It finally happened. After multiple seasons of intense debate, the NBA has a new lottery system.
A brief recap: Rebuilding was an accepted part of the NBA lifecycle until several teams (and one in particular) took the concept to extremes. These tanking efforts became obvious, calculated, and intentional. Gone was the PR spin helping the league save face. The results were not surprising. Teams were comically bad and few enjoyed watching games that damaged the league’s reputation.
This extreme tanking was met with similarly extreme proposals to reform the system. Popular proposals included the wheel or rookie free agency. These types of reforms challenge the basic philosophy that the worst teams deserved the best picks. They would drastically change rebuilding in all its forms, not just curtail the scorched earth version employed by the 76ers.
But for those of us with less revolutionary ideas, this debate signaled the need to re-balance the lottery odds. The lower the odds of getting the first pick, the lower the incentive to overtly tank.
The challenge is finding the right balance. Currently, the frustration is that the worst teams have too much of an advantage in the lottery—but that wasn’t always the case. The league’s very first lottery system in 1985 had equal odds for all lottery teams and there was no limit to how far a team could fall. There were only seven lottery teams back then. The Golden State Warriors were tied for the worst record in the league and ended up with the seventh pick. That lottery system only lasted two years because of how unfair it seemed.
Everyone knew that the lottery system needed reform, but overcorrecting was a serious possibility. Let’s explore what a balanced system should try to achieve and compare it to the league’s new model.
Balancing the Incentives
There are four main principles that a correctly balanced lottery system should strive to achieve.
1. Worse teams deserve better picks.
The reasons for this are numerous. By helping the worst teams get better, the league promotes competition, parity, and provides struggling fanbases with hope. It also just aligns with basic ideas of fairness. If you disagree with this point, then you won’t be satisfied with the league’s reforms or the rest of this discussion.
2. Teams should have no incentive to tank in an extreme way.
While worse teams generally get better odds, it shouldn’t be in a team’s best interest to be as bad the recent 76ers. A team shouldn’t ever feel the need to be the absolute worst. To put it another way, the league shouldn’t create a system where signing a few veterans or putting a minimally viable product on the floor harms a franchise’s future goals.
Already, there’s a tension between the first two goals.
3. Every team should want to make the playoffs.
Odds at the end of the lottery should be so low, that no team would prefer being in the lottery to qualifying for the postseason.
4. Lottery odds change as gradually as possible.
The more quickly lottery odds increase, the more incentive teams have to jockey for position at the end of the season. If the difference between being sixth and seventh is negligible, then teams won’t feel the need to “rest” (wink wink, nudge nudge) players at the end of the season. If the gaps are large, then we might see more late-season suckfests.
What would a system based on these principles look like? Based on the first principle, the worst teams would get the best odds. In addition, those odds should be sufficiently high so that the worst teams consistently get the best picks.
To take away the race to the very bottom, the odds should be flat for the worst teams. This means that bad teams would generally get higher picks, but you don’t have to be the very worst to maximize your lottery odds.
If you visualize the first and second second principles, the graph would be flat at the beginning of the lottery
Aside: It’s important to know how the lottery works before moving on in the discussion. The league uses 14 ping pong balls numbered 1 through 14. Four balls are randomly selected, creating a string of four numbers. This is called a ‘combination.’ There are 1000 combinations total and each team is assigned a certain number of them. The more combinations a team has, the higher their odds of getting the first pick.
Principle three, that no team should ever miss the playoffs on purpose, necessitates low odds at the end of the lottery as well.
However, the flatter and longer the two tails of the lottery are, the steeper the middle, giving middling teams more of an incentive to jockey for position.
This is where the balancing act comes in. If the ends of the lottery distribution are too flat, then the middle will be too steep. If the middle is too flat, then the ends won’t be flat enough. The challenge is finding the optimal distribution that manages this tension effectively.
This theoretical framework allows us to evaluate potential lottery systems and the incentives they create for NBA teams. Next, we’ll apply this framework and evaluate the NBA’s new lottery system.
The League’s New System
We just developed a theoretical framework to evaluate NBA lottery systems. To recap, the lottery odds should look like this:
The worst teams should get the best odds so the distribution should slope right to left. However, at the far left where the very worst teams are located, the distribution should flatten so that bad teams aren’t incentivized to be the absolute worst. On the other side, the far right where the teams just missed the playoffs, the odds should be low and flat so no team is incentivized to miss the playoffs. Finally, the middle of the distribution should slope uniformly and gradually so middling teams aren’t incentivized to jockey for position.
The new lottery system seems to take a similar approach. The odds are relatively flat on both ends with a smooth transition in the middle.
The three worst teams all get a 14% chance at the first pick. Odds stay below 2% for the three teams closest to the playoffs and the slope in the middle varies from 1.5% - 2%.
However, the new system might not be flat enough on the far right. Collectively, the teams ranked 10-14th in the lottery would have an 8% chance of getting the first pick. That means we should expect one of the best teams in the lottery to get the first pick once every 12 or so years. In the previous system, teams ranked 10-14th had a less than 4% chance at the first pick.
I doubt the difference will cause teams to miss the playoffs on purpose, but I am worried the league has overcorrected. It has become much more likely that a struggling team will be stuck for multiple seasons without a top draft pick. Without changes to free agency, this should be especially concerning to small market teams. It’s not surprising that small market owners had the most concerns about the proposed lottery changes.
In addition, the continued use of rank leads to some undesirable results. Look at the 2006 draft as an example:
Golden State and Houston both won 34 games and had roughly a 5.2% chance at the first pick (If teams have the same record, they split the total combinations designated for their two slots in the lottery ranking. That explains why the first pick percentage doesn’t exactly correspond to the number of combinations in the lottery distribution). Minnesota and Boston won one less game and their odds improved by three percentage points, up to 8.2. Toronto, on the other hand, won six fewer games yet saw their odds improve by only two percentage points, up to 10.5. That doesn’t make sense; lottery odds are supposed to be proportional to a team’s need, yet they’re completely divorced from a team’s record.
For another strange example, compare the 2017 and 1998 seasons:
In 2017, only one team won 20 games or fewer. In 1998, six teams won 20 or fewer. Does it make sense that a 20-win season one year is worth a 14% chance in one season and a 9% chance in another? Plus, if the whole point is to disincentivize really bad teams, why would Denver be rewarded over Dallas in 1998 when both of them were “bad enough?”
A better solution would be to assign odds based on wins and losses using a mathematical function that would mimic the general shape we’ve been discussing.
This would create the same basic incentive structure but would handle these odd cases better. Look at how the 2006 draft looks now:
There is now a 10% gap between Boston and Toronto, proportional to the difference in their records. Also, the cumulative odds of teams ranked 10-14th is about 5%, much more in line with the previous lottery system.
The 2017 and 1998 lotteries now look drastically different as well:
In 2017, Brooklyn was the only truly bad team so they get the highest odds. In 1998, when there was a whole stable full of terrible teams, they spread out the chance at the top pick evenly among themselves. Essentially, there’s little incentive to win fewer than 25 games and the odds track more closely with the quality of teams up until that threshold. The result is that lottery odds are more precisely apportioned while removing the justification for ‘super tanking’.
That’s the system that I think balances the incentives the best. It simultaneously removes the incentive to super tank while maintaining rebuilding as a viable strategy for small market teams. It also matches a team’s need to their odds more closely than either the old or the new lottery system.
Build Your Own Lottery System
I just presented my preferred lottery system to create an incentive structure that would balance the need for small market teams to rebuild while deterring the extreme tanking we’ve seen from Philadelphia in recent years.
To make a model, choose your specs on the left. The first choice is to choose whether the model should be based on the rank of the teams or their wins-loss record. Next, pick a season you’d like to simulate.
If you choose ‘Rank,’ a list of the combinations assigned to each team appears in the ‘Team Records’ table. Adjust these to create whatever model you like. You can also click the ‘Preset’ buttons to use the combinations of the newly approved system or the old system it replaces.
With ‘Record’ based systems, a team’s wins determine their combinations according to a mathematical function (a modified logit function for you math nerds). To modify this mathematical function, you change the ‘slope’ and ‘shift’ parameters.
If you look at the shape of the curve, there’s a high end on the left and a low end on the right. The ‘slope’ determines how quickly the curve transitions from high to low. The higher the slope, the steeper the transition.
‘Shift’ moves the graph laterally. As the ‘shift’ goes up, the graph moves right. This means more teams get the highest odds. As the ‘shift’ goes down, the graph moves left and fewer teams reach the flat part of the curve.
Note that changing the ‘slope’ significantly changes the function and typically requires modifying the ‘shift’ in response.
In either model, you can choose how many picks will be selected with the lottery using the ‘Lottery Pick’ spec. For example, if you choose 5, then five picks will be selected with the lottery and the worst team could drop all the way to the sixth pick.
The ‘Previous Seasons’ spec allows you to factor in a team’s records over multiple seasons when assigning combinations. If ‘Previous Seasons’ is set to 0 then the lottery will be determined by a single season. If ‘Previous Seasons’ is set to 2 then teams will be ranked by their records over the past three seasons (the current season plus the two previous). Note that if you’re simulating older seasons, a team has to have existed in all three seasons for it to be included in the simulation.
You can see every team’s record and their chance at the first pick in the ‘Team Records’ table. This allows you to get a sense of your system before you simulate it.
When you’re ready, hit the ‘Simulate Your Model’ button. The program will simulate the draft the number of times you choose in the ‘Simulations’ spec and approximate the chance that each team gets each pick. The more simulations you choose, the more accurate the results but the longer it takes to run.
—Willy Raedy | @WillyRaedy