This evening's NBA draft lottery reminds me that the lottery is a redistributive instrument balancing efficiency against distributive goals in much the same manner as the optimal income tax (OIT) in the public economics literature pioneered by Nobel economist James Mirrlees.
The NBA draft imposes a tax on regular season success by causing it to worsen one's draft position. It thereby promotes competitive balance but weakens incentives to win this year. Ordinarily, this doesn't cause serious incentive problems, but the NBA learned through experience that, when teams sure of missing the playoffs were ranked in strict reverse order in the draft, this could create really perverse incentives, such as trying to lose all your games so you would get a # 1 pick who was a clear standout (such as a David Robinson or Hakeem Olajuwon, back in the day). The NBA responded by weakening the draft's redistributive targeting via the lottery (under which the team with the worst record has only a 25% chance of getting the top pick), so as to weaken the perverse incentive to lose.
One difference between the NBA draft lottery and the OIT is that concern about incentive effects may be more discontinuous in the former than the latter. Under the OIT, any lost labor effort due to the tax wedge between private and social returns is regrettable. In the NBA, the point may be to make sure fans don't feel too upset about the games they are paying to watch, and short of that perhaps it doesn't matter. E.g., perhaps it's not a big problem if one reason the Miami Heat shuts down Shawn Marion for the year is that there's no longer any point to winning anyway, but it would be a big problem for the league if Pat Riley (given the active personnel) coached to lose a given game.