thats your problem.. ok not a problem really

but thats why (with the greatest respect) its pointless you giving advice to someone wanting to shoot under floodlights at football... we will never get the same quality as you and your dolly bird under studio surroundings.. we will always get noise at night but its acceptable..
to be honest i would never give advice to a portrait photographer because its well out of my comfort zone ..
meant in the best possible way
Thank you
But...
1-the OP questions whether f4 is fast enough- other people with relevant experience confirm it is not
so it is confirmed the OP needs 2.8. He has just bought the 7d so can't spend £1.6k on a lens.
2- From my testing I deduce that the sigma 2.8 is as good as the canon 2.8 for half the price (at least in terms of IQ- previously sigma 2.8 lenses have been unacceptable at 2.8, so are basically big heavy f4 lenses, therefore making the f4 IS canon a much better option). The new 2.8 OS is a good alternative to the canon 2.8 for pro-level work, the OP should seriously consider the sigma and do his own tests.
3- The OP already has a 70-200 f4, he might be better off with a fast prime- i.e. the 135L as stated, 2 stops difference- this would let him shoot in a quarter of the light with the same ISO, or 2 stops lower.
F2 will give him shots that are a cut above the 2.8 in terms of background separation, which could make the difference between an accepted image and a rejected image, or an image that's noisy and un-usable or one that's clean. I think a second body (60/50d) with a prime is a decent suggestion
I was only giving my advice from the perspective of me being surprised at the sigma lens being so good, the OP himself questions the sigma (non OS) lens, and a poster confirms that it is 'not as sharp as the canon'. The new OS lens is 'as sharp', and '1 stop faster'
These lenses are brand new and haven't been tested by many people, it is natural for people to assume they will be 'value' lenses just like the old ones- I was happy to report the 2.8 was as good as, if not better than the canon (for the OP's requirements)
Obviously I have not field tested them in harsh conditons, but hopefully my post might make someone think twice about dismissing the sigma based on previous experiences