There's a difference between photography at an event which is not supposed to be all about the photography... and an event occurring specifically FOR the photography.
If you're attending a sports event which is not centered around photography, don't be surprised to find all kinds of restrictions on what a photographer is permitted to do and what equipment they're permitted to use.
On the flip side... if what you're doing is shooting photos (perhaps for articles, promotional photos, etc.) then it's also not unusual to have a date/time setup (not a regular event with a competition, live audience, etc.) where the athletes are there SPECIFICALLY to be photographed in the performance of their sport. In those situations you might have all kinds of gear and all the rules are different -- the photographer isn't interfering, the event is FOR the photography.
I bring up these two scenarios because whichever scenario applies to you will COMPLETELY change the answer to the question.
If you're in the latter category (the athletes are performing specifically so that you can capture photos -- e.g. for promotional material, etc.) then you can switch to lighting setups for high speed flash and continuous burst photography. To make that work, you'll have clusters of your 600EX-Rt flashes, probably an ST-E3-RT on-camera, and perhaps 6 or more flashes going off at the same time. Incidentally... you "rent" these because it would probably not be practical to own 12 600EX-RT units unless you're doing this sort of thing all the time.
See:
Canon DLC: Gallery: Action Photography with the Speedlite 600EX-RT Radio System
That video you should give you some idea of how they're capturing action photography outdoors using flash and competing with the sun. The idea behind clustering the speedlites is that your power is SUBSTANTIALLY reduced when you kick on high-speed sync mode. By combining the power of lots of flashes you still have the ability to do rapid shooting and high speed sync and get enough light.
Again... if these are regular sports events (competitions) and you just happen to be there shooting... then I can't imagine you'd be allowed to use that kind of gear.