It's statistically unlikely in games like that not because the protagonist is only 1 in n characters, (though that is a factor,) but because typically the side characters are allowed to be more eccentric in a way that one or more of them tend to be very likeable -- either in general, or with a specific sub-audience. I don't know if there's anyone who prefers Commander Shepard over all of Garrus, Tali, Wrex, Mordin, and whoever else you want to throw in. Shepard themselves is just too much of a neutral blank slate, and this is in a game where you can specifically play as a "paragon" or a "renegade," and thus Shepard often does show some real personality.
I guess I have to ask, how large does the cast have to be to be "very large?"
Only the exceptions can be exceptional.