I'm evaluating a multilabel classifier. I'm familiar with the Area Under the Curve statistic, which has some nice properties (e.g. chance level is always 50%). But for some applications, it's more appropriate to use the "Mean average precision" metric which evaluates results based on the top $K$ results returned. MAP is described nicely here at fastml and here at kaggle. In my case I'm using MAP@20, so evaluation is on the top 20 results returned. (My data contains a variable number of true-positive labels for each item, up to 12.)

But: what is a good score for MAP@20? What is a bad score? What is the chance score?

(Clearly 100% is the best score and 0% is the worst.)

I can't find an online reference that discusses this. I think the chance score must depend on the ratio of positive to negative labels in your data.

It would also be helpful to know if there's a useful interpretion of the score. For AUC there's an interpretation as the probability of ranking a random positive instance higher than a random negative instance. Grateful for references or explanations.


2 Answers 2


Well, for what it's worth, here is an empirical plot of the chance values for the MAP statistic. In this plot, the x axis represents the proportion of ground-truth-positives in the data, and the y axis represents how far we go down the ranked list when evaluating MAP.

matrix plot - fades down to 20%, 10% or lower as the num positives in groundtruth increase

The code to produce the plot is here.


For this part of the question "What is the chance score?...", you could look at this paper: Exact Expected Average Precision of the Random Baseline for System Evaluation, The Prague Bulletin of Mathematical Linguistics, 2015, 103, 131–138 (https://ufal.mff.cuni.cz/pbml/103/art-bestgen.pdf).


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