The Evolution of Draft Lotteries in Professional Sports: Back to the Moral Hazard?

In several North American professional sports, teams choose (draft) new players each year in inverse order of their end-of-season standings. Since drafting early is valued highly, teams that are not doing well might be tempted not to try hard in the last few games of the season, since by losing they might improve their draft position. To alleviate this potential problem, the National Basketball Association, since 1985, has held an annual draft lottery among the teams that did not qualify for that season's playoffs. Initially the lottery was one of equal chance; it is now heavily biased in favor of the weakest teams. A very biased draft lottery has also just been instituted by the National Hockey League. We have calculated the probabilities of different draft positions by a team's regular season standings and the resulting expected draft positions for all these lottery formats. For current schemes the expected draft positions turn out to be almost what they would have been without a lottery.