Ratio bias
Also known as: Ratio-difference effect
A 9-in-100 chance can feel bigger than a 1-in-10 chance.
What it means
The tendency to judge a probability by the absolute size of its numerator rather than the ratio it forms with the denominator, so that a low-probability event drawn from a large pool feels more likely than a higher-probability event drawn from a small one. Faced with two trays, people often prefer to draw a winner from one holding 9 winning tickets among 100 over one holding 1 winner among 10 — choosing the worse odds because '9' looms larger than '1.' The bias reflects a more concrete, frequency-based mode of thinking (sometimes tied to dual-process accounts) overriding the abstract relation that actually governs the odds. It distorts risk perception in health, gambling, and insurance, and it cautions communicators that how a probability is decomposed into counts can matter as much as the probability itself.
Examples
In jellybean experiments, people prefer to draw from a bowl with 9 red beans in 100 over one with 1 red bean in 10, even though they know the second bowl gives better odds.
A leaflet warning that a side effect strikes '10 in every 1,000 patients' alarms readers more than '1 in 100' — identical risk, but the larger numerator does the frightening.
A raffle advertising 'fifty winning tickets!' among ten thousand feels more promising than one with five winners in a hundred, though the second gives ten times better odds.
First described in Denes-Raj & Epstein (1994).