At the risk of starting a row about maths, I should point out that, AFAIK momentum is a fair description.
The statement "momentum = mas * velocity" is true. However, velocity is a vector (it has a direction) and, while mass is a scalar (it has no direction), their product would be a vector. Therefore, "momentum" is a vector and, as such, is relevant to the discussion.
What is important is the component vectors. The ball starts with a velocity (momentum) because it is being carried by a player who is running. When it is passed, it is given a new velocity (momentum) in a different direction. It then moves in a third direction which can be determined by drawing a parallelogram of vectors. I can't post diagrams (and there really is no point), so consider the ball's component vectors - one component in the 'forward' direction and one in the 'sidewards' direction. If the passer throws the ball 'backwards', then after the ball leaves his hands, its forward vector component should be reduced (or at least, not increased - in the case of a flat pass). If the forward vector component is increased, it was a forward pass; if not, it wasn't. Simple.
I didn't want to be teacher. I wanted to be a train driver. I just can't help myself.