I had a brilliant idea..
For sports that require judging (gym, diving, figure skating etc). Incorporate sensors into the outfits of the competitors (or in the case of diving.. figure something out
), these sensors are then picked up by several cameras around the arena (like they do motion capture for video games). All these cameras are connected to a computer which has a huge database of various possible moves performed in the most perfect way. After the competitor completes their routine, the computer analyses all the moves in terms of perfection and give the competitor their score depedant on how perfect it was.