"Jock" certainly does have a negative connotation, suggesting a person (exclusively male) who is recognized exclusively for his athletic prowess rather than for his intellectual abilities. The term derives from that protective accessory known as an "athletic supporter" (i.e., a jockstrap).
I don't know if there is a true opposite, though "nerd" does come close, being one who is exclusively intellectual (typically focused on a single discipline, such as computers), not at all athletic.
Jocks tend to believe they are universally admired. Nerds typically demonstrate a high degree of social ineptitude.
There are so many degrees of nerd. I was not at all athletic in high school, but neither would anyone call me a true nerd. Not at all interested in sports, I did well academically, but my focus was on my band. I found it humorous that those who ignored me and my bandmates because we weren't jocks would gladly pay admission to venues where we performed, even to the point of being "fans" (and the sole source of a good income for high school students of the day). Poetic justice, as it were.