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difficulty 3/5

Mean average precision

Definition

The area under a precision-recall curve, averaged over classes — and in detection, also over IoU thresholds. The threshold you report it at decides whether it can see localisation quality at all.

Formula
AP=∑n(Rn−Rn−1) PnmAP=1∣C∣∑c∈CAPc\mathrm{AP} = \sum_{n} (R_n - R_{n-1})\, P_n \qquad \mathrm{mAP} = \frac{1}{|C|}\sum_{c \in C} \mathrm{AP}_c

Intuition

A detector does not return an answer, it returns a ranked list of guesses with confidences attached. Any single threshold on that confidence picks one point on the precision–recall trade-off, and reporting that one point tells you almost nothing — a different threshold would have given a different answer.

Average precision summarises the whole curve instead: it is "the weighted mean of precisions achieved at each threshold, with the increase in recall from the previous threshold used as the weight" [4, Definition]. Then mAP averages that over classes, so a detector cannot hide a useless rare class behind a good common one.

Detection adds a third thing to average over, and it is the one that causes the trouble. Before you can call a detection correct at all, you have to decide how well its box must overlap the real one — and that decision turns out to change the score far more than most model improvements do.

Formal definition

How it works

Where it's used

Why & when

Worked example

Pitfalls

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On the cheat sheet: Vision tasks →

Sources

  1. Zhang, Lipton, Li, Smola. Dive into Deep Learning — Anchor Boxesbook · retrieved 2026-09-14https://d2l.ai/chapter_computer-vision/anchor.html
  2. Lin, Goyal, Girshick, He, Dollár. Focal Loss for Dense Object Detection (2018)paperhttps://ar5iv.labs.arxiv.org/html/1708.02002
  3. Ren, He, Girshick, Sun. Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks (2016)paperhttps://ar5iv.labs.arxiv.org/html/1506.01497
  4. scikit-learn developers. average_precision_scoredocs · retrieved 2026-09-14https://scikit-learn.org/stable/modules/generated/sklearn.metrics.average_precision_score.html

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