Back when we only had film, people thought that having a motor drive would help them "get the shot" by holding down the shutter release and blasting through a roll of film.
John Shaw, the nature and landscape photographer, and author of a lot of great books on photography, said that motor drives were not fast enough to get the perfect shot. They were useful for making sure the camera was ready for the next shot though.
Move forward to now, when we have digitals that can shoot a lot faster. Mine can do 8 frames a second. I mostly shoot fast action and only use single shot mode, but one day was thinking about Shaw's comments and decided to do an experiment. In daylight, at 1/5000 shutter speed, while shooting some very fast action, I switched to continuous mode and mashed on it for over a second.
Later, looking at the images there was significant gaps in the action between the frames. Out of a second's worth of movement, the camera only caught 8/5000 of what went on, which left about 4992/5000 of a second unaccounted for. In other words, most of the second was missed and the odds of me getting the best action were very small as a result. I had repeatedly gotten better results by watching the action and timing my shots.
And, that's something I've heard repeatedly from pro photographers shooting baseball, and all sorts of other sports. The big name pro baseball shooters have a holy grail of getting a bat-on-ball shot and like to show the results of using the continuous mode vs. timing it, and that they have better results also, by timing it.
So, while it's cool to have a high frame rate, what is more important is that the camera can respond faster and be ready to shoot again faster, but it's your ability to pick the right moment to release the shutter that will get the best results.
Now, regarding focus while following fast action: You have to think about what the camera needs in order to focus. It needs good light, obviously, but also needs good contrast on the subject, either in patterns or changes of color.
The camera tries to locate the edges of things, and then reduce the blur of the edge by focusing until it's got the least amount of blur. When it's dealing with a monochromatic subject or very low contrast the focus can, and often will, switch to a slow seek to try to find the focus, or worse, give up after seeking several times.
You can test that by focusing on a wall with no contrast then lowering the lights and doing it again, then focusing on something with lots of contrast or patterns, then lowering the lights and doing it again. As the light levels go down, or the patterns go away, the camera has to work harder and eventually gives up. Now, imagine how much harder the camera has to work when the subject is moving all around and it's easy to understand why the camera goes out of focus often.
Nikon and Canon try to do predictive autofocus by figuring how fast the subject is moving toward or away from the camera as it's tracking, then adjust the lens' focus when you release the shutter to pre-compensate for the subject's motion toward or away from you so the image will be sharp. That's all fine, but often the lens can't focus fast enough so it is still behind or in front of the subject. A faster focusing lens can help, which is why both Canon and Nikon have their high end pro-lenses. My Canon 70-200L F2.8 AFS lens will run circles around my wife's 70-300 F4.5-5.6 lens when tracking action, but then again, my needs are different than hers.
So, having decent light and a faster focusing lens can help, but so can you, by tracking the area on the subject that will give the camera the best chance. Using the center sensor helps a lot, but where you put that sensor can make a difference, so find whatever part of the subject moves the least and keep the sensor there as you track movement. The waist and hip area moves less than arms and legs or the head so I go for mid-chest to waist or the hips. And, as the action unfolds hopefully you can keep one of those areas in view.
Even though today's cameras are much more sophisticated than ones from a few years ago, they're still not able to deliver consistent results in tough circumstances. That's when the photographer has to take over and tell it what to do, and when. You need to be able to recognize those times the camera is going to get it wrong in advance, and take over in time, or you'll miss the shots you want when the light isn't good enough or things are moving too fast.