Macro vs Micro Averaging for Multi-Class Problems

Why Averaging Matters

With more than two classes, a single precision/recall/F1 number per class tells only part of the story. We need a way to aggregate per-class metrics into one overall score. The choice between macro and micro averaging determines which classes drive the final number.

Macro-Averaging

Compute the metric (e.g., F1) for each class independently, then take the arithmetic mean across classes. Every class contributes equally, regardless of how many examples it has.

$\text{Macro-F1} = \frac{1}{|C|} \sum_{c \in C} \text{F1}_c$

Best for imbalanced data where minority classes matter. If class A has 1000 examples and class B has 10, macro-F1 gives them equal weight. A poor F1 on the minority class will noticeably drag down the macro average.

Micro-Averaging

Pool all TP, FP, and FN counts across classes into global totals, then compute the metric on those pooled counts.

$\text{Micro-F1} = \frac{2 \times \sum_c \text{TP}_c}{2 \times \sum_c \text{TP}_c + \sum_c \text{FP}_c + \sum_c \text{FN}_c}$

This is equivalent to computing accuracy (when each example has exactly one label). Large classes dominate; a minority class with poor performance barely affects the score.

Worked Example

Consider a 3-class problem with the following per-class counts:

Class	TP	FP	FN	Examples
Hardware	90	5	10	100
Theory	80	10	20	100
Ethics	5	5	15	20

Per-class F1:

• Hardware: Precision = 90/95 = 0.947, Recall = 90/100 = 0.90, F1 = 2×0.947×0.90/(0.947+0.90) = 0.923
• Theory: Precision = 80/90 = 0.889, Recall = 80/100 = 0.80, F1 = 0.842
• Ethics: Precision = 5/10 = 0.50, Recall = 5/20 = 0.25, F1 = 0.333

Macro-F1 = (0.923 + 0.842 + 0.333) / 3 = 0.699

Micro-F1: pool all counts.

Total TP = 90 + 80 + 5 = 175 Total FP = 5 + 10 + 5 = 20 Total FN = 10 + 20 + 15 = 45

Micro-Precision = 175/(175+20) = 0.897 Micro-Recall = 175/(175+45) = 0.795 Micro-F1 = 2×0.897×0.795/(0.897+0.795) = 0.844

The macro-F1 (0.699) reflects the poor Ethics performance. The micro-F1 (0.844) is dominated by the two large classes and hides the Ethics problem. When minority classes matter, report macro-averaged metrics; when overall throughput matters, micro-averaging suffices.

Summary

Averaging	How	Weight	Best for
Macro	Per-class metric then average	Equal per class	Imbalanced data, minority classes matter
Micro	Pool all TP/FP/FN then compute	Proportional to class size	Overall throughput, balanced classes

Past paper questions: y2023p3q8(b) (per-area evaluation)