Can we mention Speedball 2: Brutal Deluxe some more?
Firstly, the intro music:
Now I never had this back in the day but having played it in emulation later on, it really was excellent. Basically, the game is an ultra-violent cross between handball and ice hockey in which you take control of your team of nine trying to take possession of the ball and stuff it in the goal. The arena is bounded by walls which the ball can bounce off on all sides, and about halfway in the middle of each side's half is a sphere which, if the ball touches it, bumps it at high speed in the direction it came a bit like a pinball bumper.
There are no fouls. It is perfectly legitimate to slide-tackle, punch, headbutt, or otherwise brawl with other players regardless of whether or not they have the ball and regardless of what they are doing. There are no restarts other than after a goal so no goal kicks, corners, or throw ins - even if a goal is saved the goalie is fair game so it is perfectly legitimate to make a shot on goal, clobber the goalie as he saves it and sling the ball in afterwards. Ten points are scored for a goal and two points for successfully bouncing off and lighting up one of the stars on your side of the pitch. Ten points are also awarded for injuring an opposing player sufficiently to require medical treatment. As a result, the game becomes a panoply of punches, kicks, sounds of people falling over, and clonks as the ball bounces off the walls. You can also get score multipliers by sending the ball through a loopy thing on the halfway line or energise the ball, which causes opposing players attempting to intercept your passes to fall over.
The only thing I'll fault it for is that it suffers horribly from A Winner Is You, but so do most Bitmap Brothers games for that matter.
EDIT: It just occurred to me that this isn't as fictional a sport as thought.
Calcio storico is basically speedball in real life.