I'd recommend you at least experiment with shooting in DX crop mode and see if your results are more to your liking. I think your sample photo is fine. It is tough shooting football (at least 11v11) with just 200mm. I find using DX crop gives you not only that extra reach but also improves the AF coverage and accuracy.
If I may chime in and add one word of caution on shooting DX(ok, perhaps more than just one).... I shoot American football with both a 70-200mm f/2.8 VRII and a 200mm f/2.0 VR and do myself often utilized DX crop mode on my D610. Now that I also have the D750, the in-the-middle 1.2x crop is a welcome addition to the ability to crop at time of shutter release.
DX(or any other crop mode) does not improve or in any way affect your camera's AF accuracy. If by "improves accuracy" what was meant was that the additional DX "box" within the viewfinder might be an aid to the photographer in having it made even more obvious as to when his subject(s) are moving beyond the coverage area of the AF points, then it would have been better to state it as such. Based on the OP's provided example though, I don't suspect his technique in keeping AF points on his subject(s) is lacking.
A bit more fuzzy is the topic of 'coverage'... yes, in DX mode the AF points cover a much higher percentage of the composed area, but I would argue that from an end result, resolution perspective, the AF points are going to cover the same area of the camera's view, regardless of whether in DX mode or not. Similar to my point regarding AF accuracy, if you need or want the 'crutch' of having your AF points reach nearly from edge to edge, do so knowing that the consequence is substantially less total resolution to work with afterwards. BIF is one example I can think of though, where DX mode would be even more so a requirement.
That said, I do use my Fn button to toggle between crop modes and haven't shot a game without having been in DX mode for part of it....but very selectively.
Last thing to keep in mind... unlike landscape and portraiture, I've found myself using composition guidelines such as 'rule of thirds' much less when shooting sports action. Quite often, I want the action front, center, and filling the frame. But there are times when, looking at a shot, I do want 'leading space' in front of a player, as opposed to the player facing right up against the side of the image....even taking into consideration what his/her opponent is doing, or where they are in the shot. Shooting at full resolution is usually the factor that facilitates this flexibility of re-composing in post.
If buffer, workflow, storage, & subject tracking technique permit, shoot at full resolution unless absolutely sure the DX+ area is 'throw away'.
http://stadter.smugmug.com/Gordon-L...014/Vs-LaFayette-Ramblers-Sept-05/i-WVRsL42/A
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'We truly fail only when we quit.'