Arizona State psychology professor Michael McBeath has proposed a simple model to explain how dogs play fetch.
McBeath had previously noticed this interception strategy in professional baseball players pursuing fly balls.
[1] Tim Pennings,[2] a mathematics professor at Hope College, has found that dogs are somehow able to calculate the optimal path to a ball thrown in the water.
He showed that the dog is able to calculate the optimal point to jump into the water, a problem Pennings must resort to calculus to solve.
They propose that the dog optimizes its behaviour on a moment-to-moment basis, choosing at each moment the path that allows it to maximize its speed of approach to the ball.