How well does the A99 work for sports photography

I would recommend several options over the D800 and 5D III.

I see the D800 as being targeted towards high resolution shooters. While the D800 certainly has good AF, the 4 fps framerate is below what's usually expected of an enthusiast/professional body (they usually have 5 fps or better). You do get 5 fps when cropping, but IMO that's really not an ideal solution. You don't buy a full frame sensor to use it cropped most of the time. The large files (if you shoot raw for more flexibility, especially over noise reduction at high ISO) also makes buffer fills more likely, and will fill up cards more quickly.

The 5D III will probably do a good job (and will probably do the best job out of all the cameras I mention here), but I feel like it's overpriced without offering that much over cheaper options.

Here's what I recommend considering:

• A used D700 with a battery grip. This will come cheaper than an a99, and is pretty close to the price of a new D600 (depending on the D700's condition). You get 8 fps, along with a very good 51 point AF system.
• A used D3. You get 9 fps, or 11 fps with an APS-C crop. The 51 point AF system is very good for following action. AF point coverage, like the D700 which uses a similar if not identical system, is very good.
• A new D600. 5.5 fps is slower than 8 or 9 fps, but you also get top-end ISO performance (at least up to ISO 12800), video, and a lighter body than the D3 or D700. 24 MP can be a bit on the heavy side, though, so take that into consideration. Dust spots are a non-issue for shooting sports, because your aperture is usually wide open.

Keep in mind that the Nikon 80-200/2.8 AF-S won't cost more than $1200 or so in pristine condition, and the still adequately fast screw drive Nikon 80-200.2.8 costs around $800 used. The Sony 70-200/2.8 new costs $2000. The Sony a99 costs $2800, compared to the D600 at $2100. If you can save more than $1500 by going with Sony, consider sticking with Sony.

I went with the D600 and a 80-200/2.8 AF-S lens. So far it's doing a remarkable job.