Every model simplifies and so is wrong in some respect; the practical question is whether it is wrong in ways that matter for its purpose.
Box first wrote that all models are wrong in a 1976 paper on science and statistics, arguing that a correct model cannot be reached by ever more elaboration and that scientists should look for economical ones instead. The full phrase, adding that some are useful, appeared in his writing from 1978 and in his 1987 book with Norman Draper, which also put the practical question: how wrong a model has to be before it stops being useful.
In practice
- An epidemiologist estimates how fast an outbreak will grow from a simple model that ignores who meets whom, because it answers the question being asked.
- A bank keeps its credit-risk model after a crisis exposes its assumptions, but limits how much weight any single decision may rest on it.
- Possible explanations
- The explanation is that a model is a simplification by design: leaving things out is what makes it usable, so being wrong in detail is the price of being useful. The question is then whether it is wrong in the ways that matter for the purpose at hand.
- In its favour
- It is standard teaching in statistics and modelling, and practice bears it out: large forecasting competitions have repeatedly found simple methods competing with complex ones, and simple models are easier to check.
- Against it
- Critics note that the aphorism can excuse a poor model as merely one more wrong one, and that it offers no way to tell a useful model from a misleading one. Some statisticians also object that calling approximations wrong blurs the difference between simplification and error.
- Standing
- The wording developed across Box's writing from 1976 to 1987. Compare Better Vaguely Right Than Exactly Wrong and the Map–Territory Relation.
- Further reading
- Wikipedia
- Subject
- Science & Epistemology
- Essay
- Rules for weighing claims