For sports photography, fast lenses-large aperture and fast focus motor are necessary.  The affordable sports Nikon lens might be  Nikon 70-200mm f/2.8G ED-IF AF-S VR ($1706).

For in door sports, a great choice is Nikon 85mm f/1.4 . 

NIKKOR 300mm f/2.8G IF-ED AF-S VR may be one of the best lenses for serious sports photography. It is a high speed telephoto lens with a Silent Wave Motor for fast auto-focusing. It is also compatible with Nikon TC-17EII (1.7x), TC-14EII (1.4x) and TC-20EII (2.0x) teleconverters.

For more affordable lenses, you have to go for the third party lenses, such as Sigma 70-200mm f/2.8 DG HSM II Macro Zoom Lens ($699), or Tamron AF 70-200mm f/2.8 Di LD IF Macro Lens ($639)

Related:

Best Nikon lenses

Best wild life lenses for Nikon

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