My fix for the draft would be to weight it against consecutive playoff misses. Every team gets a lottery ball for every year they miss the playoffs. When they make it again, they're ineligible for that year's draw and a single ball is removed. An additional ball is removed for every round they win, and the Stanley Cup champs automatically get reset to 0
Same sort of rules for the lottery draw. If you get the #5 pick, a ball is removed from your pool for next year. #4 pick gets 2 balls removed and so on with the #1 overall winner losing all of their lottery balls. The rest of the draft order is based on reverse standings like normal. This way there is no incentive to tank a season, missing the playoffs by 1 point gives you the same odds increase as being last, but if your team is bad enough long enough you will get that #1 pick eventually
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