You asked
Is the nikon z 100 400mm f 4 5 5 6 vr s good for sports?
Yes, for a lot of sport. The Nikon Z 100-400mm f/4.5-5.6 VR S is stabilised and has autofocus, and it gives you 100-400mm on full frame. That reach suits sport from the sideline and larger animals. The wildlife and sport page puts 100-400mm at the sensible end for that kind of work.
It's a zoom, so it gets darker as you zoom in. f/4.5-5.6 is fine in bright stadium light or outdoors in daylight, but it will struggle in dim indoor venues.
On a full-frame body, the Nikon Z6 II is a sensible everyday partner. If you want the lens's reach on a smaller budget, the Nikon Z50 II gives it roughly 150-600mm of view. For more background, see buying used, since long lenses like this one often change hands.
Written by Claude from this site's pages.