By Shuvom Sadhuka
For the past few years, the NBA has seen a fair number of teams tanking; that is, teams lowering their level of play and purposely losing games in the hopes of receiving a higher draft pick through the lottery (the worst teams lottery to determine the exact draft order). The NBA draft is traditionally viewed as more top heavy than other leagues; LeBron James, Kevin Durant, Tim Duncan, Anthony Davis, Kobe Bryant, and Allen Iverson all were selected through the lottery, with all but Kobe being selected with one of the top two picks. As such, teams like the Philadelphia 76ers accumulated poor records to receive higher draft picks, drafting stars like Joel Embiid and Ben Simmons in the process.
In an effort to reduce tanking in the NBA, the league rolled out a new lottery system in which the very worst teams in the standings were given lower overall odds to receive a top-4 pick. The first lottery under the new system rewarded the 9th seeded New Orleans Pelicans with the first pick, hailing as a win for the league and a loss for tanking.
Figure 1: Odds Under New Draft Lottery vs. Old (from ESPN)
Compared to the old system, each of the fourteen lottery teams now has a chance at drawing a top-4 pick, lowering the probability that the very worst teams get one. So, given this new system, what is the expected value added to a team by tanking? How good of a player can the worst team expect to receive, compared to the old draft lottery system?
HSAC has previously analyzed the expected career win shares by pick and seed; I will conduct a similar analysis, analyzing all drafts from 1985 (the first year of the lottery system) to 2011. 2011 was selected for the end date because it allows enough time for an “average” NBA player to reach his peak (i.e. players who were drafted more recently have not recorded enough data for us to know how good they will be). A few additional tweaks have been made from the previous HSAC article:
- We simulate both the order of the draft and the value of the player picked at each position 100,000 times, using career win shares as the value metric. We lottery the picks according to the new lottery probabilities.
- We also use a model in which we do assume independence of draft picks; in particular, we draw each pick from a gamma distribution with parameters to match the mean and variance of that pick (choose alpha and beta to match the mean and variance of the third pick, for example). This model might work better as, empirically, some picks’ career win shares do not follow a normal distribution (see figure 2 with pick number 11, for example). In reality, some picks’ career win shares distributions are heavily skewed, with a long tail representing a few Hall of Fame players. The gamma distribution accounts for this.
Figure 2: Histogram of Career Win Shares for Players Drafted 11th Overall, 1985-2011
Win shares tend to be right skewed for each draft pick, including the 11th pick shown above. Below is a table summarizing the results when we simulate each draftee’s value from a gamma distribution:Figure 3: Table of Draft Value Simulation Results
And here is just the expected win shares for each draft pick under the new and old systems, shown as a line plot:
Figure 4: Trends in Expected Career Win Shares by Draft Seed, New vs Old
We see that expected career win shares from the first four seeds has decreased under the new system. Simultaneously, the value of seeds six through nine have noticeably increased. After the 9th seed, the draft pick values under the two systems begin to converge.
The uptick in win shares at the nine seed is due to some exceptionally strong players being selected at ninth overall (and the ninth seed has the best shot at ninth overall): Tracy McGrady, Dirk Nowitzki, Shawn Marion, Amar’e Stoudemire, Gordon Hayward, Kemba Walker, and DeMar Derozan were all drafted 9th overall. Compare this to the best players selected at eighth overall — Jamal Crawford, Andre Miller, and Rudy Gay — and it’s clear that the ninth draft pick is an anomaly.
From the table, we also see large standard deviations in the career win shares. This is reflective of uncertainty generated from two places: first, the lottery, as being the worst team doesn’t guarantee receiving the top pick. Second, once the team receives a position in the lottery, there is variance in the actual pick’s career win shares. For example, even if we know a team got the fifth overall pick, there is still a lot of uncertainty in how good their drafted player might be.
Moreover, even when we simulate other value-added metrics, such as BPM or VORP, we get similar results — the new lottery system hurts the top four seeds, helps the middle seeds, and has roughly no effect on the bottom seeds.
Figure 5: Expected VORP by Draft Seed Under the New and Old Systems
Overall, however, the differences are marginal. The second seed dropped from 63.07 expected career win shares to 53.87, about the difference between Richard Hamilton, a three-time All-Star, and Caron Butler, a two-time All-Star, respectively. Moreover, the standard deviation and skewness for each seed’s career win shares, in part, overpowers any major change in expected win shares. Considering that the largest difference in expected career win shares is only 10 win shares, it seems that teams that want to tank still have strong incentives to tank, even if the restructured NBA draft lottery makes it less likely for them to receive the best picks.
If you have questions for Shuvom about this article, please feel free to reach out to him at firstname.lastname@example.org.