All models are wrong, some are useful: revisiting George Box's ideas in the age of AI
Updated: Sep 19
George Box was one of the most influential statisticians of the last century. He was not 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, I will discuss what he meant by "wrong" and "useful." Both words are easily misread.
Understanding the Concept of "Wrong"
The instinct is to read "wrong" as "bad," "inaccurate," or "you made a mistake." However, that is not the case. A model is wrong because it is, on purpose, a simplification of reality. It leaves things out so you can reason about what remains. A model is wrong because it fails to reproduce nature and the real world, which is the heart of what Box meant. It can be wildly accurate and still be wrong in Box's sense because it is still a simplification.
Distinguishing Wrong from Inaccurate
Accuracy and truth are different concepts. A model can nail the prediction without revealing anything true about why. With a small dataset, you cannot disprove even a silly model. Conversely, with a large enough dataset, you can disprove any model you'd actually want to use. Push enough data through anything, and its cracks will show. The interesting question is where it is wrong and whether that matters.
Defining "Useful"
Useful is not synonymous with accurate. Instead, it 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, making it perfect for catching a train but useless for judging how far you will walk. The same model can be useful or misleading depending on the question. Thus, the right question is never "Is this model accurate?" in the abstract. The correct question is: Is this model accurate enough for this decision?
The Relationship Between Accuracy and Usefulness
More accuracy does not equate to 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 cannot 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 risk overfitting. In practice, select the simplest model that is good enough for the decision, then stop.
Focusing on the Right Errors
Box's other rule was to be alert to what is importantly wrong. This is crucial to prevent fussing over small errors while large ones go ignored. Knowing what your model leaves out is only half of it; the other half is understanding which omissions can actually affect the model’s utility.
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 has seen and quietly break when the world shifts underneath it. Because you can rarely inspect its reasoning, you often cannot tell which mode you are in until something goes wrong downstream. This means the rules that Box presented are not obsolete in the AI era.
A Survival Kit for Modern Models
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 denies loans or reads 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 is better than a black box you do not.
In conclusion, Box's point was never that models are useless. Instead, he emphasized that we should stop asking "Is it true?" and start asking "Is it useful for what I am 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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