Convinced that a ML technique could provide a significantly better shooting policy, we decided to try using a NN as our initial attempt. We plan to experiment with other ML techniques on the same task in the future. We first considered how we should structure the NN in order to learn a function from the current state of the world to an indication of whether the shooter should start accelerating or remain still and wait. The output of this function was fairly straightforward. It would indicate whether starting to accelerate in a world state described by the input values was likely to lead to a goal (outputs close to 1) or a miss (outputs close to 0). However, deciding how to represent the world state, i.e. the inputs to the NN, represented a core part of our research.
One option was to use coordinates 
for both the shooter
and the ball. However, such inputs would not have generalized beyond
the very limited training situation. Furthermore, they would have led
to a higher dimensional function (6) than turned out to be necessary.
Instead we chose to use just 3 easily-computable
coordinate-independent predicates.
Since the line along which the agent steered was computed before it started moving (the line connecting the agent's initial position and the point 170 units wide of the goal), and since the ball's trajectory could be estimated (with some error due to noise) after getting two distinct position readings, the shooter was able to determine the point at which it hoped to strike the ball, or the Contact Point. It could then cheaply compute certain useful predicates:
The physical meaning of these inputs is illustrated in Figure 4(a). These inputs proved to be sufficient for learning the task at hand. Furthermore, since they contained no coordinate-specific information, they enabled training in a narrow setting to apply much more widely as shown at the end of this section.