Rollover balls. Same format, but if none of your ping pong balls are drawn, they roll over to next year. Simple change, more fair over time, and more teams in the lottery (since they may have leftover balls from past years). Every time you "win" the lottery you go back to 0 balls. Got screwed? Well that means more chances next year. As a bonus, if you already have some rollover balls, you might be less inclined to tank your season, because it has a smaller impact on your total odds.
More advanced version, you lose balls based on where you pick. So if you are the worst team in the league, you get 13 balls. Get the #1 pick and you lose all of your balls for next year. #2 pick, you lose 12 balls, #3 pick you lose 11 balls, and so on. Playoff teams don't get any balls, but they could have some leftover from the last time they were in the lottery.