NBA Draft Lottery Proposal, Part 1

One of the biggest problems in the NBA is tanking.  While most analysts agree that teams do not necessarily try to lose specific games by missing shots or intentionally turning the ball over, it is evident that not all rosters are constructed to maximize winning percentage in the current season.  The incentive, of course, is to land a high lottery pick in the NBA draft and possibly turn around the fortunes of a team.  While not all lottery picks turn out to be huge assets (see Milicic, Darko), the majority of NBA All-Stars were once taken in the lottery.  In fact, many of the league's transcendent superstars (LeBron, Duncan, Durant, Howard, Rose, Davis) were taken either 1st or 2nd overall.  The draft is typically so top-heavy in the NBA that lottery picks are seen as huge assets while 2nd round picks are just trade throw-ins.  Since a team's odds of winning the lottery increases exponentially with each move downward in the standings, it is logical that some teams (presumably those with little or no shot to make the playoffs) would instead focus on securing the top draft pick.

Currently, the NBA uses a lottery system in which 1000 different number combinations are distributed among the 14 teams that did not make the playoffs.  The team with the worst record owns 250 of the 1000 combinations, and therefore has a 25.0% chance of getting the first pick.  The second worst team gets 199 combinations (19.9%), the third worst team gets 156 combinations (15.6%), and so on, down to the 14th team (which owns only 5 combinations).  At the lottery, a set of 4 ping pong balls is drawn to represent one of the 1000 combinations.  This system, however, is only used to select the top 3 teams in the draft.  After the third pick, the remaining teams chose in the order of worst record to best record, meaning that a team can only move down in the draft by at most 3 spots based on record.

Why doesn't this system work?  Obviously, the franchise-altering stars are rare commodities that every team would covet.  However, being a mediocre team almost guarantees that you will never be able to draft one.  Since 1984 (when the playoffs expanded to 16 teams), only 2 teams lower than a 4th seed have even made it to the NBA Finals (1999 Knicks and 1995 Rockets).  So if lower seeds have a minimal chance of winning a title, what incentive do they have?  Well, simply making the playoffs is good for revenue in the short term, but it doesn't necessarily allow your team to get better.  This is especially true for smaller market teams that have trouble luring free agents to sign with them.  In order to acquire an NBA star through the draft you almost certainly need to be in the lottery.  However, being one of the best teams in the lottery (record-wise) is also no guarantee.  The probabilities are weighted heavily toward the very worst teams such that teams 10 through 14 in the lottery only have a combined 3.7% chance of winning.  In fact, one of the three worst teams should win the lottery 60.5% of the time.  So if you need superstars in the NBA and the easiest way to find one is through the draft (and picking very high in the draft), then it makes sense that teams would employ a strategy of tanking.

What if I told you that there a a relatively easy way to curb the tanking problem with only minor modifications to the current system?  All we have to do is juggle some ping-pong balls and re-assign the probability that each team wins the lottery.  Check out the chart below that shows the current system (red bars) and the proposed one (blue bars): 

Probability of winning lottery based on place in standings for NBA (red) and proposed plan (blue)

As you might notice, there are 3 major changes.

1. Every team has a chance of winning (including playoff teams).  Playoff teams each have a 1% chance of winning the lottery.
2. Losing helps you... unless you finish in last.  The team with the worst record has a 3.6% chance of winning the lottery, which ranks as the 9th best probability.  Finishing with the 2nd worst record gives you a 14.4% chance of winning.
3. Only the teams with the 4 worst records have reduced odds compared to the current NBA system.  Since the distribution is flatter, a lot of the probability that the 4 worst teams would normally receive gets re-distributed to better teams.

Why will this plan work?  First of all, it would definitely reduce the level of tanking in the NBA.  The problem with tanking is that teams construct a roster that is designed to lose games.  Do you want to play with fire?  If your team is worse than every other team, you will severely diminish your lottery odds.  Therefore, if you know you are the worst team, you have the incentive to get better, not worse.  This leads to a cascade effect.  If the worst team starts winning more, it puts pressure on all of the other "bad" teams to avoid the same penalty.  In fact, due to the uncertainty of your own team's true talent level and especially other teams' talent levels, you cannot simply employ a tanking strategy and guarantee that it will actually improve your odds.  Why did I chose the 14.4% and 3.6% for the last 2 teams?  I did several simulations of NBA seasons using these values and found that this ratio (14.4 to 3.6, which is equivalent to 4 to 1) was necessary to prevent any of the bad teams from employing a "losing" strategy.  The second reason this proposal would work is that it still contains many of the same features as the current system.  It still rewards teams that do poorly to establish parity in the league.  It still gives teams a chance to win that do not finish last.  In fact, since 26 of the 30 teams actually see improved chances under the new system, it should be easy to convince owners that it is beneficial.

In Part 2, I will discuss my simulations and possible extensions of this proposal.