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When you watch a dog run--not just trot, but really run, they do so by leading with one foot. As they hit top speed, it can look like both front feet are hitting in unison, but if you watch as they are decelerating, they go back to leading with either left or right. You can also watch a dog and determine which foot they initiate forward movement with more often. They do this in horses when determining striding and approach to jumps. Incidentally, studies show that more male horses are left-handed and more female horses are right-handed.
One would have to view many dogs turning on the box in slow motion and record which foot they lead with and which direction they then turn for meaningful comparison. I would suspect (with my limited knowledge of physics) that the dog would want to hit the box so that the foot they lead with is higher on the box and on the outside of the turn to counteract the centrifugal force of the turn.
Now, the difinitive study would take a huge number of dogs of both sexes and many breeds, record which foot they tend to initiate movement with, which foot they lead with while running, and which way they turn then see if there is any correlation.
I would also suspect that because the turn on the box is a trained behavior, there are probably many dogs that are left-handed but are turning right and vice versa because that is the way they were trained and not because of a personal preference.
All that said, my club watches how a dog retrieves a dead ball and uses the 80% or better rule to determine turn direction.
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