This is instinctive behaviour, it is herding behaviour which developed from hunting behaviour. More than two or three moving live things, be it sheep, ducks, deer or small humans that look like they are behaving as a herd (ie - a soccer field - lots of little humans running up and down at the same time) tend to incite the dog to chase. This can be a very strong drive for herding breeds and can result in car chasing and seeming aggression towards joggers and bike riders. If this drive is surpressed some dogs become obssessive about all moving things - it can become as extreme as constant tail chasing just to satisfy the urge. The nipping is an integral part of that for many collies. The best way to combat this is to provide a way for the dog to use its internal drive to chase - frisbee is a great idea! I think the problem you are having is down to when frisbee is used the little humans tend to be around, still making a noise, still not doing what they should be doing!!! The dog is feeling frustrated and the nip is exactly the right way for a herding dog to cope.
Try frisbee away from an audience, try using balls (not tennis balls, something a bit bigger.....tennis balls can get lodged in the windpipe..) as a surprise, rope toys are great (not tug of war - just for throwing) and ropes with balls on them. Make these intense one on one games a reward for the dog for accepting and lying quietly while ten minutes of soccer has gone on, then for twenty, then for thirty....etc. eventually you will get to the stage where the dog can lie quietly through each half of the match well.
This will take some time to establish and a great deal of your time - you can also use one throw of the ball, frisbee,rope as a reward for any behaviour - say the dog sits on command - throw the ball once. The dog lays down the first time you say it - throw the ball.
This will reinforce the impotance of the toy for the dog and establish it as a reward.
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