The formula for recall is $$R = TP / (TP + FN)$$. To compute the macro-average recall of a multi-class classification, compute $$R$$ for each class, add them together, and then divide by the total number of classes. This can be summarized by the following formula: macro-average recall = $$(\sum_{i=1}^nR_i) / n$$, where $$R_i$$ is the recall of the $$i$$th class and there are $$n$$ classes.

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Macro-average is the average of some metric (e.g. precision or recall) among classes, where all classes are weighted equally.  Since this effectively gives a "boost" to smaller classes, macro-averages are more indicative of the precision/recall within smaller classes than within larger classes. According to the referenced article, however, macro-averaging can be bad practice when classes vary widely in their number of instances.

Macro-average

https://datascience.stackexchange.com/questions/15989/micro-average-vs-macro-average-performance-in-a-multiclass-classification-settin

Micro Average vs Macro average Performance in a Multiclass classification setting

The formula for precision is $$Pr = TP / (TP + FP)$$. To compute the macro-average precision of a multi-class classification, compute $$Pr$$ for each class, add them together, and then divide by the total number of classes. This can be summarized by the following formula: macro-average precision = $$(\sum_{i=1}^nPr_i) / n$$, where $$Pr_i$$ is the precision of the $$i$$th class and there are $$n$$ classes.

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