Of course, the behaviour of nine balls can be completely described using Newtonian mechanics, without recurrence to the term entropy. You can, but you do not have to use the term (for that kind of systems). On the other hand, a system made of one mole or so of balls is mecanically exactly as determined as one made out of nine balls is, yet it is impossible to describe it by Newtonian mechanics, due to the high number of coordinates necessary. Hence, for the kind of systems in discussion, entropy is not a necessary term in the strict sense, it is an extension of Newtonian mechanics that allows treatment of systems consistent of very high number of particles.
If the balls are atoms or molecules, the above term "Newtonian mechanics" should be read as "quantum mechanics".