[s_forbes]

We found that the most jamming came from balls being stacked vertically, just like in the pictures you just posted. We made the bottom of our hopper large so that none of the ten starting balls were stacked on top of each other. If the balls are put in in the same pattern at the beginning of each match, then it will work every time (it did for us)

I highlighted the funneling parts of the hopper in our picture. The bottom of our hopper is at about a 30 degree angle and the two strips near the bottom just keep balls from getting hung up on the walls near the bottom. We also tried to put a shelf in right over the exit to prevent stacking, and it did it's job perfectly.