I played Football in high school.
In fact I was an offensive linesman, probably the biggest jocks of the lot of them.
I'm not a terribly offensive person, and I'm reasonably intelligent. And many others were to. We had our bad apples, but most were decent enough.
And I know plenty of people as obnoxious as you describe that haven't played any sports.
Be careful with your generalizations, and realize that no matter what you are doing, the bad ones always stick out the most.
You could have a class with one student with a perfect 4.0GPA who is a very nice guy, kind, gentle, considerate, et all, and one dumb ass prick.
Everyone will talk about the dumb as prick, not the good student. Positive distinction doesn't get noticed near as much as negative.
I dunno, I'm a pretty average kinda guy, who is pretty neutral on matters of jock vs nerd vs whatever.
But I find the pricks get alot more attention than the good students, they just seem to stick out much better.