The ROCs are used to assess the association confidence that a [[*WISE*]{}]{} source in a random region in the sky, where no $\gamma$-ray source is located, has IR colors compatible with the WGS. To provide an estimate of the association confidence, we considered the distribution of the strip parameters $s_b$ and $s_q$ for all the [[*WISE*]{}]{} sources within each ROC associated to an UGS. For these [[*WISE*]{}]{} sources we estimated the confidence $\pi$ that a generic [[*WISE*]{}]{} source belongs to the same class as the $\gamma$-ray blazar candidate selected within the SR. Thus the $\pi$ value will be expressed as the ratio between the number of [[*WISE*]{}]{} sources of a particular class and the total number of [[*WISE*]{}]{} sources that lie in the ROC.

Testing the association method with blazars {#sec:test}
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We performed a test to evaluate the completeness of our association method searching for the $\gamma$-ray blazar candidates that are potential counterparts of the 2FB sample, and verifying whether our procedure correctly finds the same associations as in the 2FB sample.

Assuming that the 284 blazars in the 2FB sample have been associated to the real low-energy counterparts, we run our association procedure considering the IR colors for 