Your not going to get into the Super Bowl, Olympics or any other major sporting event just to build a portfolio. Events like that are crowded on the sidelines as it is with "working media" people. Most major sporting venues are trying to cut the number of credentials issued with sideline access, not increase them.
If your wanting to build your portfolio and use sports, stop by the local high school or jr college. Most high schools would love to have someone shoot their games. I'll do 10-11 hs football games in a year and about half the time, someone from the other team will ask if I can do their game sometime. Sorry but I am already contracted with one hs and that is it.
I was shooting from the opposing teams side last week, (sun was at my back there) and one of the coaches comes up and starts a conversation before the game. He asked if I do freelance assignments. Well yes but what do you have in mind? Of course he wants some shots on their homecoming night in 3 weeks or so. I told him I could do it but, the compensation I would have to get would be around $300 and that would be without prints. LOL He about fell over. He said when their school can build a 4.2 million dollar stadium, like the team I shoot for, he will give me a call.
I'm not trying to build a portfolio but if that is what your wanting to do, the high school is the place to start.
You don't have to have Payton Manning passing to Marvin Harrison to have a good shot. John smith catching a pass from Bob Jones can make just as spectacular shot for your portfolio.
Trust me hs football is fast paced enough to cut your teeth on. I can't imagine never having shot a football game before, or very few, and going to a Division A or pro game and shooting it.
On shooting sports...If you see it happen then you didn't get it.