Why can a spam flag be misleading?

A spam flag is evidence produced by a filter, not certainty that a message is spam. Its meaning depends both on the filter’s behavior and on how much spam was present to begin with. That starting proportion is the base rate, also called prevalence.

The fictional filter flags 90% of spam messages. This detection rate starts with all spam as its group. It also flags 10% of legitimate messages, a false-flag rate that starts with a different group: all legitimate messages. Neither percentage directly states the proportion of flagged messages that are spam.

In the first population of 1,000 messages, 100 are spam and 900 legitimate. The rates produce 90 flagged spam messages and 90 flagged legitimate messages. The flagged pool therefore contains 180 messages, half of them spam. Its denominator must include both flagged branches, not just the original spam group.

In a second population with 500 spam and 500 legitimate messages, the same assumed rates produce 450 spam flags and 50 legitimate flags. Now 450 of 500 flags, or 90%, are spam. The change comes from the starting population, not an improvement in the assumed rates. Detection and the composition of flags answer different conditional questions. These exact fictional counts explain the base-rate effect without measuring any real filter or guaranteeing that its rates stay fixed across populations.