Fixing the Lottery

By Sean Carroll | June 28, 2007 12:07 pm

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:

  • Order the teams by their record over the last two years. Break ties using this year’s record.
    In one simple stroke of genius, most of the draft’s problems are solved. A team’s two-year record is less affected by an individual loss than its one-year record is. The incentive for tanking games is correspondingly diminished. More importantly, it’s the teams that are consistently bad that really need the help, not one-year horrors. The obvious case in point is the San Antonio Spurs, who in the late 90’s were a very good team, led by David Robinson, who couldn’t quite get over the hump. Then Robinson was injured for most of the 96-97 season, the Spurs had the third-worst record in the league, and they won the lottery. They were able to choose Tim Duncan, with whom they have just won their fourth NBA championship. That’s just wrong.
  • Teams will choose in (reverse) order of their two-year records, except that a team cannot choose in the top 3 for two consecutive years. Those that would be in the top three are bumped down until they are not.
    We want to help truly bad teams, not one-year flukes, but we don’t want to reward consistent failure either. By preventing teams from choosing in the top 3 two years in a row, we let bad teams play their best basketball without feeling like they are costing the franchise a great draft pick. Note that there is no randomizing element at any step of the algorithm, but it manages to greatly reduce the incentive for bad teams to tank late-season games. Such an incentive will still exist whenever two teams are in close competition for a single once-a-decade talent, but those players have to go somewhere.

To see how this would work, here are the records of the bottom 14 teams for the combined 2005/2006 and 06/07 seasons, starting with the worst:

  1. Portland
  2. Atlanta
  3. NY Knicks
  4. Boston
  5. Charlotte
  6. Minnesota
  7. Seattle
  8. Milwaukee
  9. Memphis
  10. Philadelphia
  11. Toronto
  12. Orlando
  13. Indiana
  14. Golden State

You can see each year’s records here. The three teams with the top picks in last year’s lottery were Toronto, New York (which they had traded), and Charlotte. So, if we began the system this year, using the actual 05/06 draft order to determine the previous year’s bottom finishers, the Knicks would get bumped down one spot, and this year’s draft order would look like this:

  1. Portland
  2. Atlanta
  3. Boston
  4. NY Knicks
  5. Minnesota
  6. Charlotte
  7. Seattle
  8. Milwaukee
  9. Memphis
  10. Philadelphia
  11. Toronto
  12. Orlando
  13. Indiana
  14. Golden State

And here’s how it actually will proceed under the current system, in the so-called “real world”:

  1. Portland
  2. Seattle
  3. Atlanta
  4. Memphis
  5. Boston
  6. Milwaukee
  7. Minnesota
  8. Charlotte
  9. NY Knicks (traded to Chicago)
  10. Sacramento
  11. Indiana (traded to Atlanta)
  12. Philadelphia
  13. New Orleans
  14. LA Clippers

This year, the teams with the worst records were Memphis, Boston, and Milwaukee; in an unlikely turn of events, they were each bounced out of the top three picks by the vagaries of the lottery balls.

Admittedly, no system is perfect, but I think mine is a substantial improvement. The present lottery system did dispense come cosmic justice by preventing Memphis from getting the first pick; they are actually a decent team, who like the Spurs ten years ago suffered an injury to their best player (Pau Gasol), and should be okay again next year without the benefit of the first pick. But the two-year rule also smoothed out their record to achieve a similar result. Portland gets the top pick either way. Atlanta, who have been pretty bad for a while, would get the second pick (in a draft where two players, Greg Oden and Kevin Durant, are rated much higher than anyone else), rather than Seattle who are actually a fairly decent team. The Knicks are a special case, as Isiah Thomas is bent on running them into the ground, and one part of his strategy is to trade away all of their draft picks, so who really cares?

Most importantly, the Boston Celtics are prevented from getting one of the top two picks, despite having the second-worst record this year. That also happened in the real world, but only through a fluke. This is important because (1) everyone hates the Celtics, and (2) they were the team that most obviously tanked at the end of the season in a desperate attempt to get a better draft pick. Now, one could argue that they could have tried even harder to lose games, perhaps by having Paul Pierce kidnapped by some guys from Southie. But really, it would have been hard to tank harder than they actually did.

It’s too late for this year, of course, but there are future drafts waiting to be salvaged. David Stern, call me! Together, we can fix this thing.

  • Eric

    I was worried you were going to take away the first pick from Portland. They were a terrible team last year, got marginally better with some young talent this year, and could really start to take off with this pick (should be Oden). I should also point out that Boston was only the second-worst team for tanking, Milwaukee was slightly worse. But either way, this season was pretty bad for tanking. Agreed that the lottery needs fixing because of this. I do like the idea of the 2-year record to dilute out tanking and ensure truly bad teams earn the top picks. But how big of a shift do you see in the lottery position if you move some teams by, say 5 games this season? In other words, how closely packed are the teams? Would this really remove the incentive for tanking?

  • Ellipsis

    On a trip to Atlanta for a AAS meeting, despite my protests, Delta Airlines forced me to check my poster tube (too long for carry-on), and then (of course) just lost it. So I was stuck in Atlanta at the meeting without the poster that was the entire reason for my coming.

    They claimed that it would be along on the next flight in the morning, and to call their baggage services starting at 6 AM. So I woke up at 6 AM and started calling. Their baggage services call center is in India. They of course had no clue where the thing might be, despite my having the Delta tag number for it. They kept telling me to call back later, it should be in shortly.

    After a full day of calling, the thing never turned up. By then the poster session was over. Delta, of course, _never_ did find the poster. And they never gave me anything for it. Over $1500 for that trip was wasted.

    _Never_ fly Delta.

    Amongst a lot of bad airlines, it is the _absolute worst_.

  • Tom

    They don’t have a Kinko’s in Atlanta?

    I urge everyone to watch the draft tonight just for the player interviews alone. It packs more awkward pauses and incredulous looks into two hours than you get in an entire season of The Office.

  • Ellipsis

    Tom — the poster session was actually at 9 am that morning. The folks in Delta’s baggage call center strung me along for long enough, saying it would be there and delivered by 8 am, so that in the end there unfortunately was no time to get ripped off by Kinko’s.

  • Jimbo

    Sean has apparrently suffered thru the mind-numbing, body-aching horror known as `Internatinal Travel’, exacerbated by the crushing weight of airline, customs and security bureacracies, and returned without recouping body, mind, & soul, prior to launching this rant….
    Dare I say, very few people reading CV give a damn about the NBA, jox, or sports in general, & are much more interested in hearing your views on The Cosmos, and what’s happeing in science.
    Complaining about a one-hundred Billion $$ industry, synonomous with every travesty of justice and ethics one can imagine, is like complaining about Bush or SUV’s, and has as much chance of affecting a solution. Better to cut`n paste this one onto a sports blog where at least it might spark a dialogue amongst interested readers.

  • D

    Sean, any system that guarantees a team the top pick if it tanks hard enough is not a good system.

    I like the idea of two year average to avoid fluke luck like the one enjoyed by San Antonio 10 years ago. I don’t mind the rule of no consecutive top 3 picks, either.

    But the lottery with weighted chances must be there, in some form, or the system will get abused time and time again. The two year rule will just require a bad team to tank real hard one year. Or, in case of enormous talent like Lebron James, bad teams will be tanking two years in a row, just to make sure they get the guy.

  • Ryan Scranton

    Yet another person complaining about the lack of constant physics content on CV. Really, Sean, you should know better than to have any outside interests that might otherwise pollute the pure stream of physics flowing from your head to this blog and beamed out into the world for free. The people demand physics and they must be appeased!

    Seriously, though, I think you’re mistaking Doc Rivers’ truly atrocious coaching for intentional tanking. Granted, it’s tough to distinguish genuine incompetence from intentional flubbing, but I think the Celtics were more guilty of the former rather than the latter than Milwaukee. Of course, you being a Sixer fan and all, I can understand the temptation to attribute malice to the team that’s walked through your guys to get to the championship so many, many times. :)

  • Sean

    Ryan, I’m just being perfectly objective here. It is a fact universally acknowledged by informed basketball fans that the Celtics are the epitome of evil.

  • Dylab

    People still like basketball? Huh, interesting.

  • J

    Didn’t know you are a basketball fan, Sean. I totally agree with you. I do not think the draft system now is anywhere near “fairness”.

  • Dennis

    I think you’re being unfair to the current system. The designer of the mechanism is the NBA, and the NBA’s objective isn’t to ensure that teams don’t have the incentive to do bad things like throw games. The NBA’s objective is do something like “maximize viewership” or “maximize revenue” or something like that. There is likely no harm for a team like Boston to tank, because they have an established fan base(I don’t know this for a fact, but Boston is a big city) and won’t lose revenue much. So no reason to worry about that. Like most other leagues, the NBA wants to maintain parity, so that any team has a good change of beating any other team, and games will be close and exciting, and no one team is too good. Therefore, giving the best talent to the worst teams is a great idea. It makes it that much harder for good teams to stay good, and makes it easier for even incompetantly managed teams to win a few more games. It seems to me that the current system is doing pretty much exactly what the NBA needs. Granted, your system would do it too, but I can’t imagine the NBA would view it as worth the trouble of implementing.

  • Tyler

    It seems that this idea is made superfluous by the facts on the ground. The team with the #1 pick this year, the most desirable draft prize in many years, is a team that absolutely played its undermanned rear off the whole year, a deserving team, long troubled but clearly turning things around over the past season. And the #2 pick goes to a truly woeful franchise that needs all the help it can get; same with the #3 pick, though no amount of bailing is going to keep that death ship afloat.

    Your main concrete, non-abstract objection seems to hinge on the Spurs, which sounds suspiciously like sour grapes. They are hardly the first team to add a second star when they already had one – look at the Lakers a few years ago, for example.

    What have we seen since the end of the Jordan era? A large number of very high quality teams battling for dominance, with the Lakers and Spurs at the top but a lot of other entertaining teams rising and falling as well – Miami, Detroit, Dallas, Phoenix, etc. That sounds to me just like what the NBA should be.

    Finally, I think we’re in a transitional phase. With the exception of Phoenix, all the teams that have been dominant for the last decade have fallen or will soon begin to – the Spurs may be able to hold it together for awhile, I suppose, historically it’s unlikely but they’re such a brilliant organization you can never say for sure. But there are a lot of great, very young teams ready to rise and compete.

    I don’t see the problem. It’s not perfect, but teams will game any system, and the results are good overall. This year’s playoffs were interesting until the Finals – Spurs/Phoenix matchups should be hot for a few years to come – and the East is bound to bouce back before long with at least one decent team.

    However, a non-regional, completely seeded playoffs would be great. I think that innovation would be a lot more valuable than monkeying with the draft, though neither one is gonna happen.

  • Alex R

    Disclaimer: I haven’t really watched any basketball at all in the last decade or two…

    That said, the problem with the NBA draft, as you describe it, is that you are trying to simultaneously achieve two inconsistent goals: encouraging teams to win as many games as possible, and giving the worst teams (those that lose the most games) the best opportunities to improve. You can’t do these both at once. Even with two year records, there will still be an ordering late in the season that teams will be aware of, and trying to

    That said, here’s another, possibly better proposal: what you really don’t want is teams intentionally tanking late in the season, when playoff slots are on the line. The solution to this is simple: Don’t count the games late in the season when deciding who gets the high draft picks — only consider the first half, or maybe two-thirds, of the season. (You could do this with two seasons in a row, perhaps.) Earlier in the season, even the bad teams will still have a chance to make the playoffs, so they should be less likely to tank games intentionally. You could theoretically imagine that some teams might be thinking “let’s tank now for the draft, then try to make it up later”, but at least everyone will by trying to win all their games when their in the home stretch….

  • Santo D’Agostino


    Your idea has tremendous upside potential.

    All the best,

  • Beej

    What if we keep the current format, wherein the teams that don’t make the playoffs get the lottery picks, then instead of giving the higher probability to those teams with the worst records, give them to the ones with the better records among those lottery teams. Wouldn’t that remove the incentive of tanking and ensure a frenetic fight for wins among all teams throughout the entire 82 game season?

  • todd.

    But the lottery with weighted chances must be there, in some form, or the system will get abused time and time again.

    That doesn’t make any sense. There is a weighted-chances system now, and it’s still abused. So how does having such a system prevent abuse?

    I like Sean’s idea a lot.

  • Scott


    Looks like you put a good deal of thought into the lottery, and I like the cut
    of your jib. But next time you’re stuck in the airport for 8 hours, you should fix
    NBA playoff system. East vs. West? It’s a joke, whip up something like the
    NCAA tournament for the pros.

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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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