The Importance of Team Fit for NBA Rookies’ Career Earnings

Joseph Kuehn∗ and Filippo Rebessi†

May 28, 2021

Abstract

Workers entering the labor market often face a trade off between job matches that maximizes their

short run and long run compensation. This trade off is influenced by peers who may enhance or diminish

the worker’s productivity, and thus affecting their future salary. We study this question for rookies in the

National Basketball Association (NBA). We find that for rookies drafted between 2011 and 2017, playing

with teammates that facilitated them getting 1 additional point per 100 possessions was predicted to

increase the value of their second contract by between 9.9% - 23.6%. This implies that being drafted by

the team that provides the ‘best fit’ is an important determinant of a rookie’s future earnings.

1 Introduction

Workers searching for jobs early in their career often consider not only the salary the job is offering, but also how taking that job will affect their future earnings. Initial job placements often provide a platform for workers to showcase their skills and abilities. Thus, workers may face a trade off between taking the job with the highest salary and the one offering them the “best fit” to enhance their resume for future job opportunities.

This is especially important in work settings where intrinsic talent is noisily observed and complemen- tarities between coworkers affect individual productivity. If workers are paid according to their individual productivity, and coworkers can influence it, then these complementarities can impact an individual’s lifetime earnings. Working with peers that enhance a worker’s productivity can lead to higher subsequent wages, while working with colleagues that reduce it will depress future earnings. This is particularly important for workers early in their career since there is more uncertainty about their underlying productivity.

In this paper, we examine the importance of these complementerities for early career employees by studying the impact of “job fit” on future earnings of rookies in the National Basketball Association (NBA).

∗Department of Economics, California State University, East Bay. Email: [email protected] †Department of Economics, California State University, East Bay. Email: fi[email protected]

1 Rookies have very little choice on which team they initially play on, as initial matches are determined by a draft. In the draft, teams select players with whom they have the exclusive right to contract for a period of 4 years. Complementarities between coworkers are potentially crucial in this setting, since basketball is a team sport where productivity depends heavily on the joint production of teammates.

We first develop a simple model of compensation and player talent. In the model, the talent of a rookie player isn’t directly observed. The player’s performance provides a signal of their underlying talent, where the strength of that signal depends on teammates. A direct result of this model is that for players with high intrinsic talent, future salaries are increasing in the precision of the signal, while for players with low intrinsic talent, their future salaries are decreasing in signal precision. This implies that playing with teammates that accentuate (or hide) a rookie’s talent can affect that rookie’s future earnings.

To quantitatively assess the impact teammates have on rookie future earnings, we look at NBA rookies drafted in the first round between 2011 and 2017. Using data on salaries and player productivity, we look at how a rookie’s early productivity translates into future career earnings, and how their teammates impact that.

We first study how a rookie player’s productivity is valued in the market by testing how individual offensive and defensive value affects the second contract an NBA player signs. We find that offensive production has a significant impact, as players that generate 1 additional expected point per 100 possessions are expected to sign a second contract worth 13.3% - 13.7% more in total. We find no statistically significant effect for defensive production.

We then look at the effect that teammates’ productivity has on a rookie’s second contract. We find that being on a team with more productive teammates leads to a higher likelihood of signing a second contract and a higher predicted compensation. However, more productive teammates also decrease the returns to individual productivity. We take a deeper look at the latter finding by breaking down productivity into a component that is intrinsic to the player and what is due to a player’s teammates. We then find that while a rookie’s own intrinsic productivity is the most important determinant of the value of their second contract, the effect teammates have on an rookie’s individual productivity does play a significant role. Teammates that increase a rookie’s offensive productivity by 1 expected point per 100 possessions, are predicted to increase the value of that rookie’s second contract by between 9.9% - 23.6%.

Finally, we look at how important team fit was for the first 10 players drafted in the 2015 NBA draft.

Using back-of-the-envelope calculations, we estimate that if Karl-Anthony Towns had been drafted by any of the other teams drafting in the top 10, the predicted total salary in his second contract would be 27.55% -

54.38% lower. On the hand, if had been drafted first by the , instead of by the , his increase in offensive productivity would have translated into a 49.91% increase in total second contract salary.

2 1.1 Related Literature

The prior literature on the importance of a worker’s first job has mainly focused on either the worker learning about their skills (Antonovics and Golan (2012), Papageorgiou (2014)), or the firm learning about the worker’s productivity (Jovanovic (1984), Moscarini (2005)), which is more closely related to our work.

Rubinstein and Weiss (2006) studies how initial job placement ties to early career earnings growth, while

Topel and Ward (1992) and Wachter and Bender (2006) analyze its effect on worker mobility, which is especially impacted if workers enter the labor force during a recession (Oreopoulos, Wachter, and Heisz

(2012), Kahn (2010)).

There is also a large literature on the effects that peers have on earnings. This work has mainly focused on how coworkers affect a worker’s productivity (Mas and Moretti (2009), Nefke (2017)). The existence of peer effects in the NBA and other sports settings, has long been recognized. Arcidiacono, Kinsler, and Price

(2017) and Kuehn (2017) both find that teammate productivity has little effect on future salary, but both ignore the impact that teammates have on individual productivity. Kendall (2003) looks specifically at this interaction and finds that more productive teammates (measured as points per field goal attempt) lead to increases in own productivity. However, he does not look at the impact this has on player salary. Idson and

Kahane (2000) take into account the interaction between teammate and player productivity in the setting of professional hockey, and find that teammates have both a direct and indirect effect on future salary. Idson and Kahane (2004) extend this study to the NBA and again find that the interaction effect is important, but smaller than in hockey. This paper extends that work by using play-by-play data so that we can look at substitutions between players within a game rather than relying on switches of players across teams in different years. The data also allows us to breakdown individual production into what would be observed if the player was on any team, and what is due specifically to the team he is currently playing on.

Looking instead at baseball, Gould and Winter (2009) find that batters will increase their effort when playing with other high performing batters, but will decrease their effort if playing with high quality pitchers.

This suggests that peer effects in sports are due to interactions in the production function, not peer effects, which is consistent with the results of this paper. Other papers have also looked at the effect worker complementarities have on pay in a wide variety of fields from manufacturing (Park (2019)) to the film industry (Rossman, Esparaza, and Bonacich (2010)), and also more generally (Battu, Belfield, and Sloane

(2003), Cornelissen, Dustmann, and Schonberg (2017)).

This paper combines the literature on coworker effects with the aforementioned literature on the impor- tance of a worker’s first job match. We specifically look at how a worker’s peers in their first job can affect their future earnings. This contributes to our understanding of the importance early career decisions have

3 on future wages.

2 Background and Data

2.1 Rookie Contracts

Players entering the NBA are first matched to teams using a two round draft held each offseason. For each

round, teams are ordered in ascending order based on their record in the previous season.1 Once a team drafts a player, they have the exclusive right to sign that player. They can also trade that right to another team.

A first round draft pick’s first contract is heavily regulated by the rookie salary scale. In terms of length, each rookie contract is for 2 years, with separate team options for a third and fourth year. Both the third and fourth year options must be exercised one year in advance. The per-year salary is then closely tied to a scale that depends on the league salary cap and the position the player was drafted in. For example, for the 2019 NBA draft, the rookie scale specified that the first year salary for the first pick was $8,131,200, the

first year salary for the second pick was $7,275,200, and so on, in decreasing amounts. The actual contract that a player signs must have a first year salary that is between 80% and 120% of that specified value. A scale is also given for the player’s second year salary and the player options.

After their 4-year rookie deal expires, players become restricted free agents. This means that they can receive offers from other teams, but their current team has the ability to match these offers. Rookies can also sign a contract extension in the off-season before their fourth year, preventing them from becoming a restricted free agent.

In this paper, we look at all NBA players drafted in the first round between 2011 and 2017. For each player, we gather details from RealGM.com about whether their third and fourth year options were picked up, and the contract details of their first contract following the rookie contract. For this second contract we get the years, total salary, and whether or not it was a rookie extension signed in the summer before the player’s fourth year. Summary statistics for these second contract features are in Table 1.

We also gather player position data from BasketballReference.com. They have data on what percent of possessions each player played at a particular position (, , small forward, power forward, or ). We take a player’s position as the one they played the most, and control for position when regressing second contract value on player and teammate productivity.

1The first 3 picks of the first round are allocated by a weighted lottery among teams that did not qualify for the playoffs in the previous season, but all remaining draft positions are based on previous season record.

4 Table 1: Summary Statistics for NBA Rookies (2011-2017)

Number of Standard Mean Median Min Max Observations Deviation Year 3 Option 205 0.927 1.000 0.261 0.000 1.000 Year 4 Option 180 0.739 1.000 0.440 0.000 1.000 Second Contract Ind 158 0.671 1.000 0.471 0.000 1.000 Total Salary ($ Mil) 132 42.451 28.970 45.214 0.947 169.650 Salary Per Year ($ Mil) 132 11.137 10.125 9.151 0.605 33.930 Contract Years 132 2.932 3.000 1.426 1.000 5.000 Data comes from Real GM (http://basketball.realgm.com).

2.2 Player Productivity

We measure player productivity using play-by-play data from NBA.com, which provides us with data on each play from all NBA games from 2014 to 2019 (for 5 seasons of data). We then measure player productivity using the methodology developed by Kuehn (2017). Kuehn (2017)’s evaluation technique allows us to separate an individual player’s contribution to his team from that of his teammates. We can then use this information to learn how teammates affect a rookie’s second contract through the effect they have on the rookie’s performance.

The approach in Kuehn (2017) breaks down NBA possessions into a series of actions, and estimates the relationship between these actions, particularly how substitutable or complementary different actions in an

NBA game are. An NBA possession is modeled as a series of events taken by the players on the court, such as shooting from different locations, turning the ball over, and getting rebounds. The probabilities with which each of these events occurs determines the expected points on a possession, and a player’s ability to affect these probabilities determines his value. The probabilities that each player commits an event are based on each offensive player’s propensity to commit those actions, their teammates’ propensities to commit those actions and the substitutability between those actions, and the defensive players’ abilities to affect the probabilities of those actions taking place. Player propensities to commit certain actions are identified by the observed actions a player takes on the court compared to his four teammates.2 The relationship between different actions is then identified from how the observed probabilities of the different actions covary across all lineups and teams. The value a player brings to a team is then lineup-dependent, and depends on their propensity to commit certain actions, as well as their teammates, and their interaction. We thus get team-specific measures of player productivity that we can then use to see how much teammates in a lineup

2This is what separates Kuehn (2017) from the typical plus/minus evaluation technique that evaluates player value based on differences in team performance with substitutions between 2 players. To further identify how much of that player’s plus/minus is due to the individual’s skills and tendencies, and how much is instead a result of interacting with the 4 teammates, one needs to also see how the actions of teammates who are on the court at the same time vary.

5 influence a player’s own productivity and thus their future salary.

In the analysis below we look at several different measures of player and teammate productivity. The first is simply a measure of the value a player brings to his team in terms of expected points per 100 possessions.

For each lineup a rookie plays in, we define his offensive value as the expected points per 100 possessions he brings to his team through the predicted actions he takes in that lineup. This value depends on the rest of the lineup in various ways. For example, if his teammates are better offensive rebounders, then the negative impact of missing a shot is lower. Also, if the player is good at getting rebounds himself, this is more valuable if his teammates are better at making use of the extra possession gained from the rebound.

Offensive value also depends on the opponents on defense, and here we assume that the team is playing a lineup of 5 opposing “replacement players.” A replacement player is defined as an average player that is not in the top 250 in terms of possessions for that season.

We also measure a rookie’s defensive value as the negative of the expected points per 100 possession that a replacement player is predicted to get (playing on a team with 4 other replacement players), when playing against the rookie and his 4 teammates. We don’t allow for teammates to affect each other’s defensive skills because the play-by-play data is not detailed enough to appropriate defensive outcomes to the proper players. Thus, the defensive value measured here is very similar to the typical defense plus/minus measure.

Total player value is then offensive value plus defensive value.

Player values are calculated for each lineup the rookie is in. We then aggregate over all the lineups the player is in over the course of a year. We weight each lineup by the number of possessions that lineup had for the year, and take the weighted average to get a per-possession measure of player productivity for a given year. In the estimation below we look both at the player’s productivity in the year before he signs a second contract, and his average productivity in all the years prior to signing the second contract. Summary statistics for the 3 rookie player value measures are in the first 3 rows of Table 2.

We also calculate the same offensive value and defensive value for the player’s 4 teammates. This is calculated in the same way, and is specific to playing with the rookie player. As before, we aggregate over all lineups the rookie plays in for a year. Summary statistics for the teammate value measure are in the 4th row of Table 2.

Finally, we breakdown these player productivity measures into that which is affected by who the player is playing with and that which is intrinsic to the player. To do this we breakdown a lineup’s productivity into

4 components: (1) the rookie player’s productivity irrespective of his teammates (i.e. the value he would have on a team with 4 replacement players), (2) his 4 teammates’ productivity irrespective of who their 5th teammate is (i.e. the 4 players productivity if they played with a replacement player rather than the rookie),

(3) the impact that the 4 teammates have on the rookie player’s productivity (i.e. the additional value the

6 player brings by playing with his 4 teammates rather than 4 replacement players), and (4) the impact the

rookie player has on his 4 teammates’ productivity (i.e. the additional value the 4 teammates provide when

playing with the rookie rather than the replacement player). We do this only for offensive value since with

defensive value it is difficult to attribute defensive productivity to individual players using the play-by-play

data. Summary statistics for these 4 measures are provided in the last 4 rows of Table 2.

Table 2: Summary Statistics for Player Evaluation Measures

Number of Standard Mean Median Min Max Observations Deviation Own Offensive Value 607 16.588 16.490 3.821 2.522 31.350 Own Defensive Value 607 -15.741 -16.636 2.041 -19.732 -10.670 Own Value 607 0.847 0.739 4.253 -17.083 14.561 Teammate Value 607 6.991 5.699 6.648 -14.051 29.071 Own Value on Rep. Team (Off) 607 17.793 17.676 4.739 2.625 37.334 Teammate Effect on Own Value (Off) 607 -1.204 -0.868 1.806 -10.400 5.216 Teammate Value w/ Rep. Player (Off) 607 70.574 70.823 5.151 49.717 84.333 Rookie Effect on Teammate Value (Off) 607 -0.619 -0.563 2.830 -14.102 7.627 Measures are calculated using the technique of Kuehn (2017), and play-by-play data from the 2014-2019 NBA seasons. Own offensive value is a player’s expected offensive contribution to his observed team in terms of points per 100 possessions. Own defensive value is defined similarly but for defensive contribution, and own value is a combination of the two. Teammate value is the total contribution of a player’s 4 teammates to the team that also contains the player. Own value on a replacement team is the offensive contribution a player makes to a team of 4 “replacement players.” Teammate effect on own value is the additional own offensive value a player brings to a team with those 4 teammates rather than 4 “replacement players.” Teammate value with replacement player is the offensive contribution of the 4 teammates to a team where their fifth teammates is a “replacement player.” Rookie effect on teammate value is the additional offensive contribution the 4 teammates make to a team when their fifth teammate is the rookie rather than a “replacement player.”

3 Model

A rookie player (RP) is characterized by a level of intrinsic talent z ∈ {zh, zl}, with zh > zl. z cannot be directly observed by coaches and general managers (CGM), who have an intial belief σ(zh) of their intrinsic talent being zh. After being drafted, a RP joins a team, which gives them opportunities to display their talent during games. When CGM observe RP’s performances, which can be either good or bad for simplicity, they are not able to perfectly disentangle the importance of the RP’s intrinsic talent from the influence of their teammates, so performances constitute imperfect signals of talent. Let γ ∈ (0.5, 1) be the precision of the signal, and let g and b respectively denote good and bad performances. The probability of observing a

RP with z = zh having good performances is p(g|z = zh) = γ, while the same probability for a RP with z = zl is p(g|z = zl) = 1 − γ. Note that if the signal was perfectly informative, i.e. γ = 1, observing good

performances would reveal the RP’s talent since p(g|z = zh) = 1 and p(g|z = zl) = 0. With γ = 0.5 ,

7 good and bad performances are equally likely for RPs with different intrinsic talent, and the signal does not

provide any information to CGM.

For a given initial belief σ(zh) = σ, CGM’s beliefs over the RP’s intrinsic talent are updated in Bayesian fashion: σ0(σ|g) = σγ σγ+(1−σ)(1−γ) (3.1) 0 σ(1−γ) σ (σ|b) = σ(1−γ)+(1−σ)γ

We assume the first contract after the expiration of their Rookie deal depends on the expected level of talent of the RP. Let yi be the compensation assigned to players with z = zi, i ∈ {h, l}, with yh > yl. The expected compensation E[w(σ|zi)] offered to the RP is given by

0 0 0 0 E[w(σ|zh)] = γ [σ (σ|g)yh + (1 − σ (σ|g))yl] + (1 − γ)[σ (σ|b)yh + (1 − σ (σ|b))yl]

0 0 0 0 E[w(σ|zl)] = (1 − γ)[σ (σ|g)yh + (1 − σ (σ|g))yl] + γ [σ (σ|b)yh + (1 − σ (σ|b))yl]

We establish a straightforward result which will guide our empirical analysis: expected compensation is

increasing in signal precision γ for a RP with high intrinsic talent, and is decreasing in γ for low-talent RPs.

∂E[w(σ|zh)] ∂E[w(σ|zl)] Proposition 1. ∂γ > 0 and ∂γ < 0

∂E[w(σ|zh)] Proof. The expression for ∂γ can be rearranged as

n o σγ (2 − 2σ − γ + 2γσ) − σ(1−γ) (1 − 2σγ + γ) (y − y ) [σγ+(1−σ)(1−γ)]2 [σ(1−γ)+(1−σ)γ]2 h l

∂E[w(σ|zh)] By contradiction, suppose that ∂γ ≤ 0. This requires

γ σγ + (1 − σ)(1 − γ)2 1 − 2σγ + γ ≤ (3.2) (1 − γ) σ(1 − γ) + (1 − σ)γ 2 − 2σ − γ + 2γσ

2 h σγ+(1−σ)(1−γ) i 1−2σγ+γ γ Note that at σ = 1, σ(1−γ)+(1−σ)γ 2−2σ−γ+2γσ = 1−γ . If the right hand side of the inequality (RHS) is strictly increasing in σ, then for any σ < 1 the necessary

condition 3.2 is not met, contradicting the claim. After some tedious algebra manipulations, we obtain

∂ RHS = A (2 − 3σ(1 − σ)) ∂σ

2γ−1 σγ+(1−σ)(1−γ) where A = 2 2 > 0. Since min 2 − 3σ(1 − σ) = 1.25 > 0 , the right hand side 2−2σ−γ+2σγ [σ(1−γ)+(1−σ)γ] σ∈[0,1] γ is indeed stricly increasing in σ, and always less than 1−γ for any σ < 1, concluding the proof. A symmetric

∂E[w(σ|zl)] argument can be applied to prove ∂γ < 0.

8 An empirical implication of Proposition 1 is that we should observe that players with higher measurable indicators of talent should receive on average more lucrative contracts when they are drafted by teams that allow them to display it.

It is well recognized that the opportunity created by teams for new players depend on the level of talent of existing players. Being drafted by a team with highly talented players can reduce a RP’s playing time, and confine their performances to so-called “garbage time”3, which provides little information to CGM on their actual productivity. On the other hand, RPs surrounded by lower talent will have to play during more competitive games and will be given more opportunities to take shots and score points, which gives evaluators a more precise assessment of their talent. These are some examples of how peers can influence the precision of the signal received by CGM from observing RP’s performances, which in turn will affect the public belief of the RP’s talent level, and their second contract. In Section 4, we are looking to quantify the impact of the opportunity created by teammates on signal precision.

The methodology introduced by Kuehn (2017) allows us to identify the marginal value that players bring to a particular team lineup, both through his own individual contributions and his complementary contribution to teammates’ productivity. We use their estimates to build measures of individual RPs talent and of “team opportunity”. We combine them with salary information on RPs’ second contracts to estimate the relationship between the precision of the signal obtained from RPs’ performances and the opportunities offered by the team that drafts them.

4 Estimation

4.1 Rookie Value on Second Contract

Before assessing the role of teammates, we first look at how a rookie’s productivity to his team affects his second contract. We measure the value of the second contract in several ways. One is an indicator of whether the rookie received a second contract or not. We also look at the total salary received over the length of the contract, the average per-year salary, and the total number of years of the contract. We estimate how each of these measures of a player’s second contract are affected by the player’s value to his team. We also

3“Garbage time” refers to the end of games whose outcome has already been decided, with starters being pulled out of the competition to avoid injuries.

9 control for the player’s draft number and position. Together, we estimate the following regression model:

5 X Yj = β0 + β1PVj + β2P ickNumj + γkP osjk (4.1) k=1 where Yj is one of the 4 measures of j’s second contract, P ickNumj is j’s draft pick number, P osjk is an indicator for whether j plays position k, and PVj is j’s value to his team. We define player value using the technique discussed in Section 2.2. A player’s offensive value is the expected points per 100 possessions that player provides to the average lineup he plays on that year. A player’s defensive value is the expected points per 100 possessions he gives up on the average lineup he plays on that year. We look at this yearly measure for the rookie’s contract year, and also take an average across all the years the player is on his rookie contract. For the former, we define the contract year as either the third year or fourth year the player is in the league, depending on if they signed an extension after their third year. If the player does sign an extension after the third year, then the third year is designated as the contract year. If the player does not, then the fourth year is used to measure productivity in the contract year. To measure average productivity across all years on a rookie contract, we take the average value for a player across either the first 3 years in the league or first 4 years, again depending on whether the player signed an extension after their third year or not.

We then estimate the regression in equation (1). The results are in Table 3. The first 4 columns look only at the contract year, and the last 4 columns average productivity across all years. In each case, the 4 columns contain results using the following 4 measures of second contract value: an indicator for whether the player received a second contract, the second contract’s total dollar value, the per year value of the second contract, and the number of years of the second contract. Standard errors are in parenthesis below the coefficient estimates.

The results show that players that are more valuable to their team on offense are more likely to get their second contract, and that contract is more likely to be longer and carry more value. The coefficients on offensive value in the first columns imply that a player that gets 1 additional expected point per 100 possessions for his team on offense is 2.7 to 3.7 percentage points more likely to get a second contract.

The results in the other 3 columns imply that a player that garners 1 additional expected point per 100 possessions on offense is expected to get a total salary that is 13.3% - 13.7% higher, have a 9.8% - 9.9% higher per year salary, and get between 0.107 and 0.113 additional years added to the contract. Players that add defensive value do not see the same returns. While in all 8 specifications the coefficient on defensive value is positive (implying that players that reduce the number of expected points per possession of their opponent get better second contracts), in only one case is it statistically different from zero. This suggests that players

10 Table 3: Effect of Player Performance on Second Contract

Contract Year All Years 2nd Contract ln(Total ln(Salary Per Contract 2nd Contract ln(Total ln(Salary Per Contract Indicator Salary)($Mil) Year) ($Mil) Years Indicator Salary) ($Mil) Year) ($Mil) Years Offensive 0.027* 0.137* 0.099* 0.107* 0.037* 0.133* 0.098* 0.113* Value (0.010) (0.039) (0.027) (0.036) (0.011) (0.041) (0.029) (0.037)

Defensive 0.009 0.068 0.042 0.083 0.031 0.105 0.051 0.141* Value (0.018) (0.069) (0.048) (0.064) (0.020) (0.076) (0.054) (0.069)

Pick -0.005 -0.028 -0.023* -0.013 -0.011* -0.036 -0.029* -0.018 Number (0.004) (0.016) (0.011) (0.015) (0.004) (0.016) (0.011) (0.014)

Shooting -0.037 0.024 -0.021 0.150 -0.079 -0.036 -0.028 0.046 Guard (0.112) (0.442) (0.307) (0.411) (0.117) (0.427) (0.301) (0.384)

Small 0.057 0.575 0.475 0.263 0.060 0.662 0.547 0.320 Forward (0.108) (0.419) (0.291) (0.389) (0.116) (0.419) (0.295) (0.376)

Power -0.027 -0.302 0.002 -0.573 -0.099 -0.187 0.025 -0.355 Forward (0.112) (0.441) (0.306) (0.409) (0.114) (0.424) (0.299) (0.381)

Center 0.064 0.812 0.603* 0.563 0.086 0.831 0.619* 0.578 (0.110) (0.430) (0.298) (0.399) (0.118) (0.425) (0.299) (0.382) Obs 118 115 115 115 140 124 124 124 R2 0.105 0.215 0.225 0.176 0.206 0.230 0.237 0.200 Standard errors are given in parentheses below the coefficient estimates. Coefficients marked with a * are statistically significant at a 5% significance level. The first 4 columns measure player productivity during the player’s last year of their existing contract, and the second 4 columns measure player productivity as an average across all the years of the player’s previous contract. The first column in each set is based on results from a regression where an indicator for whether the player received a second contract is the dependent variable. The dependent variable in the second column is the natural logarithm of the total salary value of a player’s second contract. The dependent variable in the third column is the natural logarithm of the per year salary of a player’s second contract, and the dependent variable in the fourth column is the number of years of the player’s second contract.

on rookie contracts are rewarded for their offensive contributions, but not their defensive contributions.

4.2 Impact of Teammates

The above results show that rookie contract players that bring value to their team are rewarded in their

second contract, but how is the value impacted by the team they are on? The model in Section 3 showed

that the value of the second contract can be impacted by teammates based on the effect teammates have on

the precision of the signal a player’s performance generates and the intrinsic ability of the player.

We study this by including the productivity of a player’s teammates into the regression in (1). For both

the rookie player and teammates, we define productivity as the combination of offensive value and defensive

value to the average lineup the rookie plays in that year. We then look at how second contracts are impacted

by the player’s own value, his teammates’ values, and an interaction between the two:

5 X Yj = β0+β1OwnV aluej+β2T eammateV aluej+β3OwnV aluej∗T eammateV aluej+β4P ickNumj+ γkP osjk k=1 (4.2) where Yj is one of the same 4 measures of j’s second contract as above. As before, we look at both

11 productivity in the rookie’s contract year and average productivity across all years we observe the player on his rookie contract. The results are in Table 4. The columns contain the same specifications as in Table 3.

Table 4: Effect of Player and Teammate Performance on Second Contract

Contract Year All Years 2nd Contract ln(Total ln(Salary Per Contract 2nd Contract ln(Total ln(Salary Per Contract Indicator Salary)($Mil) Year) ($Mil) Years Indicator Salary) ($Mil) Year) ($Mil) Years Own Value 0.033* 0.164* 0.108* 0.151* 0.051* 0.152* 0.104* 0.145* (0.013) (0.050) (0.035) (0.047) (0.014) (0.051) (0.036) (0.046)

Teammate Value 0.002 0.029 0.014 0.033 0.015* 0.035 0.022 0.029 (0.007) (0.029) (0.020) (0.027) (0.008) (0.029) (0.021) (0.026)

Interaction -0.001 -0.006 -0.003 -0.007 -0.002 -0.004 -0.003 -0.004 (0.001) (0.005) (0.003) (0.004) (0.001) (0.004) (0.003) (0.004)

Pick -0.005 -0.027 -0.023* -0.011 -0.010* -0.034* -0.028* -0.015 Number (0.004) (0.016) (0.011) (0.015) (0.004) (0.016) (0.011) (0.014)

Shooting -0.030 0.067 0.014 0.166 -0.098 -0.055 -0.043 0.031 Guard (0.112) (0.441) (0.308) (0.406) (0.115) (0.427) (0.302) (0.385)

Small 0.066 0.589 0.481 0.285 0.033 0.608 0.509 0.288 Forward (0.109) (0.421) (0.294) (0.389) (0.115) (0.420) (0.297) (0.378)

Power -0.022 -0.282 0.007 -0.534 -0.089 -0.165 0.034 -0.319 Forward (0.112) (0.443) (0.309) (0.408) (0.113) (0.425) (0.300) (0.382)

Center 0.057 0.778 0.591 0.513 0.039 0.745 0.560 0.507 (0.110) (0.431) (0.301) (0.397) (0.118) (0.429) (0.304) (0.386) Obs 118 115 115 115 140 124 124 124 R2 0.110 0.222 0.224 0.195 0.236 0.240 0.242 0.210 Standard errors are given in parentheses below the coefficient estimates. Coefficients marked with a * are statistically significant at a 5% significance level. The first 4 columns measure player productivity during the player’s last year of their existing contract, and the second 4 columns measure player productivity as an average across all the years of the player’s previous contract. The first column in each set is based on results from a regression where an indicator for whether the player received a second contract is the dependent variable. The dependent variable in the second column is the natural logarithm of the total salary value of a player’s second contract. The dependent variable in the third column is the natural logarithm of the per year salary of a player’s second contract, and the dependent variable in the fourth column is the number of years of the player’s second contract.

The results in Table 4 suggest that teammates have a positive impact on a rookie player’s second contract, but the effect is smaller than the impact the player makes through his own productivity. The estimates imply that a player who plays with teammates that produce 1 additional point per 100 possessions (offense minus defense), is 0.2 to 1.5 percentage points more likely to get a second contact. Among those who do get a second contract, playing with teammates that produce an additional point per 100 possessions is expected to increase the total value of the contract by 2.9%-3.5%, increase the per year salary by 1.4%-2.2%, and increase the number of years by between 0.029-0.033. Only the result for a player’s second contract is statistically significant, but the coefficient is positive in all 8 specifications.

These results suggest that being drafted by a better team increases the value of a player’s second contract.

However, the interaction term in all 8 specifications is negative (but not statistically significant), implying that the returns to own productivity are decreasing in teammate productivity. This indicates that production

12 among teammates is substitutable, which makes sense in this setting where there is only one basketball to go around among 5 teammates. This suggests that playing with better teammates has two conflicting effects for a rookie player. For one, it directly increases the predicted value of their second contract. This is likely due to better teams being more willing to spend money. On the other hand, because production among teammates in basketball is substitutable, having more productive teammates also reduces the return to being more productive at the individual level. Together, these results imply that better players would want to play on less talented teams so they can showcase their skills, whereas less productive players would want to play on more talented teams where the productivity of teammates can boost the value of their second contract. This corroborates the findings of the theoretical model in Section 3.

4.3 Full Breakdown of Team Productivity

The negative sign on the interaction term is particularly interesting as it suggests that teammates don’t just impact a player’s future salary through their productivity, but also with their impact on the rookie’s productivity. We investigate this further by breaking down offensive player productivity into the component that is affected by who they are playing with, and the component that is intrinsic to the player. A lineup’s offensive productivity is broken down into: (1) the rookie player’s offensive value irrespective of his team- mates, (2) his 4 teammates’ offensive value irrespective of who their 5th teammate is, (3) the impact that the 4 teammates have on the rookie player’s offensive value, and (4) the impact the rookie player has on his

4 teammates’ offensive value. We can’t do the same for defensive value, since the play-by-play data doesn’t provide enough detail to identify individual contributions on defense. We run the same regressions as before of a rookie player’s second contract value on player productivity. The results are reported in Table 5, and the specifications in each column are the same as in Tables 3 and 4.

The results first show that the most important determinant of a player’s second contract is their own intrinsic ability. In all 8 specifications, the coefficient on own value on a replacement team is positive, and in

7 of 8 it is statistically significant. The effect that teammates have is broken down into two parts: the effect teammates have through their own productivity and the effect teammates have by affecting the productivity of the rookie player. The former effect is estimated to be mostly positive, but small in magnitude. The coefficient estimates imply that playing with teammates that are more productive by 1 expected point per

100 offensive possessions is predicted to increase the likelihood of a second contract by 0.7pp - 1.3pp, and increase the value of a second contract by 3.1% in terms of overall value and by between 2.7% - 3.8% in terms of yearly salary. The estimated coefficients on teammate value when using contract years as the dependent variable are actually negative in both cases. None of the estimated coefficients are statistically significant.

13 Table 5: Breakdown of Effect Player and Teammate Performance Have on Second Contract

Contract Year All Years 2nd Contract ln(Total ln(Salary Per Contract 2nd Contract ln(Total ln(Salary Per Contract Indicator Salary)($Mil) Year) ($Mil) Years Indicator Salary) ($Mil) Year) ($Mil) Years Own Value on 0.017 0.139* 0.092* 0.127* 0.031* 0.137* 0.097* 0.124* Replacement Team (0.011) (0.044) (0.031) (0.041) (0.014) (0.041) (0.035) (0.046)

Teammate Value with 0.007 0.031 0.027 -0.002 0.013 0.031 0.038 -0.025 Replacement Player (0.008) (0.032) (0.022) (0.030) (0.011) (0.041) (0.028) (0.037)

Teammate Effect on 0.029 0.236* 0.160* 0.186 -0.009 0.099 0.054 0.120 Own Value (0.028) (0.110) (0.076) (0.102) (0.042) (0.155) (0.108) (0.141)

Own Effect on -0.032 -0.037 -0.050 0.023 -0.013 -0.011 -0.010 0.005 Teammate Value (0.017) (0.067) (0.047) (0.063) (0.022) (0.085) (0.060) (0.078)

Pick -0.004 -0.27 -0.022 -0.015 -0.009 -0.033 -0.025* -0.020 Number (0.004) (0.016) (0.011) (0.015) (0.004) (0.017) (0.012) (0.015)

Shooting -0.040 -0.013 -0.045 0.119 -0.045 0.034 0.046 0.039 Guard (0.111) (0.445) (0.307) (0.415) (0.118) (0.438) (0.305) (0.399)

Small 0.051 0.544 0.448 0.266 0.084 0.670 0.548 0.341 Forward (0.107) (0.424) (0.293) (0.396) (0.117) (0.430) (0.299) (0.391)

Power -0.013 -0.324 -0.005 -0.602 -0.080 -0.152 0.067 -0.369 Forward (0.111) (0.446) (0.308) (0.416) (0.115) (0.434) (0.302) (0.395)

Center 0.092 0.846 0.646* 0.549 0.074 0.810 0.593 0.583 (0.111) (0.440) (0.304) (0.411) (0.119) (0.435) (0.303) (0.396) Obs 118 115 115 115 140 124 124 124 R2 0.142 0.219 0.238 0.172 0.222 0.224 0.250 0.175 Standard errors are given in parentheses below the coefficient estimates. Coefficients marked with a * are statistically significant at a 5% significance level. The first 4 columns measure player productivity during the player’s last year of their existing contract, and the second 4 columns measure player productivity as an average across all the years of the player’s previous contract. The first column in each set is based on results from a regression where an indicator for whether the player received a second contract is the dependent variable. The dependent variable in the second column is the natural logarithm of the total salary value of a player’s second contract. The dependent variable in the third column is the natural logarithm of the per year salary of a player’s second contract, and the dependent variable in the fourth column is the number of years of the player’s second contract. As for the independent variables, own value on a replacement team is the offensive contribution a player makes to a team of 4 “replacement players.” Teammate value with replacement player is the offensive contribution of the 4 teammates to a team where their fifth teammates is a “replacement player.” Teammate effect on own value is the additional own offensive value a player brings to a team with those 4 teammates rather than 4 “replacement players.” Own effect on teammate value is the additional offensive contribution the 4 teammates make to a team when their fifth teammate is the player of interest rather than a “replacement player.”

The effect that teammates have through their impact on a rookie’s own production is also generally positive, and in almost all cases is larger than the impact of teammates’ own productivities. In 2 cases, it is also statistically different from zero. The coefficient estimates imply that playing with teammates that increase a rookie’s offensive productivity by 1 expected point per 100 possessions, is predicted to increase the value of the rookie’s second contract by between 9.9% - 23.6%, and increase the per year salary by between 5.4% - 16.0%. This shows that the biggest impact that teammates have on a rookie’s next contract is through the impact they have on that player’s productivity. The magnitude of the coefficients implies that playing with teammates that enhance your productivity can be considerably beneficial to a rookie player looking for a large second contract. This again aligns with the results of the model in Section 3. Playing with teammates that enhance a rookie’s individual productivity, either by accentuating their abilities for a

14 high productivity player or hiding their abilities for a low productivity player, can have a meaningful impact on the player’s future salary.

4.4 Counterfactual 2015 Draft

The above results imply that which team a player was drafted onto can have a significant impact on their future contracts. To get a rough measure of how large of an impact that is, we look at how rookie contract players’ productivities would change if they were instead drafted by a different team. Particularly, we look at the first 10 players drafted in 2015, and measure their productivity in the 2018-2019 season if they instead were drafted by each of the other teams in the top 10.4 Then using the estimated coefficient in column (2) of Table 3, we calculate how that change in productivity in a contract year is expected to affect the total salary of the player’s second contract.

The results are in Figure 4.1. Each cell displays the change in productivity and predicted change in salary if the row player were instead drafted by the column player’s team. The top number is the change in expected offensive points per 100 possessions, and the bottom number is the predicted change in total salary based on the top number and the coefficient on offensive value in column (2) of Table 3.

Figure 4.1: Change in Pay for Top 10 2015 NBA Draft Picks

The change in the row player’s own productivity in 2018-2019 (in expected offensive points per 100 possessions) if they instead were drafted by the column player’s team is the top number in each cell. The bottom number is the implied percent change in total salary in the second contract based on the coefficient in column (2) of Table 3.

4We exclude Kristaps Porzingis because he did not play in the 2018-2019, and so there were no measures of his own productivity that season, or counterfactual lineups to put the other players into.

15 The table shows that Karl-Anthony Towns had a substantial advantage being drafted by the Minnesota

Timberwolves compared to any of the other 8 teams. If he was drafted by another team in the top 10, this is predicted to have lowered his productivity by between 2.01 to 3.97 points per 100 possessions, which translates into a 27.55% to 54.38% decrease in predicted salary in the second contract. Likewise, other players would have benefited greatly if they had instead been drafted first by the Timberwolves. The biggest beneficiary would have been Jahlil Okafor, who was instead drafted third by the Philadelphia 76ers. If

Okafor had instead played in the same lineups that Towns did in 2018-2019, his offensive productivity would have gone up by 3.35 expected points per offensive possession. This would have translated into a 49.91% predicted increase in total second contract salary.

The reason playing on the Timberwolves is helpful to rookies in 2018-2019, is that their most prominent teammate there, , has a propensity to shoot mid-range shots and three-pointers rather than shoot inside. He is also a bad shooter, and doesn’t turn the ball over. All of these increase a rookie teammate’s own value. Playing with a teammate that doesn’t shoot inside very often, helps space the floor and provides more opportunities for the rookie to shoot and score inside, which is likely the easiest way to add productivity to a team. Also, because Wiggins is a bad shooter, there are a lot of opportunities to get rebounds, which are valuable in that they add another possession (which is especially valuable for most

Timberwolves lineups that are above average offensively). Finally, playing with players that don’t turn the ball over is also valuable, since it provides the rookie more opportunities to provide value themselves.

While the effects of “fit” appear large here, they don’t necessarily outweigh the differences in initial salaries between the draft pick positions. For example, the player that would have benefited the most from dropping in the draft is D’Angelo Russell. If Russell had instead been drafted 10th to the , his expected total second contract salary would increase by 20.18%. This is a roughly $8.6 million increase for the average second contract salary of $42.45 million. However, the rookie contract scale for the 2015 NBA draft specified that a player drafted second would receive $19.24 million over the 4-year length of their rookie contract, while a player drafted 10th would receive $9.36 million in total on the rookie contract. In that case the difference in salary with the rookie contract made it worthwhile for Russell to be drafted higher at second, even though it was expected to cost him in his second contract.

For other players, though, it would have been beneficial to fall. For example, Willie Cauley-Stein would have been a better fit for the at position 6 than the at 5. Figure 1 predicts that being drafted by the Nuggets would have increased his salary by 11.4%, or $4.8 million on the average second contract. Given that the difference in total rookie contract salary between position 5 and 6 was only

$1.3 million, this fall would have been beneficial for Cauley-Stein.

16 5 Conclusion

This paper looks at how the team a player is drafted onto affects his future career earnings in the NBA. We

first look at how individual productivity affects a rookie’s second contract, and then how that is affected by his teammates’ productivities. We find that being on a team with more productive teammates is expected to increase future earnings, but that teammates also affect individual productivity in a significant way. For the

2015 NBA draft, we find that being drafted onto the team that is the most conducive to showcasing rookie production is predicted to increase the total salary of the second contract by between 22.48% to 45.91% for the first 10 players drafted.

These results suggest that being drafted onto a team that increases a worker’s own productivity is in many cases as important as the initial draft position in determining a player’s career earnings. This is important for players to keep in mind during the draft process where the goal should not necessarily be to be drafted as high as possible (which is rewarded with a higher rookie contract value), but also to be drafted by a team that enhances their productivity for future returns. While the results in Section 3.4 show there is heterogeneity in the trade-off between current contract value and the impact of team fit on future earnings, there are cases where a player is better off being drafted at a lower position onto a team for which they will be more productive and thus earn a higher salary in their second contract.

This result can also extend to other work environments where there is uncertainty about how productive a worker will be, and where complementarities between coworkers play a large role in revealing that produc- tivity. Quantifying the trade-off that workers face early in their career between a higher initial salary and working in a setting that best showcases their talent and abilities, is an important facet to understanding how workers make early career decisions and the benefits and costs of those decisions. Given the increas- ing prevalence of job switching among early professionals, extending this work to other occupations and industries appears to be a fruitful avenue for future research.

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