Considerations for the ideal sports lens are pretty standard. First, you need a quick lens, one that will deliver depth of field to the subject’s isolation and allow high shutter speeds.
You will see many of these very fast, long lenses in professional sporting events, lenses such as the Canon EF 400mm f/2.8 L IS II USM or Canon EF 200-400mm f/4l IS USM. Many sports professionals use the first lenses, enhancing the sharpness and speed of the zoom capability. But some types of shots require a zoom lens, and that what I would go with. Of course, some of these Canon costs more than my pick-up, so there’s also that, not really for non-pros.
What you need to do is to think about your needs and then check out the options that mark most of them.
For a sports lens, there are actually 4 variables to look at:
Focal length-you need to know how far the subject will be when photographing, what kind of subjects you are going to photograph and what type of framing you want (all the sand, whole body, torso, headshot, etc.)
Maximum opening-Long primers (200, 300, 400 mm and longer) are available (for Nikon/Canon at least) with an aperture of f 2.8, which makes them Uber expensive but able to muster more light on stadiums, or other sports venues.
Auto-focus response capabilities. If you plant shooting action sports, this is a must. Internal focusing motors (unlike the engines in the body) are faster and more accurate. VR/OS is not usually used in sports shooting as you will need faster SS to capture the action and avoid motion blur (so why the 2.8 or better aperture is desirable)
The ergonomics of the lens. You might not have much choice of lenses depending on your camera system, but if you do, ergonomics is something you should consider. Do you have a dedicated AF-on or AF-Lock button? Where is the focus ring?
Above all, sharpness-The lens needs to be sharpened (or very sharp enough) from the edges to the center and if it is a zoom lens, from the smallest focal length to the largest.
Factor 2– It must be fast. The objective must have a fixed and as wide as possible opening. Something like f/2.8. Certainly not worse than F/4.
Factor 3– Zoom along Telephoto. No need to say that. You will not be very close to sporting action or sports; You are more likely to be on the edge or sitting in the stadium. So the telephoto is a must. But under certain conditions the action will approach you (like the sprinters that come around your curve, etc.) so it takes a telephoto zoom. The 70 – 200 mm or 100 – 400 mm are ideal.
Based on the above, I would choose a 70-200 mm, F/2.8 (Nikon and Canon both have these and they are simply ideal).