For sports, there are of course different reasons to use the different exposure modes. I'll briefly list the advantages.
P: No advantage at all, really.
Tv: Keeps shutter speed constant. For situations where you want to have a certain motion blur, this is often good, provided you also want automatic exposure.
Av: Keeps aperture constant. Sometimes you want to use the lens fully open, to blur the background, or light is low, so you want to use it fully open to at least get as short exposure time as is possible. Can be combined with Auto ISO and auto longest allowed exposure time in varying light, to provide automation also considering the current focal length. But the shutter speed limit will then be optimized for things standing still, not for high speed sports pictures, so that may be of limited value in this application.
M: Keeps both aperture and shutter speed constant, and thus exposure as a whole (provided you have a fixed ISO setting). Good if you are shooting sportsmen with different color tones on their clothes, as otherwise a "white team" will not meter the same as the "black team". Nowadays, M can be combined with Auto ISO, if you want to keep a certain exposure time (motion blur) and aperture (background blur), but still have automatic exposure. Main drawback then is that as of today, only the 1DX will allow you to influence the exposure level in that mode.
Autofocus: The speed of the AF is related to how well the lens works with the camera. High accuracy AF requires at least f/2.8 and center point with your camera (70D). But low light performance isn't related to the max aperture of the lens, since the AF system has its own aperture anyway. It's just the physical size of the aperture that's important, due to the spread of lightrays coming in, not the amount of light coming in. Thus using an f/2 lens with a point outside the center one will not give any better performance, not even in low light, than an f/5.6 lens.
Not using the sports mode is essential for sports photography in general, even if that sounds utterly backwards. The reason is that you can usually not get rid of using all AF points at the same time in the preprogrammed modes, but there are only a few occasions when using all points at the same time actually is the right thing to do. With the 1DX I've experimented a bit more with using all points, but the reason it works pretty good in some of these situations is the iTR system in the 1DX (intelligent subject Tracking and Recognition), where an additional 100 kpixel sensor evaluates the color of the subjects, and directs the AF system to track that particular pink shirt, or whatever it is you are aiming at. Currently, only the 1DX in the EOS range supports this. With a 70D, selecting a single point is usually your best option. A single point with expansion is my favorite in that class of cameras, for the kind of sports I shoot, but it takes a 7D to support that.
Whether you want to use RAW or jpeg depends on the situation and what you intend to do with your pictures. Sports shot in good daylight, where the final destination for the images is a web album or Facebook, you can just as well shoot in jpeg. Nobody will ever notice the difference.
Sports shot in low and/or artificial light will come out better in RAW. The drawback with RAW, and that's the only drawback, is the file size. You'll need 3-4 times the storage to hold your files, something which can be essential if you want to shoot a lot.
It states above that RAW vs. jpeg affects burst mode speed, but it doesn't. Only burst mode length, before the buffer is full.
It states above that AF speed also depends on max aperture, but I've already been through that. It doesn't. Except that lenses with large openings often also have high performance AF motors, but the relationship there is financial, not optical.
I use my 70D and 70-200 for hockey.
