I’m sure the experts here already know this, so this is for those of us who aren’t experts.
Little League 10U when I’m sitting behind 2nd base with my 7D2 and 70-200 2.8 mounted on a monopod and shooting the batter at 10 fps I often get several frames (from the 2nd frame on) that are just slightly out of focus. Some are tack sharp, some are just a tad off. 
I’ll skip right past explaining all the troubleshooting steps I took, and go right to the 1st phone call to Canon Tech Support. The guy really didn’t have a clue and told me to reset the camera to factory default settings – he even told me all DSLRs should be reset at least once each month.
I reset it, but no joy. Single shots were tack sharp. Action shots – following the runner – were tack sharp.
After setting up a tripod and a static target, and shooting a couple of hundred frames using various lenses – I called Canon again. This time I got Mike. I didn’t have 50 words out of my mouth when he said, “Take it off AI Servo.”
AI Servo expects movement - changes in the focus plane of the target - and when it doesn’t see them, it “hunts” just enough to soften the focus.
So I changed it to AI Focus and zipped 20 frames at my target. All of the were tack sharp. Thank-you Mike! 
For single frames, any of the 3 settings work (but Single Shot is best). If the subject is moving when you start a continuous shot group, use AI Servo, but if you start with a subject that starts static, and then begins to move, use AI Focus. Problem solved. 
"While I do use f/2.8 a lot, and f/4 when I put on the 1.4x extender, I think I'll play with f/5 - 5.6 when I'm framing just the batter. I'd like to get the catcher a bit sharper. Although my app for DOF says at 110 ft, f/2.8, and 200mm, that the DOF is 9.3 ft. Doesn't that mean that if the catcher's plane is less than 9 ft. from the plane of the batter, focusing on the batter should result in the catcher being in-focus?"
I'd say your DOF app pretty much agrees with mine. Without knowing your shooting location, I have no answer for you about capturing both the batter and the catcher in focus. DOF is pretty subjective, though. It really depends upon what you consider to be acceptable focus.
Your lens could also have a slight back focus, or front focus, issue, too. I have used "Dot Tune" on all of my telephoto zooms, and the results have been excellent.
The shot below of a play at thrid base was at 400mm, f6.3, and shot from 30 feet outside of first base. My calculator says 14 feet, which looks to be just about what I see of the ground in this shot.
But, if you accurately know your distances, then your DOF app should be a good guide.
I don't know who's asking what questions of whom....
I'm using a 7D MKII. I've reassigned the DOF button to switch between wherever the focus point(s) has been moved to, and the center. I hit it with my right pinkie - and you're right, as a DOF preview, it's worthless.
I'm going to do the Dot Tune - thanks.
If I can get them to load, these two shots would not have been possible without 10 fps.
Thanks!
FWIW - Using Dot Tune, my 70-200 also comes up needing ZERO adjustment! 
