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Just to clarify - the "crazy" second bounce of the ball isn't actually caused by an off center core, nor the shooting strings on the stick (although they do play a part).
The ball is solid rubber, so it grips the ground when it bounces. Any spin at all on the ball will cause the bounce to alter, also any contact will cause the ball to spin. So, the ground, wall, goal post, shooting strings, etc. will all cause a spin on the ball whether it is in flight or just being propelled.
The second bounce is different from the first because the first bounce will affect the spin, then the second bounce will reflect the change from the first bounce. etc. etc.
Simple experiment - lob a ball underhand and you won't see much change as it bounces away from you. Throw it off the ground towards a wall in a manner where it will launch into the air. It will take on a back-spin which will make every second bounce from that point forward have a more forward trajectory. The ground will give it a slight forward spin which will be enhanced as it comes up and off of the wall. As the ball comes back to you it is now going the opposite direction so the spin now becomes a backspin relative to the direction that the ball is traveling. This backspin will make the first bounce seem very straight up and down and stop some of it's momentum. However, once it hits the ground for that first bounce, it's momentum and the spin will cause it to grip the ground and change the spin direction to a forward one. This will be repeated in a diminishing pattern each bounce to seem like every second bounce jumps forward.
The shooting strings actually put a backspin on the ball (or a directed spin by twisting the stick as the shot is taken). And, since the first bounce reverses the spin, this would turn into the forward spin by the time the ball hit the boards, which technically does enhance the science behind the crazy second bounce.