Can 95% accuracy mean complete failure?
A system checks answers and flags likely failures for review. Someone reports that its decisions are 95% accurate. Does that tell you whether it catches any incorrect answers?
We will investigate 200 synthetic arithmetic answers: 190 are correct and 10 are incorrect. You need counts, fractions, and percentages. No model training is involved.
Inspect what one record means
Open . Each record contains a request, an answer, the expected result, a reference label, and a frozen review score. Check a few answers yourself, including records labeled Failure.
The detector flags a record when its score is at least the chosen threshold. It does not consult the reference label. Scores are deliberately constructed ranking signals, not probabilities or outputs measured from a real model. Changing the threshold leaves the records, labels, and scores fixed.
Throughout this lesson, “positive” means a failure that should be detected. The accuracy we measure belongs to the detector, not the answer-producing system. The answers themselves remain 190/200 correct in every run.
Establish a detector that flags nothing
Use threshold . All scores are below 101. Before running, predict how many detector decisions will match the reference labels, and how many of the ten failures it will catch. Write your prediction, then select .
Next change only the threshold to 90. Predict whether catching some failures necessarily increases accuracy. Record the run and compare the four counts in the confusion matrix with your reference.
200 fixed synthetic answer records: 190 correct, 10 incorrect. Incorrect answers are the positive class (failure). Flag a record when its frozen review score ≥ threshold. Scores are constructed signals, not probabilities. Only the threshold changes; answers, labels, and scores stay fixed. No model training or API calls.
0/16 runs. Each run keeps its own inputs and results. Work stays in this tab across reloads; download a report before closing it.
Write a prediction to record your reference.
Explain which decisions became better and which became worse before opening the worked comparison.
How two different detectors both reach 95%
At threshold 101, the detector correctly passes 190 good answers and misses all ten failures. Its accuracy is , but it catches no failures.
At threshold 90, it catches two failures and flags two correct answers unnecessarily. It correctly passes the remaining 188 good answers and misses eight failures. Accuracy is still .
The same aggregate score conceals a different allocation of errors. The second detector catches something useful, but we also need to account for the cost of its false alarms.
Ask three different questions
The confusion matrix names the four outcomes. A true positive (TP) is a caught failure; a false negative (FN) is a missed failure. A false positive (FP) is a correct answer flagged unnecessarily; a true negative (TN) is a correct answer passed.
| Measurement | Question | Calculation |
|---|---|---|
| Accuracy | What fraction of all detector decisions are correct? | |
| Precision for failures | Of the flagged answers, what fraction are actual failures? | |
| Recall for failures | Of all actual failures, what fraction did we catch? |
The workbench shows these fractions as percentages. At threshold 90, precision is and recall is . They use different denominators. See the definitions of precision and recall.
At threshold 101, precision has denominator zero because nothing was flagged. It is undefined, displayed as a dash. Recall is defined and equals zero because ten actual failures were available to catch. Our display keeps this distinction explicit rather than replacing both with zero.
Catch more failures at a cost
Keep the same records and change only the threshold to 70. Predict the direction of change in recall, precision, accuracy, and review count. Record the run and choose your threshold-90 run as .
Compare the additional reviews
Threshold 70 catches six failures and produces ten false alarms, so 16 records need review. It misses four failures and correctly passes 180 good answers.
Recall rises to , but precision falls to . Accuracy falls to . A lower accuracy score accompanies more caught failures. Whether that tradeoff is worthwhile depends on the consequences of misses and unnecessary reviews.
Design your own investigation
Choose a review budget between 4 and 40 records. Write a prediction for an untested threshold, then record it. Among the available thresholds, seek the most caught failures without exceeding your budget. Name the baseline, budget, and the evidence that would rule out your choice.
Now investigate a different requirement: miss none of the failures in this fixture. Choose a threshold you think can satisfy it. Predict its review count and precision before testing. Explain why recall alone cannot tell you whether the detector is practical.
Check your constraints against the evidence
At threshold 40, the detector flags 38 records: eight failures and 30 false alarms. At threshold 10 or 0, it flags every record, catching all ten failures but requiring 200 reviews. Precision is then only .
For example, a budget of 20 allows threshold 70 with six caught failures, but excludes threshold 40. A no-misses rule requires flagging all records among these available choices. Neither result establishes a universally best threshold.
Transfer and report
Another detector flags 20 answers, of which 15 are failures. Five additional failures are missed. Calculate precision and recall. If the two values agree here, does that make them interchangeable?
Check the denominators
Precision is . There are actual failures, so recall also equals 75%. They agree only because the denominators happen to be equal. Add ten false alarms while preserving which failures are caught: precision becomes , while recall remains 75%.
Download your report with the prediction, chosen threshold, review constraint, and every calculated decision. Treat these records as a development fixture: choosing a threshold on them does not establish its performance on new users or real model outputs. A real evaluation needs relevant examples, trustworthy reference labels, and an independent held-out check. Hamel Husain discusses this problem for LLM judges in The Revenge of the Data Scientist.