Accuracy is how close your measurement is to the true value. Precision is how close your repeated measurements are to each other.
You can have one without the other:
- Precise but not accurate: A scale that consistently reads 2kg heavy. Every measurement clusters tightly - but they’re all wrong by the same amount. The error is systematic.
- Accurate but not precise: A scale that averages to the true weight over many readings, but any single reading could be off by a lot. The error is random but unbiased.
- Both: Tight cluster around the true value.
- Neither: Scattered readings that also don’t center on the truth.
The reason “precision without accuracy” is the more interesting case: it feels like knowledge. The numbers agree with each other, which creates false confidence. You get reproducible results that are reproducibly wrong.
This shows up everywhere:
- A financial model that produces consistent forecasts from flawed assumptions. The outputs are stable - the model has high internal coherence - but they don’t track reality.
- A measurement instrument with a calibration error. Every reading is off by the same factor, but the readings are beautifully consistent.
- An argument that is internally rigorous but starts from a wrong premise. Every deduction follows logically. The conclusion is still false.
The deeper point: precision is a property of your instrument (or method, or model). Accuracy is a property of the relationship between your instrument and the world. You can evaluate precision without knowing the truth. You cannot evaluate accuracy without it.
That’s what makes precision seductive and accuracy hard. Precision is self-verifiable - just check if your measurements agree. Accuracy requires an external reference, and sometimes that reference doesn’t exist or isn’t accessible.