German researchers from the University of Münster have tackled that question. In a paper published in the journal Cyberpsychology, Behavior, and Social Networking this past summer, the scientists sought to determine the relationship between online video games and friendship. They surveyed German video game enthusiasts to measure their involvement with online games, their web of friendships online and off, and their emotional sensitivity -- a behavioral marker for shyness.
After controlling for confounders like age and gender, they found that those subjects with high emotional sensitivity reported more online friends than offline when compared to those with low emotional sensitivity. High emotional sensitivity also correlated with online friendships that transformed into offline friendships.
In other words, the shier you are, the more likely you are to make more of your friends in cyberspace than meatspace, at least if you're a self-identified gamer. As Gamasutra put it, "emotionally sensitive users are using the online gaming environment differently from their counterparts. As they are shy in face-to-face interactions which translated to fewer friends, but they were able to make more friends through online videogames which its affordances (i.e., asynchronicity, visual anonymity, etc.) paved a way for them to compensate or overcome their shyness."
The full paper is behind an academic paywall, but the Gamasutra summary is worth a read.