Accuracy, Precision, Recall, and Error Cost

Once the confusion counts are visible, common metrics become easier to understand.

Accuracy asks: what fraction of all predictions were correct?

Precision asks: when the model predicted positive, how often was that prediction correct?

Recall asks: of all actual positive cases, how many did the model find?

Each metric answers a different question.

Using the previous example—18 true positives, 70 true negatives, 7 false positives, and 5 false negatives:

• accuracy = (18 + 70) / 100 = 0.88;
• precision = 18 / (18 + 7) = 0.72;
• recall = 18 / (18 + 5) ≈ 0.78.

Imagine a second model with 92% accuracy but only 55% recall on the defective class. Saying “92% is better than 88%” skips the decision context. If missed defects are the expensive error, the lower-recall model may be worse for the actual job.

Class imbalance can make accuracy look impressive

Suppose only 1% of examples are positive. A useless model that always predicts negative reaches 99% accuracy while detecting zero positive cases.

This is not a mathematical bug. Accuracy is correctly answering its question. The problem is that the question may be too broad for the evidence we need.

Metrics are measurements, not goals by themselves

A team can optimize a metric and still damage the system if the metric does not match the real decision.

Before selecting a metric, document:

• what counts as positive and negative;
• which error types exist;
• who or what experiences those errors;
• whether classes are balanced;
• what action follows the prediction.

Before moving on

Explain why a model can improve precision while reducing recall. You do not need a formula; describe the change in which predictions the model is willing to call positive.