The longer your lens, the more shutter speed you want.
The more active the sport (say basketball vs golf), the more shutter speed you want.
The less light in the venue, the bigger f/stop you want.
All of those say F/2.8 over F/4. If you want to save money, give up a few millimeters on the long end. I bought a 70-180/2.8 Tamron, and I don’t miss that 20mm on the long end. The lens is a lot more compact as well. Also shoot raw, high ISO, and use really good denoising software. But it’s always better to have sharp, noisy photos than fuzzy, smooth photos.
The longer your lens, the more shutter speed you want.
The more active the sport (say basketball vs golf), the more shutter speed you want.
The less light in the venue, the bigger f/stop you want.
All of those say F/2.8 over F/4. If you want to save money, give up a few millimeters on the long end. I bought a 70-180/2.8 Tamron, and I don’t miss that 20mm on the long end. The lens is a lot more compact as well. Also shoot raw, high ISO, and use really good denoising software. But it’s always better to have sharp, noisy photos than fuzzy, smooth photos.