All models are wrong, some are useful: revisiting George Box's ideas in the age of AI
- Amanda Duim Ferreira
- Aug 5
- 3 min read
George Box was one of the most influential statisticians of the last century, and he wasn't being cynical when he first made this now-famous statement. He first put the idea in print in a 1976 paper titled "Science and Statistics," and the full version appeared in a 1987 textbook he wrote with Norman Draper. Fifty years on, as we hand more and more decisions to machine-learning systems, the line is more useful than ever. In this blog post, we are going to discuss what he meant by "wrong" and "useful". Both words are easily misread.
What does wrong actually mean?
The instinct is to read "wrong" as "bad," or "inaccurate," or "you made a mistake." That's not it. A model is wrong because it is, on purpose, a simplification of reality. It leaves things out so you can reason about what's left. A model is wrong because it fails to reproduce nature and the real world, and it's the heart of what Box meant. It can be wildly accurate and still be wrong in Box's sense, because it's still a simplification.
Wrong does not mean inaccurate.
Accuracy and truth are different things. A model can nail the prediction without telling you anything true about why. With a small dataset, you can't disprove even a silly model, and with a big enough dataset, you can disprove any model you'd actually want to use. Push enough data through anything, and its cracks show. The interesting question is where it's wrong and whether that matters.
What does useful actually mean?
Useful is not the same as accurate. Useful means fit for the purpose at hand.
Usefulness depends on the purpose. The statistician J. Michael Steele uses the map analogy. A subway map is a glorious distortion: distances and angles are all lies, and it's perfect for catching a train and useless for judging how far you'll walk. Same model, useful or misleading depending on the question. So the right question is never "is this model accurate?" in the abstract. The correct question is: Is this model accurate enough for this decision?
More accuracy is not more usefulness. Box was obsessed with parsimony. The idea is that a simpler model is usually a better one. He argued that since every model is wrong anyway, you can't fix it by piling on detail; over-engineering a model is more often a sign of mediocrity than of rigor. Chase accuracy too hard and you overfit. So, in practice, pick the simplest model that's good enough for the decision, then stop.
Worry about the right errors. Box's other rule was to be alert to what is importantly wrong. This is very important to stop fussing over the small errors while the large ones go ignored. Knowing what your model leaves out is only half of it; the other half is knowing which of those omissions can actually affect the model’s utility.
What about models in the AI-era?
Box built his philosophy around relatively small models. Modern AI flips that concept because today's models have billions of parameters and are still frequently very useful.
A large model can be confidently wrong, fluent, plausible, and flatly incorrect, in a way a small regression rarely is. It can work beautifully on the data it saw and quietly break when the world shifts underneath it. And because you can rarely inspect its reasoning, you often can't tell which mode you're in until something goes wrong downstream. Which means the rules that Box presented aren't obsolete in the AI era.
Actually, it's the survival kit:
Know what it's missing. Treat every model output as an approximation with a blind spot, not an oracle.
Match it to the stakes. A wrong-but-useful model is fine for ranking your email; you want more transparency before it's denying loans or reading scans.
Worry selectively. Spend your scrutiny on the errors that change the decision.
Prefer the model you can explain. Sometimes, a slightly less accurate model you understand beats a black box you don't.
In conclusion, Box's point was never that models are useless. It was that we should stop asking "is it true?" and start asking "is it useful for what I'm about to do with it?" That question was good advice in 1976, and with a machine now sitting between us and most of our decisions, it might be the most practical thing a statistician has ever said.
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