I think there's a difference in the ways in which sports announcers from the U.S. and U.K. refer to the teams. If my memory serves me correctly, I think announcers in FIFA from the U.K. will use forms of verbs corresponding to a singular noun; in the U.S., I believe it's the reverse. Please, correct me if I'm wrong about the two different styles across countries, but I think my question's clear enough.
Real Madrid competes very well.
I believe that "competes" is the proper verb for the sentence mainly because of the subject verb agreement regardless of the adverb "very well"