[GeeTwo]

Without a more specific understanding of the rules (number of balls, minimum separation distance between throwers and dodgers, is catching allowed, size limits due to either rules or mandated materials), I don't think it's possible to decide between a robot that dodges based on size, acceleration or rotation.

Unless the rules are set up so that balls are coming in from a known span of directions, a kiwi drive would be on the short list. Swerve would also be worth considering, but given the short reaction times, the time to steer the wheels to the desired direction might be more costly than losing half the acceleration.

If catching is allowed and scored, I might consider building a larger robot with a net mounted on movable poles.

Multiple pickups and launchers would be tempting, but a fast turret or robot rotation is much easier and more reliable, and almost as effective.

Autonomous dodging (and possibly catching) would definitely be on the short list of desired features from the programmers. Presumably using a panoramic camera, it would have to detect a ball quickly "getting larger", then decide which way to go to get away from it based on its apparent motion left to right. As far as whether to dodge left or right, a quick decision is almost certainly better than the right decision.