Fixing the Lottery

I'm back from dinosaur hunting, no worse for wear, save for the indignities suffered upon me by Delta Airlines on the trip home. A brief report will be forthcoming. But a looming event demands our attention: tonight's NBA draft, the process by which the world's most promising young basketball talent is apportioned to the Association's various teams. A process, which, by all accounts, is in serious need of fixing. But don't worry, I have it figured out. (Hey, I was stuck in airports for over eight hours.) The basic problem is one that is common to the draft process of most professional sports leagues: the draft rewards failure. The teams that finish at the bottom of the season's standings get to choose first in the draft, funneling the best players to the worst teams. The motivation, of course, is fairness: the good teams have had their chance at success, let's give the bad ones a fighting chance. The ultimate goal is to win, so the incentive to grab a better player should be offset by the incentive to win games. In most other sports that idea basically works, but it fails drastically for basketball. The problem is that the difference in game-altering ability between the first one or two players and the next few can be huge. There are fewer players on court in hoops than in other sports, so one great player can wield a disproportionate influence. The incentive to get that very first pick can be tremendous, especially if it's between a group of teams that aren't good enough to make the playoffs anyway. As a result, a straightforward worst-pick-first draft structure leads to a race to the bottom, where bad teams intentionally lose games to have a chance to make the first pick. Repulsed by the idea that teams would purposely tank, the NBA decided to alter the incentive structure by softening the reward for losing. In 1985 the NBA instituted the Lottery: all of the teams that had missed the playoffs (seven back then, fourteen today) would be entered into a random drawing for draft position, with equal chances of getting any of the first picks. The lottery removed the incentive for finishing with the worst record in the NBA, but introduced an even worse incentive: now a team that just missed the playoffs could possibly land a franchise-caliber player if the ping-pong balls bounced their way. The last thing the Association wants is to see teams trying to not make the playoffs, so they instituted a compromise: via an ungainly formula, each non-playoff team would have a weighted chance of getting a top pick, with better chances for the teams with the worse records. This year, for example, the 14th-worse team had a 0.5% chance of getting the #1 pick. Which, of course, is the worst of all worlds! There is still some tempting incentive to miss the playoffs, but there is also incentive for non-playoff teams to lose more games. It is almost inevitable: the first pick, in the right year, can be enormously valuable, so any chance to get it will be highly sought-after, no matter how such chances are distributed. Aside from all this, there is another nagging problem with the basic idea of worst-pick-first drafts: teams can be rewarded not only because they struggled valiantly but lost with inferior talent, but also because of sheer incompetence. Good players can be steered to teams that regularly suffer from bad decision-making at the level of coaching or management. With all that in mind, here is my magic formula for fixing the NBA Lottery. (Unfortunately, I know of no way to prevent the crimes against fashion regularly committed by draft attendees.) Each year, the draft order will be chosen by the following two-step algorithm: