Any suggestions for how to get good sports photos?

Most of my photography has been of relatively stationary subjects, where I just use single-servo AF and either focus & recompose or move the single focus point to where in the frame I want the subject, or largely-individual sports like triathlon. But I've struggled getting sharp shots in team sports photography with a large number of moving people in frame.

If I try using continuous autofocus, it often focuses on the wrong subject or the background or seemingly nothing at all. If I try falling back on the techniques that work in other contexts, I usually just can't get the shot off at the right time.

I don't really understand the different autofocus options on my camera. I was mostly using what it calls "3D", but I also briefly tried "group-area". I don't really understand how group-area differs from d9 or even 3D. And my camera's manual doesn't clear things up for me. I spent a little while in manual autofocus with a fairly closed aperture, by using autofocus and then switching to manual and leaving it untouched; but this only worked when play stayed roughly the same distance from the camera for a while, so didn't really scale well.

Separate from the focus question, I spent the afternoon shooting at 1/1600. I'm not completely sure if this is fast enough, and maybe some of the blur in my photos is actually better explained by camera shake (shooting at 200 mm on a 1.5x crop sensor) or movement of the subjects. I suspect it's probably not relevant, but I thought I'd mention it just in case.

What's the best advice for how to get sharp shots in team sports photography?

(Included photo is a SOOC jpeg of a set play on the opposite side of the field from where I was...a situation that minimised my chance of focus problems.)