a study of 18 patients,” treat the result as a rumour, not evidence.

Correlation is not cause

The third trap is the slipperiest. Researchers often observe — they watch a lot of people, don’t assign anyone to anything, and notice that people who do X tend to be healthier. That is a correlation. It is not proof that X caused the health.

Say people who take a certain supplement live longer. Maybe the supplement helps. Or maybe the people who buy supplements also exercise, sleep, and see doctors more — and those habits did the work. The supplement just rode along. Observation alone can’t tell the two apart. (The fix is the controlled trial from the last item — assign the supplement at random and compare against a control group, so the only difference is the pill.) Until that’s done, “linked to” and “associated with” mean we noticed it together, not it caused it.

This is the honest way to read a result, not medical advice — how to weigh a claim, never what to take. For any real decision, that’s a conversation with a clinician who knows your baseline.

On the whole

Every number that reaches you has been chosen by someone. “50%” and “1 in 100” describe one truth, and which one you’re handed shapes how you feel about a pill before you’ve thought at all. The skill isn’t cynicism — it’s asking three quiet questions: half of what, out of how many, and compared to whom. Behind each headline is a baseline it didn’t mention, a sample size it rounded past, and sometimes a coincidence wearing the costume of a cause. You live downstream of these numbers, in the choices they nudge. Seeing the plain shape under the dressed-up percentage is what lets you stand in that current without being swept by it.