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5-2019

Trust the Process: in the NBA

Min S. Choi University of Pennsylvania

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Choi, Min S., "Trust the Process: Tanking in the NBA" (2019). Wharton Research Scholars. 182. https://repository.upenn.edu/wharton_research_scholars/182

This paper is posted at ScholarlyCommons. https://repository.upenn.edu/wharton_research_scholars/182 For more information, please contact [email protected]. Trust the Process: Tanking in the NBA

Abstract This study assumes the tournament incentives inherent in the National Association (NBA) based on a study by Taylor and Trogdon (2002). Incentive to tank or lose intentionally, which is encouraged by the reverse-order and lottery-based system of the NBA, is examined and validated. A modified ersionv of Taylor and Trogdon’s logistic regression model and the data from the 2016-17 and 2017-18 seasons are employed. My findings aligned closely with the esultsr from the original study. They suggested that the teams eliminated from the playoffs responded to tournament incentives in a predictable manner whereas the confounding effects of incentives prevent the teams that had already clinched the playoffs to behave predictably. The addition of game outcome expectation data from sports betting as a dependent variable conveyed the idea that the incentive to tank is overestimated by the public and in calculation of betting odds.

Keywords Basketball, NBA, Draft, Tanking, Tournament Incentives

Disciplines Business

This thesis or dissertation is available at ScholarlyCommons: https://repository.upenn.edu/ wharton_research_scholars/182 Trust the Process: Tanking in the NBA

By

Min S. Choi

An Undergraduate Thesis submitted in partial fulfillment of the requirements for the

WHARTON RESEARCH SCHOLARS

Faculty Advisors:

Jose M. Abito

Assistant Professor, Business Economics and Public Policy

Shane T. Jensen

Associate Professor, Statistics

THE WHARTON SCHOOL, UNIVERSITY OF PENNSYLVANIA

MAY 2019

1 ABSTRACT

This study assumes the tournament incentives inherent in the National Basketball Association

(NBA) based on a study by Taylor and Trogdon (2002). Incentive to tank or lose intentionally, which is encouraged by the reverse-order and lottery-based draft system of the NBA, is examined and validated. A modified version of Taylor and Trogdon’s logistic regression model and the data from the 2016-17 and 2017-18 seasons are employed. My findings aligned closely with the results from the original study. They suggested that the teams eliminated from the playoffs responded to tournament incentives in a predictable manner whereas the confounding effects of incentives prevent the teams that had already clinched the playoffs to behave predictably. The addition of game outcome expectation data from sports betting as a dependent variable conveyed the idea that the incentive to tank is overestimated by the public and in calculation of betting odds.

Keywords: Basketball, NBA, Draft, Tanking, Tournament Incentives

2 INTRODUCTION

In National Basketball Association (NBA), teams rebuild or refine their rosters every year by acquiring new players and releasing old and/or underperforming players. Apart from free- agency and trades, the main method by which teams engage in recruiting new players is participating in the draft, where the teams are given the right to select and sign players to the league whether from high school, college or abroad. The order that teams choose players is currently based on teams’ record in the preceding season in a reverse-order, which gives underperforming teams a chance to improve, while creating a cycle of success and failure between teams. (Tuck and

Whitten 2013) In other words, teams with worse record draft earlier, and teams with better record draft later. This structure, though beneficial to the underperforming teams, creates a dual-incentive, where the race to the championship offers an incentive to win and the race to the bottom and top draft picks offers an incentive to lose. (Preston and Szymanski 2003) A dilemma between winning and intentionally losing, also known as tanking, arises since the incentive to lose can be greater than the incentive to win for the teams at the bottom of the league.

Just as the title suggests, the and its team slogan “Trust the Process” were a major motivation for this study. “The Process” began in 2013 when the General Manager of the team, , publicly expressed his desire to eschew short-term wins in favor of long- term success by saying, “we talk a lot about process—not outcome—and trying to consistently take all the best information you can and consistently make good decisions. Sometimes they work and sometimes they don’t, but you reevaluate them all.” (Rappaport 2013) From then on, the public became aware that the 76ers were tanking in order to draft top talents for the future of the franchise.

The 76ers front office began to send away its star players like and Michael Carter-

3 Williams for draft picks and low salary players, and the tanking process reached its peak during the 2015-16 season when the 76ers ended the season with the second worst 82-games record in the

NBA history. (Scudilla 2016) The General Manager Sam Hinkie was fired at the end of the season due to the growing impatience from the ownership and fanbase. (Stein 2016) On the other hand, the 76ers were rewarded with many high draft picks during the years of tanking: the third overall pick in 2014, the third overall pick in 2015, the first overall pick in 2016, and the first overall pick in 2017. (Pompey 2018) These picks resulted in two all-star caliber players, and Ben

Simmons, and two underwhelming players who have already left the team, and

Markelle Fultz. Though it would be hasty to attribute the successful tanking process as the reason for the 76ers’ recent rise and success, the stellar performance displayed by Embiid and Simmons encourages the belief that tanking was a good decision for the 76ers despite the loss that the team incurred in terms of its popularity and revenue. (Orso 2014)

Given the draft system and a prominent example of tanking displayed by the 76ers, this study examines and aims to validate tournament incentives in the NBA by replicating the model employed by Taylor and Trogdon in their article Losing to Win: Tournament Incentives in the

National Basketball Association (2002). In addition, this study adopts betting odds data to analyze the public’s expectations on the outcome of the games with the incentive to tank in consideration.

Throughout the paper, losing intentionally and tanking are synonymous, and higher draft pick, priority draft pick, and better draft pick are synonymous.

The rest of this research paper is structured as follows: Literature Review, Overview of

Draft and Lottery System, Research Approach, Data and Methodology, Results, Discussion and

Extension.

4 LITERATURE REVIEW Tournament Structure

Lazear and Rosen (1981) introduced the concept of Tournament Theory. The idea behind the Tournament Theory was that the workers’ risk appetite can determine how they react to wage allocation when it’s based on their relative performance rather than their marginal revenue product.

The study suggested that risk neutrality ensures equal and efficient allocation of resources between two basis of wage allocation, but risk-averse workers prefer allocation based on relative performance under some circumstances. (Lazear and Rosen 1981) Although the original theory was based on a wage and compensation model, it is also applicable to individual and team sports where the teams are rewarded based on their relative performance, rather than their absolute records. (Frick 2003)

The NBA rewards draft picks to the teams at the end of the season according to their relative performance ultimately determined by their records at the end of the regular season. The previous sentence, however, does not apply to some teams because the winner of the NBA championship is determined by a tournament, as known as the playoffs. Viewing the entire NBA season as a tournament, the multiple incentives present in one tournament do not always increase the effort level exerted by the teams. (Preston and Szymanski 2003) And this multiple incentives structure inherent in the NBA leads to an unintended “tournament within a tournament.” (Price,

Soebbing, Berri, and Humphreys 2010)

Tanking

Merriam-Webster defines the word “tanking” as “to make no effort to win, lose intentionally,” and this scheme has been investigated by various scholars. NBA employs a draft

5 lottery system where the teams with worse records have a higher chance of getting the priority picks, but not guaranteed to obtain them. The research by Taylor and Trogdon (2002) examined three different NBA seasons with three different sets of lottery odds and tested how the teams responded to different levels of lottery odds after finding out that they are eliminated from or have already clinched the playoffs. As a result, they substantiated the idea that the reverse-order structure of the NBA draft inherently creates the incentive to lose and is taken advantage by the teams that are eliminated earlier in the season. (Taylor and Trogdon 2002) This finding could be reinterpreted that the draft lottery system, which was initially created to prevent the teams from tanking, is proven inadequate in serving its purpose. A more detailed analysis of Taylor and

Trogdon’s study will be expounded in the Research Approach and Data and Methodology sections of this paper.

Furthermore, Price et. al (2010) argued against Taylor and Trogdon’s findings and claimed that the traditional reverse-order draft entry does not generate strong incentives to tank and that the marginal benefit of shirking is constant. They suggested that the NBA had to implement the weighted lottery system in the draft because uncertainty is an indispensable element of professional sports leagues, and fans do not enjoy watching games that are fixed. (Mason 1999) Instead of having the order of draft fully fixed on the last day of the season, the current lottery system protects uncertainty and adds suspense, which adds more entertainment for the fans.

In general, there is a shortage in studies that closely examine the topic of tanking unlike other apparent sports phenomena. This dearth can be attributed to the ambiguous and enigmatic nature of tanking, excluding the case of the Philadelphia 76ers as they publicly announced their intentions.

6 Potential Solutions

Recognizing the potential destruction and conflict of interest that tanking can provoke,

NBA has proposed some solutions in the past, such as flattening the odds in draft lottery, but they have been insufficient in eliminating the incentive to tank. (Paxton 2019)

Other scholars have thus proposed various solutions to tanking. Lenten, Smith, and Boys

(2018) offered a solution to tanking that specifically applied to the Australian Football League

(AFL). Unlike the traditional reverse-order draft that grants picks based on the record at the end of the season, their alternative draft-pick allocation policy rewards the draft picks according to the order the teams are eliminated from playoff contention. In a quasi-natural experiment with 2288 regular-season games of data, the alternative draft-pick allocation policy resulted in an improvement of 21.7% in the probability of winning for a team eliminated from playoff contention.

(Lenten et al. 2018)

A law student named Allen Paxton suggested that tanking can be prevented by imposing fiduciary duties. Although the NBA does not explicitly claim itself as a partnership, Paxton asserted that the NBA has a fundamental partnership model, and the teams consequently owe each other fiduciary duties. Hence, tanking can be considered a breach of fiduciary duties, and the league and other teams can sue a tanking team under the New York partnership law. This accusation would then discourage teams from tanking. (Paxton 2019)

Efficacy of Draft and General Managers

The aforementioned studies conveyed that the race to the bottom was encouraged by the prospect of getting priority draft picks which allows the teams choose the best players available who best suit their needs. Nonetheless, it must be noted that drafting earlier does not always result

7 in getting the best players in the long run, because players do not always live up to the expectations and become “busts” like and Jahlil Okafor from the 76ers. Koz, Fraser-Thomas, and Baker (2011) studied the efficacy of draft across various sports leagues. The players drafted in the first round played statistically significant more games than the players drafted in the second round, but this does not prove the success of the overall draft since the success of players should be evaluated across picks in a single round instead of across rounds.

General managers (GMs) are involved in all aspects of team operations from drafting the players to firing coaches. Past research studies proved that general manager’s technical experience and GM education are positively correlated to winning and success of the team. (Juravich et al.

2017) Wong and Deubert (2010) studied the role that general managers play in Major League

Baseball, and the results indicated that general managers are ultimate decision maker of teams.

Seeing that Sam Hinkie assumed the full responsibility of the 76ers’ tanking process and was dismissed for the team’s failure, it would be safe to conclude that the general managers are the ones who take the lead in tanking decisions.

OVERVIEW OF DRAFT AND LOTTERY SYSTEM

The NBA has 30 teams and is divided into two conferences, Eastern and Western. Each conference has 15 teams and is divided into three divisions with five teams each: the Eastern

Conference has Atlantic, Central, Southeast divisions and the Western Conference has Northwest,

Pacific, Southwest divisions.

Each team plays 82 games during the regular season, which totals up to 1230 NBA regular season games per year. At the end of the regular season, the top 8 teams from each conference advance to the playoffs, and the playoff teams from each conference are seeded from 1 to 8. The

8 bottom 7 teams of each conference do not qualify for the playoffs, and their season conclues at the end of the regular season without any additional games.

Table 1: 2017-18 NBA Regular Season Conference Standings Eastern Conference Western Conference Teams W L Playoffs Seed Teams W L Playoffs Seed Raptors 59 23 Yes 1 65 17 Yes 1 55 27 Yes 2 58 24 Yes 2 Philadelphia 76ers 52 30 Yes 3 49 33 Yes 3 50 32 Yes 4 48 34 Yes 4 48 34 Yes 5 48 34 Yes 5 44 38 Yes 6 48 34 Yes 6 44 38 Yes 7 47 35 Yes 7 43 39 Yes 8 47 35 Yes 8 39 43 No N/A 46 36 No N/A 36 46 No N/A Clippers 42 40 No N/A 29 53 No N/A 35 47 No N/A Nets 28 54 No N/A 27 55 No N/A Bulls 27 55 No N/A 24 58 No N/A 25 57 No N/A 22 60 No N/A Hawks 24 58 No N/A 21 61 No N/A

The NBA playoffs begin in mid-April with 4 match-ups in each conference: the highest seeded team remaining faces the lowest seeded team remaining (1-8, 2-7, 3-6, 4-5). This arrangement serves to give the highest seeded team an advantage of facing the worst team available under the assumption that the regular season record is the best indicator of team quality. After the first round, the four remaining teams in each conference play in conference semifinals with matchups arranged in the same manner: highest seeded team remaining facing the lowest seeded team remaining. The remaining two teams after the semifinals then face each other for conference

9 finals, and the winners from each conference face each other at the NBA finals, which lasts until mid-June. Every matchup in the playoffs is played in a best of 7 series.

Figure 1: 2017-18 NBA Playoffs Tournament Bracket

While the playoff bound teams are competing in the playoffs, 14 other teams prepare for the NBA draft which is held in June after the Finals. As aforementioned, the order of draft for the

14 teams is determined by the lottery system and the odds are allocated based on the records from the previous season in a reverse-order. The winner of each pick is chosen by using 14 ping pong balls in a lottery machine and randomly selecting a combination of 4 balls. Each team is assigned a certain number of combinations out of 1,001 possible combinations: (14*13*12*11)/ (4*3*2*1).

(Boghossian 2019)

Table 2: 2005-2018 NBA Draft Lottery Odds (First Three Picks) Seed 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1st Pick 0.250 0.199 0.156 0.119 0.088 0.068 0.043 0.028 0.017 0.011 0.008 0.007 0.006 0.005 2nd Pick 0.215 0.188 0.157 0.126 0.097 0.071 0.049 0.033 0.020 0.013 0.009 0.008 0.007 0.006 3rd Pick 0.178 0.171 0.156 0.133 0.107 0.081 0.058 0.039 0.024 0.016 0.012 0.010 0.009 0.007

10 Starting in 2019, NBA is implementing a new set of odds with equal chances of obtaining the top three picks among the bottom three teams. This new set of odds drastically flattened the odds for the bottom teams getting the first overall pick. (0.250, 0.199, 0.156 to 0.140).

Table 3: 2019 New NBA Draft Lottery Odds (First Three Picks) Seed 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1st Pick 0.140 0.140 0.140 0.125 0.105 0.090 0.075 0.060 0.045 0.030 0.020 0.015 0.010 0.005 2nd Pick 0.134 0.134 0.134 0.122 0.105 0.092 0.078 0.063 0.048 0.033 0.022 0.017 0.011 0.006 3rd Pick 0.127 0.127 0.127 0.119 0.106 0.094 0.081 0.067 0.052 0.036 0.024 0.019 0.012 0.006

Though the probability of getting the first pick by the highest seeded team with 25% may appear significantly greater than any other teams, there have been many cases where the team with the best odds did not obtain the first overall pick. The number one pick was taken by the team with the worst record over the past four years, but it wasn’t the case for nine straight years from 2005 to 2014. Especially in 2014, the Cleveland Cavaliers won the first pick with the ninth worst record in the league and a 1.7% chance.

Table 4: 2009-2018 Teams with the First Overall Pick Year Team Previous Season Standing Player 2007 Portland Trailblazers 6th Worst 2008 9th Worst 2009 2nd Worst 2010 Washington Wizards 5th Worst 2011 Cleveland Cavaliers 8th Worst 2012 New Orleans Hornets 3rd Worst 2013 Cleveland Cavaliers 3rd Worst Anthony Bennett 2014 Cleveland Cavaliers 9th Worst 2015 Minnesota Timberwolves Worst Karl-Anthony Towns 2016 Philadelphia 76ers Worst 2017 Philadelphia 76ers Worst Markelle Fultz 2018 Phoenix Suns Worst

11 RESEARCH APPROACH

Taylor and Trogdon (2002) used a logistic estimation model to study the extent of tournament incentives across three distinct NBA seasons: 1983-84, 1984-85, 1989-90. These three seasons are historic to the development of the NBA draft lottery system because new changes to the draft structure were applied each year.

In the 1983-84 season, there were 12 teams in the Western Conference and 11 teams in the

Eastern Conference, and draft lottery had not existed yet. Instead, the order of the draft was determined in the traditional reverse order according to the relative record from the preceding season. In the 1984-85 season, the same number of teams existed as the previous season and 16 teams qualified for the playoffs. This season introduced a monumental concept for the NBA as the lottery system was implemented where each one of seven non-playoff team had an equal chance

(14.3%) of getting the first pick. In the 1989-90 season, four additional teams were added to the league with 14 teams in the Western Conference and 13 teams in the Eastern Conference, and 16 teams qualified for the playoffs. The NBA also switched to the weighted lottery system where the non-playoffs teams were no longer granted the equal probability of getting the first overall pick during the 1989-90 season. Different lottery odds were then granted to each team and the team with the worst record was given the probability of 16.7% at getting the first overall pick (25% in

2018).

With these different sets of draft odds allocation, Taylor and Trogdon (2002) expected and confirmed that 1983-84 season would display the greatest amount of incentive to lose intentionally since the uncertainty of lottery had not existed yet; the more games one team lost, the higher draft pick that team was guaranteed to receive. Taylor and Trogdon also confirmed that extent of such

12 incentive was the lowest during the 1984-85 season because the reward of lottery odds was equally allocated to everyone regardless of their standings in the previous season.

Building on Taylor and Trogdon’s analysis from nearly 20 years ago, this study aims to examine the recent trend of tanking in the NBA for the past two seasons (2016-17 and 2017-18).

The NBA and its draft system have gone through many changes since Taylor and Trogdon’s original data was collected, including a policy that barred high school graduates from directly entering the NBA draft. Three teams have been added to the league, which leaves a total of 30 teams and 15 teams in each conference, and the lottery odds have gone through several changes as well to accommodate the addition of new teams and to promote fair play.

DATA AND METHODOLOGY

Taylor and Trogdon’s empirical model investigated change in the effort level by the teams as the prize differential between winning and losing increased. It controlled for factors that could affect the outcome of games to isolate the effect of incentives to win or lose. The empirical model of this study is similar to that of Taylor and Trogdon with a few differences: inclusion of EXPWIN as a dependent variable and exclusion of NEUTRAL variable.

WIN EXPWIN

HOME WINPCT OWINPCT CLINCH OCLINCH ELIM OELIM

13 푊퐼푁푖푗 = 푓(퐻푂푀퐸푖푗, 푊퐼푁푃퐶푇푖푗, 푂푊퐼푁푃퐶푇푖푗, 퐶퐿퐼푁퐶퐻푖푗, 푂퐶퐿퐼푁퐶퐻푖푗, 퐸퐿퐼푀푖푗, 푂퐸퐿퐼푀푖푗)

퐸푋푃푊퐼푁푖푗 = 푓(퐻푂푀퐸푖푗, 푊퐼푁푃퐶푇푖푗, 푂푊퐼푁푃퐶푇푖푗, 퐶퐿퐼푁퐶퐻푖푗, 푂퐶퐿퐼푁퐶퐻푖푗, 퐸퐿퐼푀푖푗, 푂퐸퐿퐼푀푖푗)

Figure 2: Research Model

Variable WIN is a dummy variable equal to 1 if team i won game j, and variable EXPWIN is a dummy variable equal to 1 if team i was expected to win game j. These variables serve as dependent variables in the empirical model. Unlike variable WIN, which was the actual outcome of the game with values of either 0 or 1, variable EXPWIN is an expectation that was determined by the betting odds and has three possible values: 0, 0.5, 1. The value of 0.5 was assigned when the odds were break even between team i and its opponent for game j (spread of 0).

Variable HOME is a dummy variable equal to 1 if team i played game j on its home court.

It was included to control for the effect that home court advantage has on the outcome of the game.

Other things constant, the effect that home court advantage has on the outcome of the game is expected to be positive. Unlike in Taylor and Trogdon’s study, variable NEUTRAL was omitted because every game in the 2016-17 and 2017-18 seasons had a clear home team.

Variable WINPCT is the winning percentage of team i before game j, and variable

OWINPCT is the winning percentage of the opponent of team i before team i’s game j. WINPCT and OWINPCT were calculated by dividing the total number of wins by the number of games played up to game j. These variables were included to control for the teams’ quality with the assumption that winning percentage is a good indicator of team quality. Other things constant, the effect that WINPCT and OWINPCT have on team i’s probability of winning is expected to be positive and negative, respectively.

14 Variable CLINCH is a dummy variable equal to 1 if team i had clinched the playoffs before game j, and variable OCLINCH is a dummy variable equal to 1 if the opponent of team i had clinched the playoffs before game j. The exact date of the teams clinching the playoffs were retrieved from various sources of sports articles from ESPN to Bleacher Report. The teams that did not qualify for the playoffs were assigned 0 for the entire season. Other things constant, the effect of CLINCH and OCLINCH on the probability of winning is expected to be ambiguous with confounding effects. Teams that have already clinched the playoffs would experience less incentive to win and would decide to rest its best players to avoid injuries, preparing for the playoffs. However, the seeding structure of the playoffs also encourage the teams to continue exerting efforts to win in order to secure high seed for an advantageous playoff schedule. The team that clinched the number one seed would experience the least amount of incentive to win.

Variable ELIM is a dummy variable equal to 1 if team i had been eliminated from the playoffs before game j, and variable OELIM is a dummy variable equal to 1 if team i’s opponent had been eliminated from the playoffs before game j. The exact dates of most teams’ elimination dates were retrieved from various sources of media, but not all teams announced their elimination from the playoffs. Therefore, the exact dates of their official elimination were located by finding when the remaining number of games was less the number of wins they needed to have an equal standing with the 8th place team. Other things constant, the effect that ELIM has on the probability of winning is expected to be negative because the high draft picks that ensue a lower standing appear greatly lucrative to the teams in the midst of a rebuilding process at the bottom of the table.

It is true that the teams may still have the incentive to win for the sake of ticket sales and its fans, but they should not have a significant effect on the teams’ effort level unless the team publicly announce their intention to tank like the 76ers.

15 Table 5: Descriptive Statistics for 2016-17 Season Variable Mean SD Range WIN 0.500 0.500 [0,1] EXPWIN 0.500 0.492 [0,1] HOME 0.500 0.500 [0,1] WINPCT 50.0 17.9 [0,100] OWINPCT 50.0 17.9 [0,100] CLINCH 0.060 0.237 [0,1] OCLINCH 0.060 0.237 [0,1] ELIM 0.040 0.195 [0,1] OELIM 0.040 0.195 [0,1] (Total of 32 games were removed because every team has an undefined WINPCT before the conclusion of game 1)

Table 6: Descriptive Statistics for 2017-18 Season Variable Mean SD Range WIN 0.500 0.500 [0,1] EXPWIN 0.500 0.492 [0,1] HOME 0.500 0.500 [0,1] WINPCT 50.0 16.9 [0,100] OWINPCT 50.0 16.9 [0,100] CLINCH 0.048 0.214 [0,1] OCLINCH 0.048 0.214 [0,1] ELIM 0.063 0.243 [0,1] OELIM 0.063 0.243 [0,1] (Total of 32 games were removed because every team has an undefined WINPCT before the conclusion of game 1)

The dataset that this study uses differ in a few aspects from Taylor and Trogdon’s dataset from 1983-84, 1984-85, 1989-90 seasons. The mean of CLINCH variable for Taylor and

Trogdon’s dataset was greater at 0.075 compared to 0.060 and 0.048 for 2016-17 and 2017-18 seasons. It can be inferred that the teams clinched the playoffs later in the recent seasons than in the earlier era of NBA. In contrast, the mean of Taylor and Trogdon’s ELIM variables average at

0.006 (1983-84), 0.007 (1984-85), and 0.019 (1989-90) compared to 0.040 and 0.063 for 2016-17

16 and 2017-18 seasons. This conveys that the teams are eliminated from the playoffs earlier in the season nowadays.

Following Taylor and Trogdon’s methodology, maximum likelihood technique of logistic regression is employed to the model with WIN and EXPWIN as dependent variables for each equation and for each season of` data. Logit coefficients, associated marginal effects on the probability of winning, and associated marginal effects on the odds ratio will be reported for each variable. The reported results from a total of four logistic regressions will then be compared: WIN on 2016-17, WIN on 2017-18, EXPWIN on 2016-17, EXPWIN on 2017-18.

RESULTS

Table 7: Random-Effects Logit Estimation Results, Dependent Variable: WIN

2016-17 Season Associated Marginal Effect on Associated Marginal Variable Logit Coefficient the Probability of Winning Effect on the Odds Ratio HOME 0.736 *** 0.165 2.087 WINPCT 0.022 *** 0.005 1.022 OWINPCT - 0.022 *** - 0.005 0.978 ELIM - 0.451 * - 0.101 0.637 OELIM 0.451 * 0.101 1.570 CLINCH 0.038 0.009 1.039 OCLINCH - 0.038 - 0.009 0.963

2017-18 Season Associated Marginal Effect on Associated Marginal Variable Logit Coefficient the Probability of Winning Effect on the Odds Ratio HOME 0.699 *** 0.156 2.011 WINPCT 0.023 *** 0.005 1.023 OWINPCT - 0.023 *** - 0.005 0.977 ELIM - 0.984 *** - 0.219 0.374 OELIM 0.984 *** 0.219 2.675 CLINCH - 0.344 - 0.077 0.709 OCLINCH 0.344 0.077 1.410 * Significant at the 10% level; ** Significant at the 5% level; *** Significant at the 1% level

17

In both 2016-17 and 17-18 seasons, having a home court advantage was a strong predictor of teams’ victory. With Logit coefficients significant at the 1% level for variable HOME, teams that were playing on the home court were approximately two times more likely to win other things constant. Conversely, teams that were playing on the road were approximately two times less likely to win.

The Logit coefficients of variables WINPCT and OWINPCT were statistically significant at the 1% level in both seasons. A 1% increase in team’s winning percentage resulted in approximately 0.5% increase in team’s probability of winning. In turn, a 1% increase in opponent’s winning percentage resulted in approximately 0.5% decrease in team’s probability of winning.

Though the results from both seasons confirmed the incentive to lose intentionally among the teams eliminated from the playoffs, the effect that elimination from the playoffs has on the team and its opponent differed between two seasons. In the 2016-17 season, the Logit coefficient of ELIM variable was -0.451, which was significant only at the 10% level, and teams eliminated were 1.6 times more likely to lose other things constant. The effect of playoff elimination was greater in the 2017-18 season with Logit coefficient at -0.984 and significant at the 1% level, and the teams eliminated were 2.67 more likely to lose other things constant.

CLINCH and OLINCH variables were statistically insignificant in both 2016-17 and 2017-

18 seasons, which confirms the prediction of confounding effects caused by the intention to protect players and the seeding structure of the playoffs. The Logit coefficients and associate marginal effects of clinch variables interestingly pointed to different directions in each season.

18 Table 8: Random-Effects Logit Estimation Results, Dependent Variable: EXPWIN

2016-17 Season, Dependent Variable: EXPWIN Associated Marginal Effect on Associated Marginal Variable Logit Coefficient the Probability of Winning Effect on the Odds Ratio HOME 2.919 *** 0.334 18.514 WINPCT 0.100 *** 0.012 1.106 OWINPCT - 0.100 *** - 0.012 0.904 ELIM - 1.322 *** - 0.151 0.267 OELIM 1.322 *** 0.151 3.749 CLINCH 0.649 * 0.074 1.913 OCLINCH - 0.649 * - 0.074 0.523

2017-18 Season, Dependent Variable: EXPWIN Associated Marginal Effect on Associated Marginal Logit Coefficient Variable the Probability of Winning Effect on the Odds Ratio HOME 2.410 *** 0.284 11.131 WINPCT 0.103 *** 0.012 1.109 OWINPCT - 0.103 *** - 0.012 0.902 ELIM - 2.671 *** - 0.315 0.069 OELIM 2.671 *** 0.315 14.451 CLINCH - 0.806 ** - 0.095 0.447 OCLINCH 0.806 ** 0.095 2.239 * Significant at the 10% level; ** Significant at the 5% level; *** Significant at the 1% level

Home court advantage still served as a strong win predictor in betting odds. With Logit coefficients significant at the 1% level for variable HOME in both seasons, teams playing on the home court were expected approximately 18.5 times more likely to win during the 2016-17 season and 11.1 times during the 2017-18 season other things constant. The associate marginal effects on the odds ratio were 10 times and 5 times those from the actual game outcomes.

WINPCT and OWINPCT’s Logit coefficients were statistically significant at the 1% level.

A 1% increase in the team’s winning percentage resulted in approximately 1% increase in the team’s probability of winning in both seasons, which was double the amount of effects from the regression with WIN as the dependent variable.

19 Status as teams eliminated from the playoffs had a significant influence on the betting odds prediction and its effects differed greatly between two seasons. In the 2016-17 season, the Logit coefficient of ELIM variable was -1.322 and significant at the 1% level, which means that the teams eliminated were 3.8 times more likely to lose other things constant. The effect of playoffs elimination was greater in the 2017-18 season with Logit coefficient at -2.671 and significant at the 1% level; the teams eliminated were 14.5 times more likely to lose other things constant.

CLINCH and OLINCH variables were statistically significant in both 2016-17 and 2017-

18 seasons. However, the results conflicted with each other as the Logit coefficient of CLINCH variable in 2016-17 season was positive while it was negative during the 2017-18 season. This conflict in direction aligns with the results from WIN as the dependent variable and confirms the confounding effect of clinching the playoffs.

Overall, compared to the results above with actual game outcomes, the results with betting odds and expectations are more extreme with greater absolute values and statistical significance.

This exhibits the idea that the betting market and the public consider the independent variables of this study, especially playoff elimination and clinch status of teams, when making predictions on game outcomes.

DISCUSSION AND EXTENSION

The results from this study aligned closely with the results from Taylor and Trogdon’s study (2002) yet differed considerably in terms of absolute values. The Logit coefficients and associated marginal effects of the independent variables, except for statistically insignificant

CLINCH and OCLINCH, still pointed to the same direction: whether they increased or decreased

20 the probability of winning. As discussed before, the results in Taylor and Trogdon’s study were expected to vary between seasons because many changes were made each season.

Unlike the case above, there weren’t any changes implemented to the draft and league structure between the 2016-17 season and 2017-18 season, but the results still varied greatly between these seasons. This suggests that the difference between the results in Taylor and

Trogdon’s study over the seasons were not necessarily caused by the changes in draft odds and tournament incentives. Instead, these variances could simply be attributed to random chances and to the fact that no two seasons are the same. Fundamental differences over multiple seasons were exemplified by the discrepancy between average value of elimination and clinch variables.

At the outset of this study, the associated marginal effect of playoff elimination was expected to be greater in the recent seasons because the value of draft picks is expected to have increased over time. Since the draft and lottery system now have decades of history, more data points have been collected, and these data points would help the teams to have a better idea which attributes are important in player’s success and how to measure them. Accordingly, teams must have gotten better in approaching the draft and evaluating players, eventually decreasing the uncertainty in player evaluation and increasing the value of draft picks. However, the associated marginal effect on both probability of winning and odds ratio in recent seasons were not significantly greater than those from Taylor and Trogdon’s study.

Stark differences between the results from the regressions with EXPWIN and WIN as dependent variables are noteworthy. Other things constant, the teams eliminated from the playoffs were 1.6 and 2.6 times more likely to lose in actual game results, but the betting odds predicted that the teams eliminated from the playoffs were 3.8 and 14.5 times more likely to lose. While the

21 results confirm the existence of incentive to lose, they also indicate how the public and sports betting sphere overestimate the impact that playoff elimination has on the effort level exerted by the teams. After all, these extreme results were inevitable because betting odds are often a product of analyzing the past.

Furthermore, there are two major shortcomings of this model worthy of discussion. Firstly, the only way that the teams could be declared eliminated from or clinched the playoffs was finding out when they were officially declared so from the articles and/or when it was statistically impossible (possibility of 0%). However, teams like the Golden State Warriors and Cleveland

Cavaliers were aware that they were playoff bound simply because of their exceptional team quality. Hence, assuming the official date of playoff elimination and clinching as the critical juncture of the tournament incentive during the season would not be accurate.

Secondly, teams often trade their draft picks before or during the draft for other draft picks or players. Therefore, the team that has already traded away its draft pick(s) is not motivated to exert effort to win or lose based on its standing at the end of the regular season because the draft pick has already been designated to another team. For example, the 8th pick of the 2018 draft originally belonged to the , but the pick was transferred to the Boston Celtics 5 years before the trade from a trade deal in 2013, and the pick eventually ended up in the hands of the

Cleveland Cavaliers. The Nets did not experience the incentive to tank as expected from this study despite their playoff elimination status because losing did not bring any benefits to the team.

This study further confirms Taylor and Trogdon’s argument that the teams respond to the tournament incentive in a predictable manner. When teams are eliminated from the playoffs, they do engage in and take advantage of tournament incentives. This study also examines the

22 expectation that the public and the sports betting sphere have towards the teams in the NBA and discovered that the teams do not engage in the incentive to lose intentionally as much as the betting odds imply. As discussed, a set of new draft lottery odds are introduced in 2019 that can potentially reconstruct the incentive structure for the teams eliminated from the playoffs. Running the model of this study with the data from the 2018-19 season would further reveal the effect of change in lottery odds has on the incentives disregarding the differences caused by random chances. Further research with additional independent variables would improve the separation of tournament incentive effects captured by the elimination and clinch variables.

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29 APPENDIX

Code used for analysis on R

#2016-17 season PrevSeason <- read_excel("Downloads/FinalData.xlsx", sheet = "1617Data") #2017-18 season NewSeason <- read_excel("Downloads/FinalData.xlsx", sheet = "1718Data")

#function for marginal effects on the probability of winning Fernihough (2011) mfx <- function(x,sims=1000){ set.seed(1984) pdf <- ifelse(as.character(x$call)[3]=="binomial(link = \"probit\")", mean(dnorm(predict(x, type = "link"))), mean(dlogis(predict(x, type = "link")))) pdfsd <- ifelse(as.character(x$call)[3]=="binomial(link = \"probit\")", sd(dnorm(predict(x, type = "link"))), sd(dlogis(predict(x, type = "link")))) marginal.effects <- pdf*coef(x) sim <- matrix(rep(NA,sims*length(coef(x))), nrow=sims) for(i in 1:length(coef(x))){ sim[,i] <- rnorm(sims,coef(x)[i],diag(vcov(x)^0.5)[i]) } pdfsim <- rnorm(sims,pdf,pdfsd) sim.se <- pdfsim*sim res <- cbind(marginal.effects,sd(sim.se)) colnames(res)[2] <- "standard.error" ifelse(names(x$coefficients[1])=="(Intercept)", return(res[2:nrow(res),]),return(res)) }

#running logistic regression on WIN for the 2016-17 season PrevWINLine <- glm(WIN ~ HOME+WINPCT+OWINPCT+ELIM+OELIM+CLINCH+OCLINCH, data=PrevSeason, family = binomial(link = "logit")) summary(PrevWINLine) #summary of results mfx(PrevWINLine) #marginal effect on the probability of winning

#running logistic regression on WIN for the 2017-18 season NewWINLine <- glm(WIN ~ HOME+WINPCT+OWINPCT+ELIM+OELIM+CLINCH+OCLINCH, data=NewSeason, family = binomial(link = "logit")) summary(NewWINLine) #summary of results mfx(NewWINLine) #marginal effect on the probability of winning

#running logistic regression on EXPWIN for the 2016-17 season PrevEXPWINLine <- glm(EXPWIN ~ HOME+WINPCT+OWINPCT+ELIM+OELIM+CLINCH+OCLINCH, data=PrevSeason, family = binomial(link = "logit")) summary(PrevEXPWINLine) #summary of results mfx(PrevEXPWINLine) #marginal effect on the probability of winning

#running logistic regression on EXPWIN for the 2017-18 season NewEXPWINLine <- glm(EXPWIN ~ HOME+WINPCT+OWINPCT+ELIM+OELIM+CLINCH+OCLINCH, data=NewSeason, family = binomial(link = "logit")) summary(NewEXPWINLine) #summary of results mfx(NewEXPWINLine) #marginal effect on the probability of winning

30