Weighing a rare thing

Picture 1,000 emails. 10 of them are scams. A filter catches 9 of those 10 scams — but it also wrongly flags 50 of the 990 honest emails.

So the filter flags 59 emails in all: 9 scams and 50 honest ones. If an email is flagged, the chance it is really a scam is 9 in 59 — about 15%. Most flagged emails are honest, even though the filter is "90% accurate" at catching scams.

This is the idea of a base rate. When the thing you are looking for is rare, even a good test turns up mostly false alarms. Counting in whole numbers — out of a thousand — makes this far easier to see than percentages.