Exploring incentives to lose in professional team sports: do conference games matter?

Soebbing, Brian P. ; Humphreys, Brad R. ; Mason, Daniel S. 等

Exploring Incentives to Lose in Professional Team Sports: Do Conference Games Matter?

Professional sports leagues in North America and Australia use unbalanced schedules mainly in order to increase game attendance (Lenten, 2011). An unbalanced schedule is a schedule in which teams play other teams a different number of times over the course of the regular season (Noll, 2003). Unbalanced schedules have been understudied in the academic literature (Lenten, 2008). In North American professional sports leagues, unbalanced schedules exist within the conference system (Lenten, 2011), where groups of teams are organized into conferences according to geographic location. By designing a schedule under which teams play conference opponents more times than nonconference opponents during the regular season, the league reduces teams' travel costs and encourages rivalry and competition amongst conference teams. This focus on competition amongst closely located competitors ideally results in higher game attendance and increased consumer interest in the league (Baumann, Matheson, & Howe, 2010; Lenten, 2008). In addition, the conference system affects participation in the postseason tournament (playoffs), which determines the league champion at the end of the regular season in North American leagues.

Scheduling in a conference system, along with the use of a reverse-order entry draft to allocate new players to teams and postseason tournaments to determine the league champion, generates incentives for teams to take actions detrimental to certain league objectives. The common draft format used in professional sports leagues in North America and Australia is reverse-order, in which the worst team in the league receives the first overall selection, the second-worst team has the second overall selection, and so on until all teams have selected a player. Draft position can be improved by virtue of a worse win-loss record than other teams. In some professional leagues in North America and Australia, teams that have been mathematically eliminated from appearing in the postseason and still have regular-season games to play face an incentive to intentionally lose games to increase their prospects in the upcoming reverse-order amateur entry draft, an outcome called tanking. Tanking, defined as not putting forth the level of effort necessary to maximize the number of regular-season wins, is a strategy designed to improve the position of a team in the upcoming amateur entry draft (Borland, Chicu, & Macdonald, 2009; Soebbing & Mason, 2009).

Tanking has been a particular concern in the National Basketball Association (NBA) since the early 1980s. Since that time, the NBA has changed the format under which the rights to incoming amateur players are allocated to teams four times. Taylor and Trogdon (2002) and Price, Soebbing, Berri, and Humphreys (2010) analyzed the probability that NBA teams eliminated from the postseason won regular-season games under different draft formats. Results showed that these teams responded to league incentives in which the reward for tanking was the highest. However, neither study controlled for the unbalanced schedule and the fact that NBA teams play more games against members of their own conference. Soebbing and Humphreys (2013) examined the point-spreads of NBA regular-season games under the latest weighted lottery draft format and found bookmakers took into account the additional incentives for eliminated teams tanking in conference games compared to nonconference games.

The unbalanced schedule may be important to the strategic behavior of eliminated teams competing for the top-draft position under different draft NBA formats. A loss to a geographical competitor could entail too high a social cost due to the greater media and fan scrutiny of these rivalry games. In addition, conference rivalry games may also feature individual player rivalries, which may make it very difficult for players to not compete vigorously against one another. For this reason, the present research explores the impact of the conference system and unbalanced schedules on the incentive for eliminated NBA teams to win regular-season games under four different NBA draft formats: the final season of the reverse-order format (1983-1984) and the first season of each of the three lottery formats (1984-1985, 1989-1990, and 1993-1994). We examine only these seasons to focus on the initial reactions by eliminated NBA teams to changes in league entry draft policies. Results show that different draft formats generated different team behavior in conference games at the end of the regular season. This finding has important implications for professional sports leagues, since leagues want to ensure that policy changes do not lead to undesired outcomes such as reduced effort in late season games.

The NBA and Its Teams

To understand the relative importance of conference and nonconference games and, by extension, unbalanced schedules, it is important to understand the objectives of a professional sport league like the NBA. The primary aim of a league is to maximize the joint profits of all the owners in the league (Scully, 1995). Sports leagues sell competition, reflected in uncertainty of game outcome. Competition is defined "as a setting in which the goal attainment of participants is negatively linked, so that the success of one participant inherently comes at the failure of the other" (Kilduff, Elfenbein, & Staw, 2010, p. 944). (1) The outcome of each game is zero-sum; one team wins while the other team loses. Szymanski (2003) posited that an organizer of a sports contest, like a sports league, elicits effort from the participants (the teams within a league) using prizes, including making the playo s and the opportunity to win the league championship.

Each agent (team) is assumed to maximize profit and, in doing so, may reduce the amount of revenues that can be generated by the principal (the league). (2) This presents a problem for the principal, who can react by altering or developing league policies to align agent interests with the overall goals of the principal (Mason, 1997). Some policies that North American professional sports leagues can adopt or modify include revenue sharing arrangements, rules regarding the salary cap and/or luxury tax, free agency rules, amateur draft policy, scheduling, and playoff design.

Currently, the NBA contains two conferences, and each conference contains three divisions containing five teams each. Eight teams from each conference qualify for the playo s. A team can qualify for the playo s in two ways: by finishing with the best regular-season record in its division, or by finishing with one of the five best regular-season records among the non-division winning teams in its conference. The result is competition throughout the season to secure one of the eight conference playoff spots. The top eight teams from each conference make the playoffs, so it is more important for a team to win conference games than nonconference games in terms of both qualifying for the playoffs and seeding in the playoffs, because a win in a conference game results in a loss for a conference opponent, generating a two-game net gain in the conference standings for the winning team. When a team plays an opponent from the other conference, a win against that opponent only generates a one-game increase in the conference standings.

If an NBA team makes the postseason tournament, the team earns additional revenues. A team could host between two and sixteen home playo games, depending on how far it advances in the postseason tournament. The largest cost facing NBA teams is player salaries (Siegfried & Zimbalist, 2000). NBA teams who make the playo s do not incur additional salary expense by playing additional games. Playoff teams keep most of the revenues generated by home playoff games; (3) therefore, qualifying for the postseason generates additional profit (Noll, 1991). At the beginning of the season, all teams are assumed to have the goal of clinching a spot in the playo s to increase revenues. This aligns with the NBA's objective of high uncertainty of game outcome and competitive balance.

To further increase the competition between teams in the regular season, the NBA uses an unbalanced schedule in which teams play conference and divisional opponents more times than they play teams from the other conference. Unbalanced schedules have been neglected in the literature, specifically the e ect of unbalanced schedules on league policy and league-wide competitive balance (Lenten, 2008). Weiss (1986) examined the effect of unbalanced schedules in North American sports leagues and concluded that strong teams won less when a league used an unbalanced schedule. The implication is that when strong teams win less, weaker teams win more due to the zero-sum nature of sporting contests. As a result, competitive balance--the disparity of win percentage amongst all league members--improves, resulting in an increase in consumer demand for games (Neale, 1964; Rottenberg, 1956). However, it should be noted that competitive balance in the NBA has been declining over the past two decades (Berri, Brook, Frick, Fenn & Vicente-Mayoral, 2005). There is empirical evidence in previous research stating that fans attending NBA games are not sensitive to the competitive imbalance of the NBA (Berri, Schmidt, & Brook, 2006).

Given the importance that NBA league executives place on the integrity of competition, the unbalanced schedule may have additional implications for eliminated NBA teams' incentive to win late season games. An NBA team is eliminated from playoff contention when it does not have enough regular-season games remaining to overcome the difference in total wins between the eliminated team and the last playoff team. When this occurs, an eliminated team might have a reduced incentive to put forth effort to win its remaining games. Also, an informal tournament to determine the order of selection in the next amateur draft can arise in which participants intentionally lose games late in the regular season in order to move up in the draft and select first overall. The intentional losing of games presents an agency problem for the league that can damage its legitimacy and result in a loss of sponsorship revenue for the league, a decrease in the amount of money it receives from the national media contracts, and negative publicity from local and national media (Friedman & Mason, 2004; Soebbing & Mason, 2009).

Incentives to Tank

As described above, supplying enough effort to win a game may not be the optimal strategy for a team eliminated from playoff contention. In the NBA, selecting higher in the entry draft means that teams intentionally losing games late in the season can receive rewards from these losses. This differs from other leagues because, in other leagues, the performance of amateur players in the professional league is more difficult to forecast (Borland et al., 2009) and the revenue generated by individual players is lower. The strategic decision to tank once eliminated from playoff contention depends on the amount of revenue a team can gain from the player it selects by moving up in the draft. The additional revenue comes from two main areas: the revenue generated from a player above his salary and the gate revenue associated with increased winning.

A team can generate a surplus, the amount of revenue generated directly by a player minus his salary, from each player on its roster. Krautmann, von Allmen, and Berri (2009) found that the median surplus generated by an NBA player with less than four years of professional service was approximately $732,000 per season. Krautmann et al. (2009) divided players into starters and nonstarters and found that the median surplus extracted to be $2,700,000 for starters and $564,000 for nonstarters. Hausman and Leonard (1997) found that superstar players accumulate sizeable revenues for their own team, the league (in terms of TV ratings), and the opposing team (in terms of attendance, concessions, parking, etc.). Price et al. (2010) found that one-third of first overall draft picks attained superstar status in the NBA. (4) As a result, an NBA team can generate a significant surplus from a player selected in the amateur draft, thus increasing the incentive a team might have to tank once eliminated from playing in the postseason.

In addition to the surplus, an NBA team realizes an increase in gate revenue from top draft picks. Price et al. (2010) estimated that an NBA team with the first overall pick saw an increase in gate revenue of $4.5 million. The team with the second overall pick saw a gate revenue increase of $2.25 million in the following season. If a team pursued a tanking strategy in the previous season, the team would realize a loss in gate revenue for that season due to a decrease in the uncertainty of game outcome and poor team performance (Price et al., 2010). The break-even point, in terms of the number of games, between the revenue lost in the current season with a tanking strategy and the revenue gain related to the first overall selection in the next season is 20. Since 20 games is approximately 25% of a full season schedule, there appears to be a further financial incentive for eliminated teams to intentionally lose games late in the regular season.

Not only can top draft picks improve the financial outlook for these teams, but these players can also turn around the on-court performance of teams. Price et al. (2010) showed that first overall draft picks produced 45 wins over the first five years of their career. In the first season, number one picks produced 7.2 wins on average. This evidence supports the rationale professional sports leagues use for amateur drafts--to improve the quality of weaker clubs.

NBA Draft Policy and Research Hypotheses

However, the amateur entry draft also generates incentives for teams to tank in the NBA. The amateur entry draft is also the mechanism by which leagues in North America and Australia allocate incoming amateur talent. The justification put forth by league executives and team owners for the amateur draft is the need to both control player costs and improve competitive balance (Booth, 1997; Fort & Quirk, 1995). Historically, the most common draft format used in professional sports leagues is reverse-order, in which the worst team in the league receives the first overall selection, the second-worst team has the second overall selection, and so on until all teams have selected a player. The amateur draft, owners and the league officials claim, is important for league-wide competitive balance (Kaplan, 2004), because if the strong teams select the best amateur talent, then the disparity in winning percentage between strong teams and weak teams would increase, weakening the competitive balance of the league (Alyluia, 1972) and reducing fan attendance [according to the uncertainty of outcome hypothesis proposed by Rottenberg (1956)].

Table 1 summarizes previous NBA draft formats and the existing empirical evidence of tanking under each format. The first NBA draft, in place from 1966 to 1984, used a reverse-order format. Under the reverse-order format, teams with the lowest winning percentage in each conference flipped a coin to determine who received the first overall selection. The loser of the coin flip selected second overall in the draft. The rest of the order was determined by winning percentage first of the non-playoff teams, then the playoff teams. Evidence of tanking under this draft format from previous research is mixed. Taylor and Trogdon (2002) used a random effects logistic regression model to examine the final season of the reverse-order draft format (1983-1984) and the first season of each subsequent lottery formats. Their results concluded that eliminated teams were tanking under the reverse-order format. Price et al. (2010) examined NBA regular-season games from 1977 through 2007 using a fixed-effect logistic regression model. They concluded that eliminated NBA teams were not tanking under the reverse-order format.

Again, a team attempting to improve its position in the NBA draft (or the probability of winning the draft under the lottery format) could move down the standings faster when playing conference opponents compared to nonconference opponents. The reason is a loss against a conference opponent directly results in a win for a conference foe and prevents the opponent in gaining in the "contest" for last place in the conference. This two-game net "gain" would have been critical under the reverse-order format used in the 1983-1984 NBA season, when teams had to finish at the bottom of a conference for a chance at the first overall selection. Thus, Hypothesis 1:

Hypothesis 1: Teams that engaged in tanking under the NBA's reverse-order format (1966-1984) were more inclined to tank in conference games rather than nonconference games due to the two-game "gain" in the standings from losing in a conference game.

The NBA changed the draft format from a reverse-order format to an equal-chance lottery because of the perception that teams were tanking and the consequences of tanking from a league's perspective (Soebbing & Mason, 2009). Under the equal-chance lottery, all non-playoff teams received the same probability of selecting the first overall pick in the draft. Thus, the financial incentives for eliminated teams to tank did not outweigh the uncertainty generated by the draft format change. Previous research supported the belief that teams were not tanking under the equal-chance lottery format, since moving down in the standings did not increase the probability of getting the first overall pick in the next entry draft (Taylor & Trogdon, 2002; Price et al., 2010). Hypothesis 2 reflects the same belief in regards to teams tanking in conference and non-conference games.

Hypothesis 2: Eliminated teams are not more likely to tank in conference games than nonconference games because the league did not provide an incentive for eliminated teams to tank under the equal-chance lottery format from 1985 to 1989.

After the change to the equal-chance format starting in 1984-1985 season, some executives questioned whether the purpose of the draft should be to deter tanking or improve competitive balance. The league altered its draft format again in 1989, switching to a weighted-draft lottery format, which gave the worst teams in the league a higher probability of receiving the first overall selection than teams that just missed the playoffs (Soebbing & Mason, 2009). Under the first weighted lottery-format, all eliminated NBA teams still had a chance to win the lottery format. Facing pressure from franchise owners, front office executives, and fans, after the Orlando Magic won the draft lottery for the 1993 draft, the NBA voted to increase the probability that the worst team was awarded the top draft pick and adjusted the other draft probabilities (Soebbing & Mason, 2009). The second weighted-lottery format began with the 1994 NBA draft and is still used today.

Previous research found that eliminated NBA teams tanked late in the regular season under these two formats (Taylor & Trogdon, 2002; Price et al., 2010). Soebbing and Humphreys (2013) concluded that bookmakers adjusted the point spreads of regular-season NBA games under the second weighted lottery because of the belief that eliminated teams were tanking. How does the unbalanced schedule affect eliminated teams' incentive to tank under the two weighted lotteries? Under a draft lottery format, all the eliminated teams from each conference are pooled and ranked by win percentage rather than by rank order within their respective conference. A team finishing at the bottom of its conference is not guaranteed the first or second overall pick, as had occurred previously under the reverse-order format. However, conferences still mattered to the extent that some conferences were weaker in some seasons than others. This situation affected playoff eligibility. For example, a team with a 0.500 winning percentage could make the playoffs in one conference, but a team with a 0.600 winning percentage might not make the playoffs in the other conference.

Due to the design of postseason play requirements, NBA teams place greater significance on conference games than nonconference games. Even though draft position under weighted lottery formats is not based on conference finish, teams know that conference games are worth two games in the standings compared to one game against nonconference opponents. These reasons inform Hypothesis 3:

Hypothesis 3: Because teams place more value on conference games than nonconference games, eliminated teams are more likely to tank in conference games compared to nonconference games under the two weighted lotteries.

Schedules also reflect geography and rivalries. Rivalries can also arise due to the geographical arrangement of divisions and conferences. Rivalry is defined as "a subjective competitive relationship that an actor has with another that entails increased psychological involvement and perceived stakes of competition for the focal actor, independent of the objective characteristics of the situation" (Kilduff et al., 2010, p. 945). Specifically, within the sporting context "sporting rivalries are followed with great interests by fans, typically hyped by the media to engender additional interest, and often result in outstanding athletic performances because of the intensity of the competition and comparable talent of the two opponents" (Wiggins & Rodgers, 2010, p. xi).

One reason the NBA arranges its conferences geographically is to reduce travel costs because teams play nearby conference teams more frequently than nonconference teams. Another reason is that firms located closer to each other geographically compete more fiercely than firms located farther from each other (e.g., Yu & Cannella, 2007). In the NBA context, assigning teams into conferences based on geography should result in a more competitive environment amongst members of each conference because they are competing against those in close geographical proximity. The present research does not attempt to measure the intensity of rivalries in the NBA as Kilduff et al. (2010) did for the NCAA. However, the presence of geographic competition and the rivalries that may form from close geographic proximity is acknowledged. Close geographic competition may have an effect on an eliminated team's strategic decision not to put forth maximum effort to win regular-season games. Games between close geographic cities, especially geographic rivals, receive extra attention from players, management, local media, and fans among others, and may have an impact on the strategic behavior of teams. Because conferences are arranged geographically, tanking against conference opponents would come at a higher social cost for the team. In other words, it may be diffcult for teams put forth less effort in games against conference teams even though doing so would increase the chances of receiving the top pick in the amateur draft. This leads to a final hypothesis:

Hypothesis 4: NBA teams tanking under the weighted lottery draft formats are more likely to tank in nonconference games compared to conference games due to the high social cost of tanking against teams that are in close geographic proximity or perceived geographic rivalries.

These hypotheses are tested below.

Model

To investigate the effect of the unbalanced NBA schedule on tanking, outcomes of all regular-season NBA games from the final season of the reverse-order draft format (1983-1984 season) and the first seasons of the equal-chance lottery (1984-1985), weighted-lottery (1989-1990), and the second weighted-lottery formats (1993-1994) were analyzed. Analyzing the last season of the reverse-order format and the first season of each of the three lottery formats provides information about the initial effects of policy changes on team behavior. The last year of the reverse-order draft was used instead of the first year because the first year of the reverse-order draft took place before the adoption of the three-point field goal in the NBA. The second reason for using the final year of the reverse-order format was the fact that media reports of tanking first began to surface at that point (Soebbing & Mason, 2009).

Data on NBA regular-season games were collected from multiple sources, including the New York Times, Washington Post, Los Angeles Times, and DatabaseBasketball. For each game, there are two observations in the dataset. These two observations are for the two teams that play in a given contest. Table 2 presents the summary statistics for the game and eliminated variables.

There are 8,090 team-game-season observations in the sample. (5) Notice on Table 2 that conference games compose 69% of the sample, which emphasizes the importance of conference games under an unbalanced schedule. Notice that the percentage of games involving a team eliminated from playoff contention increased throughout the sample. Over the sample period, many more games occur when at least one of the teams was eliminated from playo contention, which presents increased opportunities for teams to engage in tanking.

The dependent variable indicates if the team under observation won the game; the dependent variable is dichotomous and equal to 1 if the observed team won and 0 if the observed team lost. Equation 1 presents the initial empirical model that is similar to the models of Taylor and Trogdon (2002) and Price et al. (2010):

[WIN.sub.ijk] = f ([HOME.sub.ijk], [NEUTRAL.sub.ijk], [WINPCT.sub.ijk], [OWINPCT.sub.ijk], [CLINCH.sub.ijk], [OCLINCH.sub.ijk], [ELIMDC.sub.ijk], [OELIMDC.sub.ijk], [ELMIC.sub.ijk], OELIMIC.sub.ijk], [[epsilon].sub.ijk]) (1)

Equation 1 explains observed variation in game outcomes using variation in game site, team winning percentages, and six variables that reflects the team's current position in the race for the NBA postseason. In Equation 1, i denotes teams, j denotes games, and k denotes seasons. HOME is an indicator variable showing whether team i was the home team in game j in season k. Identifying the home team is important because the literature indicates a large home field advantage for NBA teams (Gandar, Zuber, & Lamb, 2001).

Some games, especially in the 1983 and 1984 seasons, occurred at a neutral site. Because neither team played in its home market, the variable NEUTRAL indicates if team i's jth game was played at a neutral site in season k. WINPCT is team i's winning percentage entering game j in season k. OWINPCTis team i's opponent's winning percentage entering game j in season k. The winning percentage variables control for the quality of both teams in game j. Quality reflects injuries that have occurred as well as player transactions (e.g., trades, player signings, and player releases) the team has completed up to game j in the season. Previous research examining unbalanced schedules raised issues about whether winning percentage reflects the true quality of the team when leagues use an unbalanced schedule (Lenten, 2011; Weiss, 1986). Soebbing and Humphreys (2013) concluded winning percentage is an accurate indicator of a team's quality in the case of examining tanking in the NBA.

CLINCH and OCLINCH are indicator variables for teams that had already clinched a playoff berth when team i played game j. The two variables, ELIM and OELIM, in Equation 1 are indicator variables for teams that had already been eliminated from the postseason. To account for the difference in games, the present research interacts an indicator for the type of game with the elimination indicator variables. The variable ELIMDC is equal to one for if team i has been eliminated from playoff contention and is playing a conference game in game j. A negative and significant result is interpreted as a team is tanking in a conference game. The variable OELIMDC is equal to one if team i's opponent has been eliminated from playoff contention and is playing a conference game in game j. A positive and significant sign would indicate the opponent tanking in a conference game since it gives a greater probability of team i winning game j. The variable ELIMIC is equal to one if team i has been eliminated from playoff contention and is playing a nonconference game in game j. In this case, a negative and significant result is interpreted as a team is more likely to tank in a nonconference game. The variable OELIMIC is equal to one if team i's opponent has been eliminated from playoff contention and is playing a conference game in game j. A positive and significant sign would indicate a team tanking in a nonconference since it gives a greater probability of team i winning game j. We use separate elimination variables for each draft format in order to examine eliminated team's behavior under each draft format.

Econometric Issues

There are three econometric issues associated with this empirical approach. The first is the use of random versus fixed effects to control for unobserved team heterogeneity. In previous research, Taylor and Trogdon (2002) used random effects while Price et al. (2010) used fixed-effects. The Hausman test is a formal test that can help determine whether random or fixed is more appropriate. The null hypothesis for the Hausman test is that the two estimators do not differ substantially. A rejection of the null hypothesis indicates that fixed effects is more appropriate (Hausman, 1978). For the present research, one can reject the null hypothesis and use fixed effects.

The second econometric issue is [heteroscedasticity.sub.ijk] is assumed to be a mean zero constant variance random variable; the variance of the equation error term is assumed to be the same for all teams in the sample. However, in Equation 1, heteroscedasticity may be present; the variance of the equation error term may differ across teams. The reason is NBA teams are located in different markets. Within those markets, there are unobserved characteristics that vary across these different markets leading to unequal variance of the equation error term. Both Taylor and Trogdon (2002) and Price et al. (2010) assumed and corrected for heteroscedasticity. We also perform a heteroscedasticity correction, using the standard White-Huber sandwich method.

The final econometric issue deals with computing the marginal effects for the interaction terms in Equation 1. In a logit model with no interaction terms, one can easily compute the marginal effects for any independent variable. Computing marginal effects for interaction variables is not straightforward (Ai & Norton, 2003; Norton, Wang, & Ai, 2004). As a result, the same approach as Price et al. (2010) is used, which estimated a fixed-effect linear probability model (LPM) and compared those estimated parameters to the estimated parameters from the fixed-effect logit model. We then use the marginal effects from the LPM estimates, given that the LPM parameter estimates have the same qualitative implications as the logit estimates. Table 3 contains the results. (6)

Results

Table 3 contains parameter estimates and estimated standard errors from Equation 1 for both the team fixed-effect logit model and the team fixed-effect LPM using a pooled sample of data from the 1983-1984, 1984-1985, 1989-1990 and 1993-1994 NBA seasons. Table 3 also shows the marginal effects of a one unit change in each of the explanatory variables on the probability of winning the game in these tables. The coefficients for the LPM also can be interpreted as marginal effects. Table 3 indicates a strong home-court advantage in the NBA, reinforcing earlier research conducted in multiple disciplines on the home-court advantage in professional basketball (e.g., Gandar et al., 2001). If team i is the home team, its chance of winning a game increases between 28 and 32% depending on the model used in Table 3.

The marginal effects on team winning percentage indicate that a one percent increase in the winning percentage is associated with a less than one percent increase in the probability of winning game j in both models. Similarly a one percent increase in the opponent's winning percentage results in a less than one percent decrease in team i's probability of winning game j. If team i has clinched a postseason playoff spot, it is more likely to win game j. If team i's opponent has clinched a postseason spot prior to game j, team i is less likely to win game j. These results make sense because, even if a team has clinched a playoff spot, it is trying to win games to improve its seed in the playoffs and perhaps gain home-court advantage for one or more playoff series.

The variables ELIM and OELIM identify teams eliminated from the playoffs. The results in Table 3 indicate that eliminated NBA teams were not more likely to tank in conference games in the 1983-1984 season. We hypothesized that since teams had to be last in their conference standings in order to have a chance to obtain the first overall selection, teams would be more likely to lose in conference games in order to get to the bottom of the standings. The results on Table 3 reject Hypothesis 1. This result supports Price et al. (2010). When the NBA adopted the equal-chance lottery format, previous research concluded that teams had no incentive to tank (Price et al., 2010; Taylor & Trogdon, 2002). With no incentive to tank, the coefficients for ELIM84*DC and OELIM84*DC should be insignificant in both the Logit and LPM models. The results indeed indicate that there was no incentive to tank in conference games under the equal-chance lottery format. Thus, the results support Hypothesis 2.

Two hypotheses (3 and 4) were developed regarding the strategic behavior of eliminated teams under the two weighted lottery formats. The results from Table 3 contain weak evidence that teams were more likely to tank in conference games than nonconference games, as only one elimination variable is significant (OELIM89*DC) compared to both variables (ELIM89*IC and OELIM89*IC) for nonconference games. As a result, Hypothesis 4 can be rejected. Even though an incentive existed for teams to tank and previous research concluded that eliminated teams were tanking, the social cost of tanking in conference games appears to have been high enough to deter eliminated NBA teams from tanking under the first weighted lottery format. The results from the linear probability model are similar to the logit model.

Under the second draft format, the results from Table 3 shows that eliminated teams are more likely to tank in conference games compared to nonconference games. Thus, one can fail to reject Hypothesis 3. Teams appear to have altered their tanking behavior under the second weighted lottery format. Why did the behavior of eliminated NBA teams change under the second weighted-lottery format? One reason could be the new probabilities of winning the lottery assigned to teams under this second format. Comparing the probabilities reported in Price et al. (2010), a more nonlinear structure was created in the second weighted lottery format. Lazear and Rosen (1981) showed that nonlinearity in prize structures promoted competition and encouraged the participants to put forth effort to move up in a contest. In this context, that means losing more games. The probabilities reported by Price et al. (2010) for the second draft lottery format indicate that the reward for moving up one position is higher under the second weighted draft format than under previous draft lottery formats. Overall, the results suggest that the unbalanced NBA schedule had different effects on the behavior of eliminated teams. Teams were not tanking under the reverse-order and equal-chance draft formats. However, when the NBA increased the probabilities, eliminated teams first responded by tanking in nonconference games compared to conference games. However, with a further increase in probabilities, eliminated teams tanked more in conference games than nonconference games, despite the social cost associated with tanking against geographic competitors and rivals.

Discussion and Conclusion

All North American professional sports leagues use unbalanced schedules. The present research examined the impact of an unbalanced schedule on the incentive of eliminated NBA teams to intentionally lose games late in the regular season to increase the likelihood of getting the first overall selection in the next amateur entry draft. From a financial standpoint, the first overall draft pick provides an opportunity to obtain a franchise player at a relatively low cost (Hausman & Leonard, 1997; Krautmann et al., 2009). In addition, previous research showed teams' gate revenue increases the season after they make the first overall selection (Price et al., 2010). This increase in gate revenue provides a financial incentive for eliminated teams not to put forth effort to win a game, jeopardizing the legitimacy of the league. Over the past 30 years, the NBA has strategically altered the amateur draft format to manage the issues of tanking and competitive balance.

The evidence generated here provides a deeper understanding of the incentives that teams face to tank under the last four different draft formats in the NBA. The results show that tanking was more likely to occur in conference games under the current weighted lottery format, but not under the previous draft formats. Under the previous formats, eliminated NBA teams were more likely to tank in nonconference games or not to tank at all. Overall, the present research provides a better understanding of the strategic behavior of teams that are eliminated from playoff contention and the impact that the unbalanced schedule and other policy mechanisms have on team behavior.

These results have implications for league policy. From a design perspective, leagues need to be cognizant of the unintended consequences generated by changes in league policies. Attempting to manage these consequences is a difficult task. However, mitigating these incentives is important for realizing the league's goal of maximizing the joint profits of all teams. The results suggest that the NBA may need to alter its draft policy or the unbalanced schedule to discourage tanking behavior. Under the current draft lottery format, teams are more likely to tank in conference games. Thus, the NBA may want to schedule more nonconference games towards the end of the regular season. However, doing so would sacrifice the interest generated by conference teams competing for playoff positions.

These issues reveal the complexities of tanking and the manner in which leagues attempt to mitigate tanking. The present study focused on a single dimension of tanking in one league: the incentives for NBA teams to tank in conference and nonconference games. The present research approach has some limitations. This research, as well as Taylor and Trogdon (2002), treats the tanking decision as static. The decision to tank could depend on the value that teams place on the amateur players available in the upcoming draft. Soebbing and Humphreys's (2013) research found that bookmakers adjusted the point spread each season, which could indicate that they perceived the strength of the top amateur players available to differ over seasons. The incentive to tank could vary across seasons, depending on a team's perceptions of the relative quality of amateur players available in the next draft, the composition of the existing roster, or the team's projected future roster needs. In addition, it may take time for an organization to learn and adjust to changes in league draft policy. For example, a team may not tank (or elect not to tank) immediately after a draft policy change. However, after observing that other teams that tanked improved after receiving higher picks in the entry draft, these teams might employ a tanking strategy.

This learning effect suggests an area for future research on tanking. The decision for an eliminated team to tank is not a decision made by players. NBA players attempt to maximize their lifetime earnings, and some may be playing for a future contract. As a result, players may be reluctant to tank, because it involves supplying lower e ort in games. The initial research on tanking focused on the organizational level. Future research should focus on identifying strategies that coaches and team executives could implement in order to intentionally lose games. For example, a team could play younger players more on average in games it wants to lose than in other games, decrease the starters' minutes, or increase the number of players used in a game. Identifying the mechanism through which teams tank would help the league modify the player contracts to eliminate tanking, which is an undesired behavior from a league's perspective.

However, the other goal of the amateur draft is to increase the competitive balance by strengthening the weaker teams of the league. Future research could also examine how competitive balance in the NBA is affected by modifications to the draft policy as well as the unbalanced schedule. Future research could also measure the intensity of rivalries between NBA teams in an attempt to further assess the impact that rivalries have on tanking. To measure the intensity of rivalries, future research could examine the number of times two teams played each other on national television, the newspaper coverage dedicated these games, and national media articles on a particular team during a season.

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Endnotes

(1) Kilduff et al. (2010) definition of competition comes from Deutsch's (1949) definition of competition.

(2) It is generally accepted that teams in North American professional sports leagues are profit maximizers, and teams in European professional leagues attempt to maximize wins instead of profits. However, "this is not to say that there are some owners with different ambitions" (Fort, 2000, p. 440).

(3) Teams do incur some costs with hosting playoff games. Some of these costs include utility expenses and paying employees such as ushers and concession employees. When comparing player salaries to the costs of hosting games, these costs are minimal.

(4) Superstar status is defined as player whose wins produced per 48 minutes (WP48) is greater than 0.200.

(5) This is the final number of observations. All observations where a team was playing its first game of the season were removed since no winning percentage exists yet for the team.

(6) The variables elim83*IC, oelim83*IC, elim84*IC, and oelim84*IC were dropped due to collinearity.

Brian P. Soebbing [1], Brad R. Humphreys [2], and Daniel S. Mason [3]

[1] Louisiana State University

[2] West Virginia University

[3] University of Alberta

Brian P. Soebbing is an assistant professor of sport management in the School of Kinesiology at Louisiana State University. His interests include the strategic behavior of sports leagues and teams, as well as the social and economic impacts of gambling.

Brad R. Humphreys is an associate professor in the College of Business & Economics at West Virginia University. His areas of research interest include the economics of sports, sport finance, and the economics of gambling.

Daniel S. Mason is a professor of physical education and recreation and adjunct with the School of Business at the University of Alberta. His research focuses on sports leagues and franchises, cities, events, and infrastructure development.

Table 1: NBA Draft Format Summary

Time period    Draft format                   Evidence of tanking?

1966-1984      Reverse-order                  Mixed
1985-1989      Equal-chance                   No
1990-1993      First weighted-probability     Yes
1994-present   Second weighted-probability    Yes

Table 2: Summary Statistics for 1983, 1984, 1989, and 1993 NBA Seasons

Variable                              Mean    Std. Dev

Neutral site game                     0.006   0.078
Clinched playoff berth                0.077   0.267
Opponent clinched playoff berth       0.077   0.267
Eliminated in 1983 season             0.005   0.069
Opponent eliminated in 1983 season    0.005   0.069
Eliminated in 1984 season             0.005   0.074
Opponent eliminated in 1984 season    0.005   0.074
Eliminated in 1989 season             0.014   0.118
Opponent eliminated in 1989 season    0.014   0.118
Eliminated in 1993 season              0.017   0.128
Opponent eliminated in 1993 season    0.017   0.128
Conference game                       0.690   0.462

N=8,090

Table 3: Logit and LPM Results, Pooled Sample

                          Logit                      LPM
Variable        Coef.      Robust   Marginal    Coef.      Robust
                           Std.     Effect                Std. Err.
                           Err.     on Win

Home team      1.365 **    0.051    0.329     0.290 **     0.010
Neutral site    -0.093     0.394    -0.023     -0.020      0.072
Winpct*100     0.022 **    0.002    0.006     0.004 **     0.000
Owinpct*100    -0.026 **   0.002    -0.007    -0.005 **    0.000
Clinch          0.241 *    0.116    -0.06      0.043 *     0.022
Oclinch        -0.279 *    0.116    -0.069    -0.052 *     0.022
Elim83*DC      -0.585      0.401    -0.142     -0.113      0.067
Oelim83*DC      0.559      0.392    0.136      0.110       0.066
Elim84*DC       -0.203     0.368    -0.051     -0.043      0.067
Oelim84*DC      0.231      0.360    0.058      0.049       0.064
Elim89*DC       -0.553     0.304    -0.135     -0.077      0.046
Oelim89*DC     0.754 **    0.299    -0.18      0.115 *     0.046
Elim89*IC      -1.792 *    0.857    -0.357    -0.248 *     0.086
Oelim89*IC     1.948 **    0.849    0.376      0.281 **    0.086
Elim93*DC      -1.038 **   0.288    -0.239    -0.151 **    0.039
Oelim93*DC     1.073 **    0.281    0.246     0.161 **     0.038
Elim93*IC       -1.561     0.852    -0.326    -0.214 **    0.078
Oelim93*IC      1.589      0.890    0.331     0.224 **     0.080
Constant       -0.415 **   0.173      --      0.409 **     0.036

* =p-value<0.05, ** =p-value<0.01

Dependent Variable=1 if team i wins game j in season k