70-300L does pretty good keeping up with a running dog, even towards the camera but:

Older cameras:

Change from one-shot AF to Servo AF. By the time the shutter releases, the dog will have moved. You need focus tracking.

Change the release from shutter to focus. This should be set for both the first shot, and subsequent shots. Shutter release takes the picture when you press the shutter, great for getting very specific timing, best if pre-focussed... not ideal for tracking a moving animal. Until this point, the camera has been tracking the moving dog, but not predicting it, and you'll get a blurry dog with a sharp tail. When you choose focus release, the camera will start predicting the motion, focussing slightly in front of the dog so that when the shutter opens the dog will be in focus. Note, this *can* cause a delay before the first shot of a burst is taken, as motion must be detected, predicted, and focus updated.


Newer cameras (basing on my R7's manual... no actual running dog experience with this camera yet):

Either, Enable Servo AF, or, change One-Shot release priority to Focus. As above. You don't seem to need to change Servo AF to focus release priority anymore. I guess that's because there's no delay with moving mirrors (or perhaps it's a limitation of the R7).


All cameras:

Your lens needs to move glass around much further to change focus near the camera, making it harder to maintain focus. Tracking when at 300mm will work far better than attempting to track at 70mm. Do not change zoom mid-burst. Focus tracking doesn't know what's going on if you're zooming out to keep the dog framed... the dog will maintain good framing longer at 300mm than at 70mm.