Hello jjan, and welcome to the friendly Camera Labs forum!
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Nice camera that you own! And a 70-200/2.8 is surely the best complement for sports!
The Nikon 80-200mm is a little dated but still good. In your case I'd try the Sigma. But make sure you get a good copy and buy it somewhere without a prohibitive restocking fee.
Thomas (beware: Nikon-fanboy and moderator!) My Lens Reviews
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