Mean Average Precision

Accuracy assumes one prediction per example: the model says a label, the label is right or wrong, divide correct by total. A detector breaks that assumption before you can even start counting. One photo might produce zero predictions, three, or eleven, and the number of predictions has no fixed relationship to the number of real objects in the scene.

A prediction can also be right and wrong at the same time: correct class, badly placed box; well-placed box, wrong class; or a box that overlaps two real objects and cannot be cleanly credited to either. “Accuracy” has no sensible definition here, because there is no fixed-size list of comparisons to divide correct by total.

The fix is the same two numbers a plain classifier uses, redefined for boxes. Precision asks: of everything the model flagged, how much was real? Recall asks: of everything real, how much did it catch? “Correct” now means the predicted box overlapped a real one enough — the IoU threshold from the earlier chapter — and cleared the model’s confidence threshold too.

Ten fixed detections below are already labelled correct or incorrect against that IoU test, sorted by how confident the model was. Slide the threshold down and more of them get flagged: precision and recall move, and not always in the direction you would guess.

Notice precision does not fall smoothly as the threshold drops — it dips whenever a false alarm gets included, then partially recovers when the next correct detection joins. Pick any single threshold to report and you are making an arbitrary call about where on that jagged curve to stand.

Average precision sidesteps the choice: instead of one threshold, walk down the sorted list and note the precision each time another real object is caught. Add those up and divide by the number of real objects in the scene — so an object the detector never found contributes zero. In the panel above that is (1 + 1 + 1 + 0.8 + 0.83 + 0.75) / 8 ≈ 0.67. It is a way of scoring the whole trade-off curve with one number instead of committing to a threshold nobody agreed on in advance. Mean average precision then averages that score again, across every object class the detector was tested on — one AP for “pedestrian”, one for “bicycle”, one for “traffic light”, meaned into the single number that gets reported.

The panel’s ten detections, walked down by hand.

# Ten detections sorted by confidence, each already marked correct or not# by an IoU check. There were 8 real objects; 2 were never found at all.correct = [True, True, True, False, True, True, False, True, False, False]real_objects = 8 hits = 0precisions_at_hits = []for rank, is_hit in enumerate(correct, start=1):    if is_hit:        hits += 1        precision = hits / rank        precisions_at_hits.append(precision)        print(f"rank {rank:2}: hit,  precision {precision:.2f}, recall {hits / real_objects:.3f}") ap = sum(precisions_at_hits) / real_objects   # a missed object adds 0print(f"average precision: {ap:.2f}")

It prints the same 0.67. Flip one of the last two detections to True and see how much a single late hit is worth.

mAP quietly bakes in a choice it never surfaces: the IoU threshold that defined “correct” in the first place. mAP at IoU 0.5 is a much easier bar to clear than the stricter mAP averaged over IoU 0.5 through 0.95 that benchmarks like COCO now report — the same detector can score respectably on one and mediocrely on the other, and “mAP” alone does not say which was used.

It also treats every miss as equally costly, which is never true in practice. A detector that misses a parked car and one that misses a pedestrian stepping into the road produce the same deduction from AP, and only one of those two failures matters at highway speed. A single mAP number is a fair summary of overall detection quality and a poor guide to which failures you can actually tolerate.