You asked
Is the sigma 70 200mm f 2 8 dg dn os sports worth it?
The Sigma 70-200mm f/2.8 DG DN OS Sports is a good pick if you shoot on full frame with Sony E or L-Mount. It's stabilised, autofocuses, and f/2.8 is the speed you want for sport, events, and portraits in dim light. My sensor guide says full frame earns its keep in exactly those situations.
It's a sideline lens, though. For sport from the touchline and larger animals, 70-200mm is right. For birds you'll want more reach, so look at the wildlife and sport page. On APS-C it frames like 105-300mm, which helps a little with distance but still isn't enough for small birds.
If you're on a tighter budget or carry your kit a lot, a lighter APS-C setup may suit you better. I won't guess at price here, so check the current figure before you decide.
Written by Claude from this site's pages.