4.1 Data

To measure the effects of tanking, we collected team-by-season level on-court performance and team financial information from two main sources for the 2004-05 through 2020–21 NBA seasons.^{8, 9} We first gathered on-court performance data from basketball-reference.com and hoopshype.com. These data include winning percentage, payroll, points per game, roster age, and average margin of victory. Second, we use financial information gathered from Rodney Fort's Sports Business Data. These data include total revenues, total costs, and Forbes valuations of franchises. Team profits, called operating income in the data, are calculated by subtracting costs from revenues. Table 1 contains summary statistics for these measures for the Philadelphia 76ers compared to the rest of the league.

Given the dynamics and non-stationarity in many of these variables' time series (e.g., Forbes valuations), traditional summary statistics may be somewhat misleading. Regardless, the 76ers tend to look like a slightly below average NBA team over the course of the sample. In many ways, getting away from this mediocrity was a major motivation for Hinke. Interestingly, the average Forbes valuation of the 76ers is almost 20% less than that of the rest of the NBA's average. Their valuation could be misleading as valuations increase exponentially over the sample period and the average could be susceptible to large outliers from teams like the New York Knicks, Los Angeles Lakers, and Golden State Warriors. Coincidentally, the 76ers average profits also seem to be about 25% below league average.

4.2 Synthetic Control Method

The synthetic control method (SCM) is a statistical approach used to analyze the impact of an event or intervention that occurs for only a single treated unit (an NBA team in this case). The goal of SCM is to create a “synthetic” version of the treated unit before the aforementioned event or intervention takes place. The synthetic unit is created using a weighted average of other units that had not gone through such an event or intervention. These units are often referred to as a “donor pool.” Once a synthetic unit has been constructed, the researcher can observe how the outcomes for both the “real” and “synthetic” units evolve following the intervention. Since the synthetic unit is constructed from units that had not experienced the event or intervention that the real one experienced, the synthetic unit can be thought of as a counterfactual to the real unit. In other words, the synthetic unit represents the outcome of the real unit in the absence of the intervention. In the case of the 76ers, the outcomes of the synthetic 76ers team represents the outcomes of the real 76ers if they had never hired Hinkie and engaged in such severe tanking.

In the most simple terms, SCM assigns weights to teams in the donor pool such that the weighted average of their outcomes throughout the pre-period is as close to that of the 76ers as possible. SCM also typically includes a regularlization term, similar to that of LASSO regression, that effectively reduces the weights of relatively unimportant units to zero. This way, only a handful of units are chosen to make up the synthetic. Synthetic control also allows for the inclusion of covariates, which help to both predict the outcome as well as eliminate confounding factors. In other words, by including covariates, the researcher can ensure that the synthetic unit matches the real unit in multiple dimensions, ensuring that any differences can indeed be attributed to the treatment.

Once a synthetic unit is estimated, the difference between the synthetic and real units represents the treatment effect. With traditional statistics, however, simply estimating a difference does not mean that the difference is statistically different from zero. To make inference or perform a hypothesis test, one needs an estimate of the standard error to check if zero is within the estimate's confidence interval. Unfortunately, there is no way to calculate traditional standard errors for the SCM at the time of writing. Instead, practitioners typically perform something called a permutation test.

The idea behind the permutation test is to estimate a synthetic control for each unit in the donor pool excluding the treated unit. In theory, since these units did not have any substantial intervention, their estimated treatment effects should simply be noise. The collection of these treatment effects represents a distribution of treatment effects under the null hypothesis (no effect). Therefore, an “exact” p-value can be estimated as the proportion of placebo treatment effects as large as, or larger than, the observed treatment effect. In more concrete terms, if the observed treatment effect is the 3rd largest out of 50 total (1 “real” and 49 “placebo”), the p-value would be $$\frac{3}{50}=0.06$$. Some permutation tests place requirements or restrictions on pre-treatment fit, and other tests compare ratios of post-treatment to pre-treatment fit. See Firpo and Possebom (2018) for additional, technical details.

In many ways, the SCM can be thought of as a generalization of the more popular quasi-experimental method difference-in-differences. The SCM has the particularly attractive ability to rigorously estimate the effects of an intervention even when the number of treated units is small (or in many cases a singleton), which difference-in-differences struggles with. In other words, the SCM allows for the quantitative statistical analysis of case studies that would have otherwise only been able to be studied qualitatively in the past.

Previous studies employed the SCM to study topics in sports such as the impact of sports stadiums on localized commercial activity (Bradbury, 2022, 2024), crime related to Major League Baseball (Pyun, 2019), college football scandals (Johnson & McCannon, 2022), employment growth associated with the National Football League (Islam, 2019), and the mega-events and economic growth (Kobierecki & Pierzgalski, 2022). We use the SCM to evaluate the effectiveness of the Philadelphia 76ers tanking strategy, which represents the first study to use the SCM to study tanking in the NBA.

The first step in constructing a synthetic Philadelphia 76ers organization is choosing appropriate outcome variables to answer our research question. Though exploring the effects of tanking on on-court success, or rather whether teams tank, is well documented in the literature, we explore winning percentage as one of our outcomes as a way to demonstrate the SCM. It is worth noting that maximizing winning percentage was not necessarily Hinkie's goal when the 76ers started tanking, but rather a highly correlated byproduct. Unfortunately, neither binary outcomes (e.g., winning a championship, making the playoffs) nor binary covariates (e.g., fixed effects, CBA agreements) lend themselves to the SCM framework. Next, to explore off-court financial success, we use team profits as our second outcome. As is conventional, we only consider our outcome variables in 3-year increments (2004, 2008, 2012), rather than every year, in the creation of the synthetic. This is done to avoid the over-valuing of the outcome variables in the determination of the units comprising the synthetic (Kaul et al., 2015; Wiltshire, 2021a).¹⁰

The second step to estimate our counterfactual 76ers organization is choosing covariates that capture team performance and roster construction. The selected covariates to predict winning percentage include averages from the 2004-05 through 2012-13 NBA seasons for the margin of victory/loss, points scored per game, average roster age, and team salary adjusted for inflation.¹¹ When evaluating profits as the synthetic outcome, we include the same set of covariates but also include the winning percentage in the selected covariates.

As a final note, the classic SCM may potentially yield biased estimates. Bias-correction procedures to address the biases were proposed by Abadie and L'hour (2021) and Ben-Michael et al. (2021), based on the approach shown by Abadie and Imbens (2011) to handle inexact matching on predictor variables. To account for potential bias, our results are established using bias-corrected synthetic control estimates utilizing the allsynth STATA package developed by Wiltshire (2021b).

This approach automates the estimation of bias-corrected synthetic control gaps through the use of regression-based adjustments that mitigate potential biases in classic synthetic control estimates resulting from differences in predictor values between the synthetic and donor units. For each outcome variable, the biased-corrected synthetic control outperforms the classic synthetic control by yielding a better pre-treatment fit as measured by the root mean square prediction error (RMSPE). The approach also automates the estimation of RMSPE-ranked p-values calculated using an in-space placebo treatment. This approach allows us to assess the statistical significance of the gap between the 76ers and the synthetic 76ers in each post-treatment season. For more information regarding this model, see Abadie and L'hour (2021), Wiltshire (2021b), and Ben-Michael et al. (2021). For a similar empirical example, see Cameron et al. (2023).

4.3 Net Present Value

Tanking in professional sports is a special case of foregoing immediate benefit in favor of future benefit. Economists have developed tools to evaluate opportunities similar to tanking insofar that there are upfront costs and delayed payoffs. Of course, just because an opportunity may generate positive benefits in the future does not necessarily make it is a good investment if the initial costs are sufficiently high.¹² A tool often employed by economists to measure the overall quality of such an opportunity is Net Present Value (“NPV”), which is simply the sum of discounted costs and benefits.

If an investor's personal discount rate is lower than the estimated upper-bound, then the investor would prefer the 76ers engage in tanking. Factors that can impact one's personal discount rate include inflation, liquidity preferences, and risk aversion. Hence, for a risk-neutral investor without strong preferences for liquidity,¹³ their personal discount rate should reflect their personal inflation expectations. Therefore, if the estimated upper bound is greater than reasonable inflation expectations, an investor would likely prefer tanking to the status quo.

The interest rate in the NPV calculation for on-court performance is less interpretable, but the idea is similar. Patient fans who value the future and present similarly will have low discount rates. A discount rate of zero would indicate indifference about time. In addition, ideas like inflation and liquidity preferences do not apply to winning, but the idea of risk aversion can be extended. We assume fans have symmetric valuations for wins and losses, though previous research shows fans indeed discount the futures of their favorite teams (Coates & Humphreys, 2018).

5.1 Winning percentage

Using dynamic simulation models, Tuck and Whitten (2013) show the presence of incentives for teams to tank in win-maximizing leagues with reverse-order drafts. This study complements this previous research by empirically examining if adopting a tanking strategy led the Philadelphia 76ers to be more successful in winning relative to the team's predicted performance if it had not tanked.

Our synthetic Philadelphia is comprised of six teams, given the aforementioned covariates. Table 2 reports the name of, and weight assigned to, each of these teams. The two highest weights are assigned to the Minnesota Timberwolves and Chicago Bulls, which make up just above 50% of the synthetic. The other teams, in order of weight, are the Orlando Magic, Portland Trailblazers, Cleveland Cavaliers, and the Oklahoma City Thunder. Table 3 presents averages for the real and synthetic 76ers.

Figure 2 displays the time series of winning percentages for the real and synthetic 76ers teams, while Figure 3 displays the bias-corrected gap between the real and synthetic 76ers' winning percentages. Filled-in circles denote significance at the 10% level.¹⁴ The figure provides a visualization of the expected team performance when tanking. In the pre-period fit, the two lines stay close to one another, with 2009 being the only real exception, which indicates the model performed well when estimating the 76ers' synthetic counterpart.

Between the 2013 and 2020 NBA seasons, the post-period, the 76ers played four seasons where they performed worse than if they had theoretically not tanked. This is not unexpected since the literature emphasizes that teams intentionally lose games once they are eliminated from being a playoff contender (Price et al., 2010; Taylor & Trogdon, 2002). Over-resting players could be one of the shirking mechanisms behind their under-performance (Gong et al., 2022). However, our findings agree with Lenten (2016) in that despite the initial losing, the 76ers began winning at a rate higher than its synthetic in the years to come.

Even though Hinke's decision to tank was effective in eventually turning the franchise into a winning team, it is important to consider fan preferences toward supporting a losing team for multiple seasons. Following the 2020–2021 season, the final season in our sample, the sum of the winning percentage differences between the real 76ers and the synthetic 76ers is positive. In other words, Hinke's strategy led to more winning than losing relative to the counterfactual. If 76ers fans in 2013 were able to perfectly predict the team's future, and did not discount time or exhibit any loss aversion, they have would have preferred tanking given its relatively higher cumulative winning percentage. Of course, assuming away both time discounting and loss aversion is heroic and unrealistic. Unfortunately, we cannot account for loss aversion in this setting without making other strong assumptions about fan utility functions, but we can explore time discounting. We calculate the NPV of the sum of the differences in team winning percentages across different time discount rates and display the results in Figure 5. We find positive NPVs only when the discount rate is less than 2.2%. This suggests that only the most patient fans, ones who are indifferent about time, would be interested in tanking as a strategy to ultimately win basketball games. If fans discount time at a rate greater than 2.2%, the winning that occurs later in the sample would be valued less than the losing earlier in the sample, resulting in a negative NPV. Fans with discount rates higher than 2.2% would have preferred the status quo.

Of course, underpinning this discussion is the assumption that fans enjoy wins as much as they dislike losses. If the pain of losing is greater in magnitude than the joys of winning, there would likely be no positive discount rate that would make for a positive NPV over this sample. We make this assumption for simplicity; however, previous research suggests that fans do not have symmetric loss functions (Card & Dahl, 2011; Cardazzi et al., 2024; Ge, 2018). It should also be noted that the synthetic 76ers consistently lost over 50% of games. If the synthetic team always won 50% of its games, the interest rate would also be negative. In sum, while Hinkie's strategy ultimately successfully created a winning basketball team, it's unlikely that the costs to fans were worth it unless they do not heavily discount long-term wins.

5.2 Profitability

We find strong evidence that Hinkie's method was successful in eventually turning the 76ers into a winning franchise by the end of the sample. However, to add nuance, our ex-post NPV calculations suggest the initial losing period may have only been acceptable to the most patient and forward-looking fans. Regardless, if a team aims to maximize profits rather than wins, then the 76ers could be unconcerned by putting out a poorly performing basketball team so long as their profits did not suffer. This section analyzes this possibility by applying the synthetic control framework to analyze the impact of tanking on the 76ers' operating income relative to its synthetic counterpart. Due to the importance of championships to team value relative to the team's season winning percentage (Ulas, 2021), team owners likely perceive the expected benefit to be greater than the cost of underperforming in the near future. Moreover, since Philadelphia did not win a championship during our sample, the results presented are likely a lower bound for the financial benefits of engaging in tanking.

Table 4 displays the pool of teams that make up this version of synthetic Philadelphia, while Table 5 contains the balance table. Interestingly, two of the teams in this synthetic Philadelphia, the Orlando Magic and Minnesota Timberwolves, appeared in the previous synthetic for winning percentage. It is also worth noting that the profitability of sports teams is highly dependent on the market they serve. As an example, franchises in New York and Los Angeles are typically some of the most valuable regardless of their performances. As a sanity check, the weighted average of the populations of the metropolitan areas of the selected teams is about 5.8M while the metropolitan population of Philadelphia is about 6.1M.¹⁵ While we do not explicitly use market size in the creation of the synthetic, the real and synthetic 76ers appear to serve similarly sized markets. Since success in tanking is directly linked to a team's ability to draft superstar players, similar to the financial impact the presence of a superstar has on a team (Perri, 2014; Price et al., 2010), we find that an effective tanking strategy also leads to greater levels of team earnings.

Second, Figure 6 displays both the time series of the real and the synthetic 76ers' profits. Surprisingly, we find an immediate increase in team profits in the first season after Hinkie takes over. Following this, profits for the real 76ers tend to track those of the synthetic. However, in 2017, when the team turned in its first winning season, the profits of the real 76ers eclipsed those of the synthetic. Figure 7 shows the difference between the real and synthetic 76ers. We only find the differences of the first two seasons to be statistically significant at the 10% level.¹⁶ Not finding significance here is likely a result of noise in the financial data rather than a true null effect given the relatively large magnitudes. Moreover, most studies that use synthetic control have a treatment that is monotonic in nature, whereas tanking does not necessarily have the same sort of dynamics, which could complicate finding a significant result from placebo tests. Even an insignificant result in this case has practical importance, though. If profits cannot be told apart from one another, then the results could be interpreted as teams being indifferent between tanking and the status quo, which is a novel finding in and of itself.

We posit a few mechanisms for the change in observed profits for the 76ers. Initially, there were large reductions in player personnel costs driven by Hinkie trading away many of the large contracts he inherited from the previous regime. One of the ways by which Hinkie caused the 76ers to tank was by constraining the level of talent on the roster, which resulted in reduced player costs. Morevoer, as we discuss in a later section, the 76ers tended to draft poorly and their players were often injured or simply did not perform relative to expectations. Therefore, the rookie-scale contracts of these players did not often mature into bloated second-contracts like those of many other lottery picks, which kept costs low for the 76ers. In addition to the decrease in personnel expenses, the NBA employs a revenue-sharing structure in which teams redistribute revenues from television, streaming, advertisement, merchandise, parking, and concession.¹⁷ Even though there are income components such as the revenue from ticket sales, which are not shared among teams, gate revenue only accounts for about 16% of a team's total revenue on average. Thus, given the large share of revenue derived from the revenue-sharing structure, the 76ers seem to have leveraged this to subsidize its tanking strategy.

We also calculate the NPV of the difference in profits for the real 76ers relative to its synthetic in Figure 9. We find the NPV at the timing of Hinkie's hiring remains positive for all discount rate values between −10% and 110%, which is likely due to the initial increase in profits from substantial reductions in roster costs. If, however, we ignore the first year's anomalous profits and instead treat this number as zero, we still find a rather large interest rate of 23.3%. This is substantial, and indicates that tanking was a highly profitable strategy for the 76ers. As a reminder, this number can be interpreted as the maximum inflation expectation that a risk-neutral investor without strong preferences for liquidity can have that would make them indifferent between tanking and the status quo. Especially since inflation expectations were historically low during this time period, the profits associated with tanking are clearly preferred to the profits of the status quo.

Put differently, if an investor believed inflation would be 0% per year over the course of the post-period, they would choose the strategy that yielded the larger sum of total cash flows. This strategy would be tanking. However, since most of the benefits of tanking come later in the sample, higher discount rates (or inflation expectations) would shrink the difference between the NPV of tanking and the NPV of the status quo. An investor believing inflation to be 23.3% per year over the course of the post-period would make them indifferent between the two NPVs. Any discount rate higher than 23.3% would encourage the impatient investor to choose the status quo strategy. Of course, this is a hyperbolic example given the highest yearly inflation rate the US has seen since 1960 is about 13.55%, indicating that tanking is preferred by investors under nearly all reasonable circumstances.

An alternate way to interpret the synthetic 76ers is as a weighted portfolio of donor teams. In this case, the NPV represents the returns of investing in the tanking 76ers relative to the return of investing in a weighted portfolio of teams that had similar pre-tanking returns. Of course, there are differences in risk when investing in a portfolio versus a single asset. For this exercise, we assume away these differences in risk since the synthetic 76ers still represents investing in a single team. The idea of a portfolio of teams is simply a way to estimate the performance of Philadelphia if it did not tank.

Lastly, we compute the required interest rate that zeros out the NPV of either winning percentage or profits for each season following Hinkie's hiring. The results are displayed in Table 6. These findings indicate that on-court performance has a strictly negative NPV until 2019. However, the interest rate that sets the NPV to zero in 2019 is negative, which would (implausibly) require fans who heavily discount the present in favor of the future. As mentioned before, even in 2020, the required interest rate is still near zero at 2.2%, suggesting tanking to be preferred to the status quo for only the most steadfast of fans. On the other hand, profits were strictly positive for 2013 and 2014, and 2018 through 2020. The only time an individual would plausibly prefer the status quo to tanking would be those individuals with particularly low discount rates and relatively short time horizons (3–5 years) for their investment to mature. Otherwise, all other investors would prefer tanking.

It should be noted that owning an NBA team is not like owning a typical business, and the season-to-season profit stream (i.e., dividends) is probably not the main motivation for investing in or owning an NBA team. Individuals who buy into NBA teams (team owners or ownership groups) are likely fans themselves interested in the novelty, potentially treating the team like an investment in real estate or some other appreciating asset. In this case, profits are made upon the sale of the asset.