---
title: "Inverse relation of precision and recall"
subject: "Data Mining"
chapter: 3
key: "semester_7/data_mining:precision-recall-inverse"
source: https://www.bctengineer.com/q/semester_7/data_mining/precision-recall-inverse
site: BCT Engineering
---

# Inverse relation of precision and recall

Data Mining · Chapter 3: Classification

- Asked in: year not given
- Video: [Confusion Matrix. Accuracy. Error rate. Recall. Precision - Machine Learning by #Moein](https://www.youtube.com/watch?v=D4UTA4vCElg) — Moein Instructor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/data_mining/precision-recall-inverse
- Whole chapter: https://www.bctengineer.com/md/semester_7/data_mining/chapter-3

## Question

Explain the inverse relation between Precision and Recall of classifier model.

## Short answer

Precision and recall trade off: lowering threshold increases recall but decreases precision, and vice versa. This inverse relationship is balanced using the F-measure.

## Answer

**Precision** = TP/(TP + FP): of the records predicted positive, the fraction that are really positive (exactness).
**Recall** = TP/(TP + FN): of all real positives, the fraction the classifier finds (completeness).

#### Inverse relationship
For a given classifier, improving one of them usually reduces the other, because both depend on the decision threshold.

- **Lower the threshold** (predict "positive" more readily): more real positives are found, so FN falls and **recall rises**. But more negatives are also wrongly accepted, so FP rises and **precision falls**.
- **Raise the threshold** (predict "positive" only when very sure): FP falls, so **precision rises**, but many positives are missed, so FN rises and **recall falls**.
- Extreme cases: predicting *every* record positive gives recall = 100% but low precision; predicting only one very certain record positive gives precision = 100% but very low recall.

*Example*: 100 real positives in 1000 records.
| Threshold | TP | FP | FN | Precision | Recall |
| --- | --- | --- | --- | --- | --- |
| High | 40 | 5 | 60 | 40/45 = 0.89 | 40/100 = 0.40 |
| Medium | 70 | 30 | 30 | 70/100 = 0.70 | 70/100 = 0.70 |
| Low | 95 | 200 | 5 | 95/295 = 0.32 | 95/100 = 0.95 |

Because of this trade-off, the two are combined into the **F-measure** (harmonic mean), F₁ = 2·P·R/(P + R), and shown in a precision-recall curve. Each application chooses its own balance: cancer screening and fraud detection favour high recall, while spam filtering favours high precision (so that important mail is not wrongly blocked).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Lowering the decision threshold usually:
   A. Raises recall and lowers precision
   B. Raises both
   C. Lowers recall and raises precision
   D. Changes neither
   Answer: A. More positives are accepted, so more FP and fewer FN. (Key point: Lower threshold)

2. Raising the threshold makes:
   A. Recall rise and precision fall
   B. Precision rise but recall fall
   C. Both rise
   D. FP rise
   Answer: B. Fewer FP but more missed positives. (Key point: Raise threshold)

3. Predicting every record positive gives:
   A. Precision 100%
   B. Both 100%
   C. Recall 100% but low precision
   D. Recall 0%
   Answer: C. All positives are found but many FP. (Key point: Extreme case)

4. F1 is:
   A. Arithmetic mean of P and R
   B. P times R
   C. P minus R
   D. Harmonic mean 2PR/(P + R)
   Answer: D. F1 balances the two. (Key point: F-measure)

## Related in Data Mining

- [Confusion matrix and performance measures](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aconfusion-matrix-measures) — Data Mining, chapter 3
- [Measures from confusion matrix (152, 130)](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aconfusion-matrix-152-130) — Data Mining, chapter 3
- [Measures from cancer confusion matrix](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aconfusion-matrix-cancer) — Data Mining, chapter 3
- [ROC curve for model selection](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Aroc-curve) — Data Mining, chapter 3