1 Player Compensation and Team Success in the National Hockey

Player Compensation and Team Success in the National Hockey League

Stephanie Hao

March 11, 2016

Econ 191A-B

Prof. Ross Starr

Abstract:

This paper examines the relationship between inequalities in player compensation in the NHL and two measures of team performance: season winning percentage and team revenue. I find that, for seasons before the salary cap, taking a “superstar” approach to player compensation for centers, left wingers, and defensemen is insignificantly related to winning percentage, while compensating right wingers more equally may yield an increase in wins. Taking a superstar approach to signing centers and right wingers and a more egalitarian approach to signing left wingers may yield an increase in team revenue. For seasons after the implementation of the salary cap, there is an insignificant relationship between inequalities in player compensation and season winning percentage for all forward positions, while allocating cap space more equally among defensemen is related to higher winning percentages. Finally, higher inequality in compensation for right wingers is associated with increases in revenue after the salary cap.

I. Introduction and Literature Review

Before the introduction of a salary cap, wealthy franchises in the National Hockey

League had the resources to offer the best players incredibly lucrative contracts. Thus, teams such as the Toronto Maple Leafs, Montreal Canadiens, and Edmonton Oilers were able to dominate the NHL for years at a time. However, NHL franchise owners sought to restrict growing player salaries; in doing so, they hoped to increase the NHL’s popularity among wider audiences by promoting parity within the league. The 1994-1995 lockout, which resulted in a 48-game season, attempted to address the issue of player salaries, but ended without the adoption of a salary cap or a luxury tax. Finally, after a full-season lockout from 2004-2005, the NHL collective bargaining agreement (CBA) implemented a hard salary cap in 2005 that limited the total amount of money a team can spend to pay its players each season.

The salary cap ceiling is set as a percentage of previous years’ revenues, while the cap floor is set at $16 million less than the cap ceiling. Teams cannot spend more than the cap ceiling or less than the cap floor and may spend at most 20% of the cap ceiling on a single player. A player’s cap hit is the average annual value of his contract—that is, the total dollar amount of his contract, including signing and performance bonuses, divided by the number of years on the contract. The NHL and the NHLPA renegotiated the CBA in 2013 after a lockout during the 2012-2013 season, which resulted in a lower cap ceiling and limitations on the variation of a player’s salary within a contract.

A team’s general manager must now find a way to allocate a limited amount of resources among players under the restrictions of the salary cap. Some franchises use a

“superstar” approach in compensating players; that is, they spend a large portion of their

2 cap space on a few stars and must fill in remaining positions with lower-paid players.

This approach may lead to a team with large disparities in both player compensation and player performance. Other franchises may instead fill their roster with more evenly compensated, mid-tier players, resulting in a team with relatively little disparity. Using panel data from the 1994-1995 season to the 2014-2015 season, I would like to determine the relationship between player compensation allocation for each position (center, left wing, right wing, and defense) and two measures of success: team performance and team revenue.

This paper proceeds as follows. In the remainder of this section, I present a brief introduction to the structure of an NHL team and a review of current theoretical and empirical literature. I present two models in Part II and the data I use in Part III. Part IV contains my estimation results, and I conclude in Part V.

a. Structure of Teams in the NHL

In regular five-on-five play in the NHL, there are six players on the ice at a time: one goaltender, two defensemen, and one line of three forwards. The role of a forward is primarily to score goals, while the role of a defenseman is primarily to keep the opposing team from scoring. However, due to the speed of the game, many forwards are defensively responsible and many defensemen can produce offensively; thus, unlike in baseball and football, it is difficult to measure offensive and defensive performance separately. An NHL team’s roster usually consists of twenty players: two goalies, three pairs of defensemen, and four lines of forwards with three forwards (a center, a left winger, and a right winger) in each line, although some teams may substitute a forward with a seventh defenseman. The defensive pairs and offensive lines play in shifts of

3 around 45 seconds each, while a goalie usually stays on the ice for the duration of a 60- minute game. Additionally, because hockey is a full contact sport, teams may use

“enforcers” or “goons,” usually on the fourth line, to retaliate against hits on more skilled players by the opposing team. Although these enforcers may not produce as well offensively, they deliver hits or start fights and may be a significant appeal for spectators.

Thus, a player’s salary may depend not only on the number of points scored but also on the number of hits delivered or penalty minutes taken.

b. Theoretical Literature

The effects of wage dispersion have been explored by Lazear and Rosen (1981),

Akerloff and Yellen (1990), and Levine (1991). Lazear and Rosen introduce a rank-order tournament in which compensation depends on a worker’s ordinal rank, rather than production, when compared to his peers. In this tournament, the “winner” with the highest ordinal rank receives a payment much higher than that of the “losers.” Thus, workers are incentivized to invest more effort into increasing their rank and consequently their payment, and as the difference between the payment of winners and losers increases, so too does this investment. However, investment comes at a cost to workers.

Firms must therefore find an optimal spread of payments that not only encourages workers to invest but also sets the workers’ cost of investment low enough to prevent them from seeking better opportunities elsewhere. In this light, it is possible to view the

National Hockey League as a tournament in which players compete with each other for recognition, cap space, and positions on the starting lineup and special teams. General managers may recognize this and offer the best-ranked players of a team much larger

4 contracts in order to increase each individual team member’s investment, thereby increasing the production of the team overall.

On the other hand, Akerlof, Yellen, and Levine argue that large differentials in salary may decrease team performance. According to Akerlof and Yellen’s fair wage- effort hypothesis, workers will invest effort into their work relative to their wage; thus, if workers are paid below what they perceive to be the “fair” wage, they will not produce as much as workers who are paid fairly. Introducing high salaries for “superstar” players in the NHL may therefore lead to feelings of antipathy among lesser-paid teammates, a reduction of effort by these lesser-paid players, and a lack of team cohesion.

Similarly, Levine argues that firms whose production depends on cooperation between workers should reduce the disparity between wages. He presents a model in which both cohesion and production among high-skilled workers and low-skilled workers are greater when wage differential is smaller. An increase in wage disparity will therefore negatively impact a firm’s performance. Levine acknowledges that it may be difficult to sustain high levels of cohesion between workers in firms with competitive environments, because “star” workers may leave in search of higher salaries. However, such movement is limited in the NHL because only players who are free agents may continuously seek higher pay.

c. Empirical Literature

Empirical studies of the relationship between player compensation and team performance have been primarily on data from the NFL, NBA, and MLB. Borghesi

(2008) estimates the effects of “justified” and “unjustified” player compensation in the

NFL on team performance using data from 1994 to 2004; he finds that while unjustified

5 dispersions in defensive base pay negatively impact defensive performance, spending more on defensive bonuses overall positively impacts performance. Both the Gini coefficient and the mean of unjustified base pay have a negative impact on offensive performance. Thus, Borghesi’s findings suggest that teams taking a “superstar” approach perform worse than teams with a more egalitarian pay structure.

Katayama and Nuch (2011), using not only season-level but also game-level data from the 2002 to 2006 NBA seasons, measure salary inequality three ways: the

Herfindahl-Hirschman Index (HHI), the Gini coefficient, and a coefficient of variation adjusted for number of minutes played by each player per game. They regress these measures on team performance, proxied by a ratio of the points scored by the player’s team to the points scored by the opposing team, and find that salary inequality has no significant impact on team performance on the game- and the season-level for any of the three measures used. Thus, Katayama and Nuch find no evidence in favor of either the rank-order tournament theory proposed by Lazear or the fair wage-effort hypothesis proposed by Akerlof and Yellen. However, they do find that the coefficients for measures of salary inequality were negative, indicating that they could be significant when estimated using a larger set of data.

Annala and Winfree (2011) examine the effect of salary distribution on team performance in Major League Baseball. Using data from 1985 to 2004, they find that the

Gini coefficient is negatively and significantly related to performance, measured by season winning percentage, for both a pooled regression and a fixed effects model.

Similarly, Depken (2000), using data from 1980 to 1998, estimates a fixed effects model and a random effects model and finds that the HHI has a negative and significant impact

6 on season winning percentage in both cases. Both studies also conclude that a higher total salary will result in better team performance. However, MLB is unique amongst major

North American sports leagues in that it uses a luxury tax instead of a salary cap to maintain competitiveness between teams; thus, the lack of a salary cap may result in a higher degree of salary inequality among professional baseball players when compared to hockey players.

Empirical studies on the relationship between wage disparity and team performance in the NHL have been conducted by Sommers (1998), Marchand et al.

(2006), Frick et al. (2003), and Stefanec (2012). Sommers, using data from the 1996-

1997 NHL season, calculates Gini coefficients for the 26 teams that then comprised the league. He then uses ordinary least squares to regress each team’s Gini coefficient and average salary on its season-ending points total (in which teams receive 2 points for a win, 1 point for an overtime loss, and 0 points for a regulation loss). Sommers finds that a team’s average salary has a positive and significant relationship with its SEPT, while the

Gini coefficient has a negative but insignificant relationship; thus, inequalities in compensation have little effect on SEPT.

Marchand et al. use two different approaches to explore the relationship between salary dispersion and team performance over 4 seasons in the NHL; in each approach, they distinguish between the “star effect”—describing the positive effect of highly-paid superstar players who cause their teammates to perform better—and the “journeyman effect”—describing the negative effect of players who feel resentment because they are not paid the median salary and thus perform worse. Marchand et al., using OLS, first regress income inequality, represented by the Gini coefficient, on team performance

7 during the season, represented by SEPT, and find a significant positive relationship.

Marchand et al. also find that a larger salary distribution positively and significantly affects individualistic behavior (proxied by the spread of goals scored) but has no statistically significant effect on cooperative behavior (proxied by the spread of assists made). In all cases, the star effect overrides the journeyman effect, indicating that teams in the NHL perform better when income is distributed unequally.

Conversely, Frick et al. compare the NHL, NFL, NBA, and MLB and discover that, while the relationship between salary dispersion and the season winning percentage is positive in the NBA and negative in MLB, salary dispersion had no impact on performance in the NHL and NFL.

In contrast to Sommers, Marchand et al., and Frick et al., Stefanec measures wage disparity by the HHI rather than the Gini coefficient. Stefanec represents performance by the team’s winning percentage and estimates a fixed effects model to find a statistically significant negative relationship between wage disparity and team performance.

Empirical research has also been conducted on determinants of salary in the NHL.

While most of this research has focused on potential discrimination against French-

Canadian players, Jones et al. (1999) and Vincent and Eastman (2009) also explore the relationship between salary and productivity in the NHL. Using player data from the

1989-1990 season, Jones et al. find that goals per game, assists per game, penalty minutes per game, All-Star game invitations, trophies won, veteran status, and draft ranking are positively and significantly related to player salary for both offensive and defensive positions, while nationality and linguistic ethnicity are not significant.

Vincent and Eastman use a quantile regression approach to examine these factors more closely. Because the returns of the on-ice actions of a lesser-paid fourth-line enforcer may be different from those of a highly-paid first-line star, Vincent and Eastman estimate separate equations at the 10th, 25th, 50th, 75th, and 90th quintiles of the earnings distribution for offensive and defensive positions and compare these results with those from the conditional mean estimated using OLS. Using data from the 2003-2004 season, they find that number of games played, selection to All-Star teams, draft ranking, and penalty minutes per game are positive and significant for both offensive and defensive players overall, while weight is negative and significant at the 10% level for offensive players. The results of the quantile regressions yield more specific results. Vincent and

Eastman find that experience, points per game, All-Star game invitations, and draft ranking positively and significantly impact salary for forwards at all quantiles, while height and plus-minus differential have no significant effect. Penalty minutes taken are significant and positive only for forwards whose salaries fall above the median. For defensemen, All-Star game selection is significant if players’ salaries are within the 10th and 25th quantiles, while draft ranking is not. Vincent and Eastman thus conclude that the determinants of a player’s salary may differ depending on the quantile in which his salary falls.

I conclude that the conflicting results presented by studies concerning the NHL— a negative relationship between wage disparity and team performance found by Sommers and Stefanec, a positive relationship found by Marchand, and no relationship found by

Frick—leave room for further analysis. None of these studies use data from after the

2005 salary cap, nor do they examine the relationship between wage disparity and team revenue.

II. Methodology

In this paper, I apply a model adapted from Borghesi (2008), who differentiates between “justified” and “unjustified” compensation in the NFL, to data from the NHL. I believe that perceived fairness in salary distribution may affect a team’s success more than actual fairness: because players likely recognize their own status within a team, lower-paid members may feel resentment towards higher-paid members if the difference in pay is seemingly unjustified. On the other hand, members who see higher-paid teammates contribute more in terms of productivity may not feel as slighted, yielding better team cohesion and performance.

I first calculate “justified,” or explainable, compensation for each player in each season based on observable factors such as experience, productivity, and physical characteristics; the difference between this justified compensation and a player’s actual compensation is then termed “unjustified.” To find justified player compensation, I regress the following model using OLS:

Cit = β0 + β1EXPit + β2STARit + β3BIOi + β4PRODit + error, (1) where, for player i in season t, C is a player’s salary for the 1994-1995 to 2003-2004 seasons and a player’s cap hit for the 2005-2006 to 2014-2015 seasons. EXPit is a vector that includes GPit (games played divided by the total number of games in the season),

TOIit (time on ice divided by the number of games played), Veteranit (a dummy variable that indicates 1 if the player’s age is at least 30 and 0 otherwise) and Rookieit (a dummy

10 variable indicating age of at most 24). I include these variables because older players may bring experience and leadership to teams, while rookie players are required to sign smaller entry-level contracts that may not be representative of their actual on-ice productivity. STARit is a vector that captures a player’s “star power”; it comprises

AllStarit (the accumulated number of All-Star game invitations a player has received),

Trophyit (the accumulated number of individual NHL trophies won), and Cupit (the accumulated number of Stanley Cups won). BIOi includes Heighti (height in inches),

Weighti (weight in pounds), Draft1i and Draft2i, (dummy variables indicating if a player was drafted in the first round or second round), Draft4i (a dummy variable indicating if a player was drafted in the fourth round or after), and Undraftedi (a dummy variable that indicates that a player was undrafted). PRODit is a productivity vector that consists of

Pointsit (points per game), Shotsit (shots per game), Hitsit (hits per game), and PIMit

(penalty minutes per game). I divide the productivity variables by the number of games the player participated each season in order to adjust for the lockout-shortened 1994-1995 and 2012-2013 seasons, during which teams played only 48 out of 84 games in 1994-

1995 and 48 out of 82 games in 2012-2013. The variables I use as determinants of justified compensation are based off the findings of Jones et al. (1999) and Vincent and

Eastman (2009).

Using the coefficients obtained as a result of regressing (1), I calculate the justified and unjustified compensation for each player in each season; I then find the standard deviation of unjustified compensation for each position (center, left wing, right wing, and defense) in each team in each season. I normalize the team standard deviations as follows:

σit = StdDevit / AvgStdDevt, (2) where, for team i in season t, StdDevit is the team’s standard deviation of unjustified compensation and AvgStdDevt is the league-wide standard deviation of unjustified compensation. Furthermore, I calculate the Gini coefficient for each position in each team each season.

Finally, to determine the relationship between player compensation and team success, I estimate the following model using OLS:

Sit = β0 + β1Posit + β2σit + β3Giniit + β4Ownerit + β5GMit + β6Coachit + error, (3) where, for team i in season t, Sit represents team success, measured either by season winning percentage or team revenue (normalized to adjust for changes in dollar value over time). Posit is the difference between the total amount of payroll a team spends on a specific position and the average total amount spent on that position across all teams, divided by the average total amount spent across all teams. Thus, teams with higher Pos values spend more overall on certain positions compared to other teams in the league.

The coefficient on Pos tells us if investing more cap space into certain positions yields better performance or higher revenue for the team. σit represents the normalized standard deviation of unjustified compensation as determined above. Teams with larger σ may suffer from a lack of cohesion between members because of higher variation in unjustified compensation. Giniit is the Gini coefficient; unlike σ, the Gini coefficient is not related to “justice” in compensation. Rather, it represents the payment structure of a team: teams using a “superstar” approach will have a Gini coefficient close to 1, while teams composed of players who are paid more uniformly will have a Gini close to 0.

Finally, Ownerit, GMit, and Coachit are dummy variables indicating 1 for a change in

12 owner, general manager, and head coach respectively and 0 otherwise. I include these variables because changes in major front office and coaching positions may affect both a team’s success and the strategy by which a team compensates its players. Using the coefficients of (3), I can determine the relationship between payroll inequality and team performance.

Lastly, the salary cap was established to promote competitiveness within the NHL and to prevent a small number of teams from embarking on dynastic runs. To determine the effectiveness of the cap, I also compare the Gini coefficient for season winning percentage before and after its implementation using the following:

GiniWinningPerct = β0 + β1Capt + error, (4) where GiniWinningPerct is the Gini coefficient for season winning percentage in season t and Capt is a dummy variable that indicates 1 if the salary cap is in place that season and

0 otherwise.

If the cap is effective, I expect to see a high Gini for winning percentage in the seasons between 1994 and 2004, and a low Gini in the seasons between 2005 and 2015; that is, winning percentages are becoming more equal across teams in the years following the establishment of the salary cap.

III. Data

In this paper, I explore the relationship of between player compensation and team success for twenty seasons using panel data from 1994-1995 to 2014-2015; I divide the data into ten seasons before the salary cap (1994-1995 to 2003-2004) and ten seasons after (2005-2006 to 2014-2015) and run separate regressions. I collect data on player

13 productivity (points per game, shots per game, hits per game, and penalty minutes per game), experience (games played and time on ice per game), “star power” (number of

All-Star invitations received, number of Stanley Cups won, and number of individual trophies won), and biographical information (height, weight, and draft round) for the player-season observations in regression (1) from NHL.com and ESPN.com. The NHL only began recording time on ice per game starting from the 1997-1998 season and hits per game starting from the 2002-2003 season; thus, I omit those variables from the regression for the years in which they were not recorded.

Player salary data from the pre-cap era (the 1994-1995 season through the 2003-

2004 season) is obtained from The Hockey News and USA Today via

HockeyZonePlus.com and WarOnIce.com. Player compensation data from the post-cap era (the 2005-2006 season through the 2014-2015 season) is found on CapFriendly.com,

GeneralFanager.com, and WarOnIce.com, which include information about players’ contracts and cap hits as well as their annual salary. Because these websites are not officially affiliated with the NHL, there is a probability that some of the data may be inaccurate; therefore, I supplement this data with sources such as news articles to check for inconsistencies. In the lockout-shortened 1994-1995 and 2012-2013 seasons, in which only 48 games were played, players were not paid their full salary; however, I use their full contracted salary in my regression because these are the amounts used by a team’s general manager to sign players and allocate cap space. I also exclude players who participated in fewer than ten games in a regular-length season and players who participated in fewer than five games in the shortened 1994-1995 and 2012-2013 seasons, because they are paid only a small percentage of their reported compensation.

I was unable to find player compensation data for 686 out of 14,054 total player- season observations; most of this missing data corresponds to lesser-known, low-paid players for seasons in the pre-cap era, when player salary information for non-“star” players was not widely reported or easily accessible online. I therefore use the minimum

NHL salary in these seasons for their compensation C; the minimum salaries, according to the 1995 NHL CBA, are as follows:

Minimum Season NHL Salary 1994-1995 $125,000 1995-1996 $125,000 1996-1997 $125,000 1997-1998 $125,000 1998-1999 $150,000 1999-2000 $150,000 2000-2001 $150,000 2001-2002 $165,000 2002-2003 $175,000 2003-2004 $180,000

Lastly, I collect season winning percentages from NHL.com and team revenue data from Forbes.com for the team-season observations in (3). However, while I have revenue data for all ten seasons in the post-cap era, I was only able to obtain three seasons (1999-2000, 2000-2001, and 2002-2003) of pre-cap revenue data. Additionally,

Forbes.com does not have access to NHL teams’ actual books; therefore, its revenue figures are only estimates based off news reports and previous transactions.

IV. Results

a. Forwards

Pre-Cap Results

I include the summary statistics for variables in regression (1) from pre-cap seasons (from 1994-1995 to 2003-2004) in Table 1. The average player salary before the salary cap was $1,362,099 for centers, $914,028.4 for left wingers, and $1,191,697 for right wingers. The average number of points per game scored by all forwards post-cap was 0.44; on average, centers scored the most, 0.49 points per game, while left wingers scored the least, 0.37 points per game. Right wingers attempted the most shots on average, while left wingers delivered the most hits and received the most penalty minutes. However, the standard deviation of hits and penalty minutes for both winger positions are higher than those for centers, indicating that the higher mean may be due to several wingers who perform primarily “enforcing” roles. The average height and weight for forwards was 72.73 inches and 202.68 pounds respectively; left wingers were both tallest and heaviest on average. The average height and weight for players in all forward positions were lower than for players in defense positions; this is expected because the role of a defenseman typically requires more physicality in order to deliver hits and block shots.

Table 3 lists the results of regression (1) for the 1994-1995 season. As stated before, I omit time on ice and hits per game from this regression due to the lack of data.

For centers, the coefficients of AllStar, Trophy, and Points are all positive and significant at the 1% level, while the coefficient of Cup is positive and significant at the 5% level and the coefficient of Weight is positive and significant at the 10% level. These results are all expected: players with more All-Star game invitations, trophies, Stanley Cups, and points are likely to be compensated more. For left wingers, the coefficient of Shots is positive and significant at the 1% level, and the coefficients of AllStar and Draft1 are

16 positive and significant at the 5% level. Again, these results are expected. The role of a winger is primarily goal scoring; thus, players who shoot more are likely to be paid more.

The coefficients of AllStar and Shots for right wingers are positive and significant at the

1% level, and the coefficient of Trophy is positive and significant at the 5% level.

Interestingly, the coefficient of Cup for right wingers is negative and significant at the

5% level; this result may have occurred because there might be lower-paid players on

Stanley Cup-winning teams who benefit from the efforts of their teammates.

Using the coefficients from regression (1), I calculate “justified” and “unjustified” compensation by position; the summary statistics are included in Table 5. The means of unjustified compensation for all three offensive positions from 1994-1995 to 2003-2004 are close to zero, suggesting that on average, players in the NHL after the salary cap are compensated equitably. Centers have both the maximum and minimum unjustified compensation of all four positions. The normalized standard deviations in Table 7

(denoted by σ) represent the ratio of a team’s standard deviation of unjustified compensation to the league average; of the forwards, right wingers have the highest average σ, while centers have the lowest average σ. This suggests that right wingers are compensated the most inequitably with respect to performance. The average Gini coefficient for centers from 1994-1995 to 2003-2004 is 0.39, while that for left wingers is

0.31 and that for right wingers is 0.36. The results therefore suggest that teams pay centers less equally than other forward positions but that this inequality may be relatively justified; that is, teams seem to take a “superstar” approach to signing centers more so than wingers. Left wingers have the lowest average Pos (the total amount a team spends on a certain position relative to the league average); however, the standard deviations of

Pos for both left and right wingers is higher than that of centers. Thus, the amount of payroll allocated to wingers varies more across teams than the amount of payroll allocated to centers. Finally, in the pre-cap era, the average season winning percentage is

44.8%, while the average team revenue, based on the three seasons of pre-cap revenue data, is $64,700,000 per year. The 1995-1995 Detroit Red Wings have the highest season winning percentage (79.9%) and in fact hold the current record for most wins in 70 or more games.

Table 9 includes the regression results from (3) for each position with season winning percentage as the dependent variable, using data from before the salary cap. For centers, when the season winning percentage is regressed on Gini alone, they have a significant positive relationship, implying that teams that take a superstar approach to signing centers will perform better. However, the Gini coefficient is no longer significant after adding σ, Pos, and the dummy variables to the regression. Pos is positively and significantly related to season winning percentage at the 1% level for centers. This is expected; good players will command higher salaries, so teams that spend more to pay players will likely be more successful than teams that do not—or cannot—spend as much. Interestingly, while insignificant, the coefficients of Gini and σ are both positive, suggesting that teams that pay their centers unequally will win more games. For left wingers, while both the coefficients of Gini and σ in regression (3) negative, neither are significantly related to season winning percentage. The coefficient of Pos is positive and significant at the 10% level; however, it is much smaller than the coefficient for centers or right wingers, suggesting that increasing payroll spent on left wingers may not lead to as much of an increase in team performance as increasing payroll spent on the other two

18 offensive positions. For right wingers, the coefficient of Gini is negative and significant at the 10% level; thus, paying right wingers more equally may lead to a higher season winning percentage. The coefficient of Pos for right wingers—like that for the other forward positions—is positive, as expected, and significant at the 1% level. Finally, the coefficient of Coach is both negative and statistically significant at the 1% level for all three regressions; this may be because a large number of losses may lead management to replace the coaching staff.

Table 10 lists the regression results from (3) with normalized revenue, using the data available from the 1999-2000, 2000-2001, and 2002-2003 seasons, as the dependent variable. When Gini is the only independent variable in the regression, its coefficient for centers is positive and statistically significant at the 1% level; after adding σ, Pos, and the dummy variables to the regression, the coefficient is still positive but no longer significant. However, the coefficient of σ is positive and significant at the 5% level, while the coefficient of Pos is positive and significant at the 10% level. These results may occur because centers are considered a highly “visible” position with regards to audiences and sponsors; thus, spending more on superstar centers to promote as the face of a franchise may yield higher revenues, even if the players’ salaries are necessarily justified based on on-ice performance. In contrast, the coefficient of Gini for left wingers is negative and significant at the 5% level. Pos is positively and significantly related to revenue; therefore, increasing the amount of total payroll spent on left wingers while paying them more equally may lead to an increase in revenue. Finally, like for centers, the coefficient of Gini is positive and statistically significant at the 1% level for right wingers when regressed on its own but no longer significant after adding σ, Pos, and the dummy

19 variables. The coefficients of σ and Pos are both positive and significant for right wingers at the 5% level. Thus, while paying right wingers more equitably may lead to more wins, it may also lead to lower revenues.

Post-Cap Results

The summary statistics for variables in regression (1) from post-cap seasons (from

2005-2006 to 2014-2015) are included in Table 2. Over the entire post-cap period, the average cap hit was $2,023,661 for centers, $1,860,448 for left wingers, and $1,880,347 for right wingers. The average number of points per game scored by all forwards post-cap was 0.44; similar to the seasons before the cap, centers scored the highest, at 0.45 points per game. Right wingers attempted the most shots on average (1.81 per game), while left wingers delivered the most hits (1.28 per game) and received the most penalty minutes

(0.81 per game). Again, the standard deviation of hits and penalty minutes for both winger positions are higher than those for centers; this may be due to teams signing more enforcers to winger positions. The average height and weight for forwards is 72.86 inches and 202.69 pounds respectively, and, like before, left wingers are both tallest and heaviest on average.

Table 4 lists the results of regression (1) for the 2014-2015 season. For centers, time on ice per game is positively and significantly related to compensation at the 5% level as expected, likely because better (and thus more highly compensated) players will spend more time playing per game than lower-tier players. The coefficient of Rookie is negative for centers and statistically significant at the 1% level, also as anticipated, because the 2005 CBA imposed stricter upper limits on rookie salaries. On the other hand, the coefficient of Veteran is positive and significant at the 1% level for all

20 forwards, suggesting that front office personnel may value the leadership and experience older players bring more than any possible age-related decline in productivity.

Interestingly, while the coefficient of AllStar is positive and significant for all forwards, the coefficient for Trophy is negative. This may be because All-Star game invitations are largely based off a player’s fame and on-ice productivity, both of which may lead to higher compensation. Trophies, however, vary in importance and may reward factors not necessarily taken into consideration when negotiating a player’s contract, such as charity work or sportsmanship. The coefficient of Points is positive and significant at the 1% level for centers, also as expected. Finally, the coefficients of Shots for centers and left wingers are positive and significant.

The summary statistics for justified and unjustified compensation for each position in the post-cap era are included in Table 6. Centers have both the maximum and minimum unjustified compensation of all four positions, as well as the highest σ of the forwards. The average Gini coefficient for centers between 2005-2006 and 2014-2015 is

0.40, while those for left wingers and right wingers are both 0.35. Thus, teams pay centers less equally than other forward positions, and this inequality may be relatively unjustified; like before, teams seem to take a superstar approach to signing centers. Right wingers have the lowest average Pos while centers have the highest; however, the standard deviations of Pos for both left and right wingers is higher than that of centers.

Again, this suggests that there exists a greater variation in cap space allocated to wingers than in cap space allocated to centers. Finally, in the post-cap period, the average season winning percentage is 55.9%, while the average team revenue is $99,903,333 per year.

The 2012-2013 Chicago Blackhawks have the highest season winning percentage

(80.2%), due to a 24-game point streak (with 21 wins and 3 overtime losses) in the lockout-shortened 48-game season, while the 2014-2015 New York Rangers have the highest annual revenue ($229 million).

Table 11 includes the post-cap regression results from (3) with season winning percentage as the dependent variable. The coefficient of Gini for centers is only positive and significant at the 10% level when excluding σ, Pos, Owner, GM, and Coach. With these additional variables, the coefficient of both Gini and σ are negative but not significant, while the coefficient of Pos is positive and significant at the 1% level. Thus, spending more cap space on centers overall may increase winning percentage; however, inequalities in cap hit between players, whether justified or unjustified, are unlikely to result in any significant effect. Similarly, neither the Gini coefficient nor σ for either wing position are significantly related to season winning percentage. For right wingers, the coefficient of Pos is again positive and significant at the 1% level. Finally, the coefficients of Owner and Coach are both negative and statistically significant in all three regressions; again, this may be because losses can lead to changes in ownership, which in turn may lead to a replacement of coaching staff.

Table 12 lists the regression results from (3) for post-cap seasons with normalized revenue as the dependent variable. For centers, while the coefficients of Gini and σ are positive, they do not appear to be significant. Pos, however, is positively and significantly related to revenue at the 1% level; therefore, spending more cap space on centers may not only increase season winning percentage but also revenue. Neither the Gini coefficient, σ, nor Pos is significantly related to revenue for left wingers in the post-cap era. For right wingers, the Gini coefficient is positively and significantly related to revenue at the 5%

22 level; thus, taking a superstar approach to allocating cap space amongst right wingers may yield an increase in revenue. Finally, changes in ownership are negatively and significantly related to revenue; again, this may be because owners are more likely to sell teams that struggle to bring in income.

b. Defensemen

Pre-Cap Results

As shown in Table 1, over the pre-cap period (1994-1995 to 2003-2004), the average salary for defensemen was $1,100,239. The average number of points per game scored by defensemen pre-cap was 0.26; as expected, this number is lower than that for forwards. Defensemen also attempted 1.22 shots per game on average, while they delivered more hits per game than any forward position. The average height and weight for pre-cap era defensemen was 73.89 inches and 210.35 pounds respectively; again, defensemen were on average taller and heavier than forwards.

The results of regression (1) for defensemen in the 1994-1995 season are also included in Table 3. The coefficient of GP (games played in the season) is positively and significantly related to compensation at the 1% level, as are the coefficients of AllStar and Shots, as expected. However, the coefficient of Cup is negative and significant at the

5% level, while the coefficient of Trophy is negative and significant at the 1% level.

Thus, it is possible that these coefficients reflect the salaries of lower-paid (and possibly less talented) defensemen on Stanley Cup-winning teams.

According to Tables 5 and 7, defensemen have both the highest minimum and lowest maximum unjustified compensation from 1994-1995 to 2003-2004, as well as the lowest standard deviation of unjustified compensation. The average Gini coefficient for

23 defensemen for these ten pre-cap seasons is 0.36, and the standard deviation of the Gini coefficient for defensemen is smaller than those for forward positions. Defensemen also have the highest average Pos and the lowest standard deviation of Pos from 1994-1995 to

2003-2004; thus, there seems to be less variation in the way teams across the league spend on defensemen compared to forward positions.

Table 9 shows the results of regression (3), with season winning percentage as the dependent variable, for the pre-cap era. When winning percentage is regressed against the

Gini coefficient alone, they have a positive and significant relationship at the 1% level; however, with the addition of σ, Pos, Owner, GM, and Coach, the relationship is still positive but no longer significant. The coefficient of σ is negative but not significant, indicating that inequality in the compensation of defensemen in a team may not lead to changes in winning percentage. Furthermore, as expected, the coefficient of Pos is positive and significant at the 1% level; thus, spending more money on defensemen overall may lead to increased team performance. Finally, the coefficient of Coach is negative and significant at the 1% level.

Table 10 lists the regression results from (3) with normalized revenue as the dependent variable using pre-cap data. While the coefficients of Gini and σ are negative, they are not significant. Thus, overall, there seems to be an insignificant relationship between revenue and inequalities in payroll distribution, whether justified or unjustified, for defensemen. However, the coefficient of Pos is positive and significant at the 1% level, indicating than an increase in the total amount of salary paid to defensemen is associated with an increase in revenue.

Post-Cap Results

As shown in Table 2, the average cap hit for defensemen from 2005-2006 to

2014-20015 was $2,042,252, the highest out of all four positions. The average number of points per game scored by defensemen post-cap was 0.28; as expected, this number is lower than that for forwards. Defensemen also attempted 1.23 shots per game on average, while they delivered 1.27 hits and received 0.70 penalty minutes per game in the post-cap era. Defensemen, on average, stood at 73.77 inches and weighed 209.17 pounds.

The results of regression (1) for defensemen in the 2014-2015 season are also included in Table 4. Like for forwards, time on ice per game is positively and significantly related to compensation; however, the coefficient of TOI for defensemen is smaller than that for forwards. This may be because there are only three pairs of defensemen on a team (rather than four lines of forwards), so defenseman are already expected to spend more time on the ice than forwards and thus are compensated relatively less for each minute they play. The coefficients of Rookie and Veteran for defensemen, similar to those for forwards, are significant at the 1% level and negative and positive respectively. AllStar for defensemen is also positively and significantly related to cap hit at the 1% level. Finally, the coefficient of Draft1 is positive and significant at the 5% level. The coefficient of Draft1 for defensemen in particular is much higher than those for forward positions; this may be because teams tend to pick goal-scorers and highly productive offensive players early in the draft, and thus any defenseman who is selected in the first round is likely talented enough to induce a general manager to choose otherwise.

According to Table 6, defensemen have a higher standard deviation of unjustified compensation when compared to the other three positions in the post-cap era. The

25 average Gini coefficient for defensemen between 2005-2006 and 2014-2015 is 0.38, which is higher than that of both left and right wingers; however, the standard deviation of the Gini coefficient for defensemen is smaller than those for forward positions. Thus, variations in talent and productivity among defensemen may be larger than the variations in cap hit. Like in the pre-cap era, defensemen still have the highest average Pos and the lowest standard deviation of Pos after the implementation of the salary cap; thus, teams seem to have similar approaches of allocating cap space to defensemen across the league.

Table 11 shows that the coefficients of all dependent variables in regression (3)

(with season winning percentage as the dependent variable) are statistically significant for defensemen in the post-cap period. Interestingly, the coefficient of σ is positive, suggesting that winning percentage increases as the standard deviation of unjustified income increases. However, the coefficient of Gini is negative; thus, taking a superstar approach to signing defensemen is related to a decrease in winning percentage. Because the coefficient of Pos is also positive and significant, teams that spend more on defense overall compared to the league average have higher winning percentages. Lastly, the coefficients of Owner, GM, and Coach are all negative and significant.

Table 12 lists the regression results from (3) for defensemen with normalized revenue as the dependent variable. Like in Table 11, the coefficient of σ is positive and the coefficient of Gini is negative for defensemen, but they are no longer statistically significant. The coefficient of Pos, on the other hand, is still positive and significant at the

1% level; thus, allocating more cap space to defensemen may increase revenue as well.

Finally, the coefficient of Owner is negative and significant at the 5% level.

c. Effect of the Salary Cap

The summary statistics of GiniWinningPerc, the Gini coefficient of the season winning percentage, and the results of regression (4) are included in Table 13. The mean

Gini coefficient of season winning percentage is 0.12 for the seasons before the salary cap was enacted and 0.08 for the seasons after. The salary cap had a negative and statistically significant effect on the Gini coefficient, as shown in Table 13; thus, I find that winning percentages have become more equal across teams after the establishment of the salary cap, and that the cap has achieved its objective of increasing parity within the

NHL.

V. Conclusion

I therefore conclude that before the salary cap, there was an insignificant relationship between inequality in player compensation (measured by the Gini coefficient and by the standard deviation of unjustified compensation) and winning percentage for centers and left wingers, while there was a negative relationship between the Gini coefficient and winning percentage for right wingers. Thus, compensating right wingers more equally may yield an increase in wins. Furthermore, as expected, increasing overall payroll spent on all forward positions is also associated with a higher season winning percentage. Finally, taking a superstar approach to signing centers and right wingers and a more egalitarian approach to signing left wingers may also lead to higher team revenue.

For defensemen before the salary cap, there seems to be an insignificant relationship between inequalities in salary distribution and either winning percentage or revenue; however, an increase in the total percentage of team payroll spent on defensemen is associated with an increase in both winning percentage and revenue.

Neither the Gini coefficient nor the standard deviation of unjustified compensation is significantly related to season winning percentage for centers, left wingers, or right wingers after the salary cap, suggesting inequalities in cap hit, whether justified or unjustified, among forwards has little impact on team performance. However, an increase in the overall percentage of cap space spent centers and right wingers may yield an increase in season winning percentage. On the other hand, the Gini coefficient is positively and significantly related to revenue for right wingers in the post-cap era; therefore, taking a superstar approach to signing right wingers may lead to an increase in revenue.

For defensemen after the salary cap, a superstar approach may in fact lead to a decrease in season winning percentage, while allocating more cap space to defensemen in general is associated with both higher winning percentages and higher revenue.

Furthermore, inequalities in cap hit among defensemen are not significantly related to changes in revenue. Finally, I find that the salary cap was effective because it has decreased the inequality of season winning percentages in the NHL, thus promoting competition between teams.

Suggestions for future research include testing for a structural change in the coefficients (3); this may tell us if approaches to allocating salary and cap space between players has changed before and after the salary cap. Additionally, limitations on my data may impact the results of this research: I am missing compensation data from several players, and I use Forbes’ estimates of team revenue rather than teams’ actual revenue in regression (3). Finally, changing the determinants of justified salary in regression (1) may yield different results. “Fancy stats”—that is, advanced metrics—such as Corsi and

Fenwick, which measure shots for and against, may be better assessments of a player’s productivity than points scored. These statistics, especially for seasons before the salary cap, are not as common or as widely available as in baseball; however, they are becoming more commonly measured and may be of interest to future researchers.

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Table 1: Summary Statistics from (1) for Pre-Cap Seasons

Position Variable N Mean Std. Dev. Min. Max.

C C 1558 1362099 1712547 113693 1.70E+007 GP 1558 0.7436174 0.2585183 0.1341463 1.02439 TOI 1558 10.84199 7.554689 0 25.56667 Rookie 1558 0.2702182 0.444215 0 1 Veteran 1558 0.3408216 0.4741377 0 1 AllStar 1558 0.8035944 2.152786 0 16 Cup 1558 0.275353 0.7740466 0 6 Trophy 1558 0.2220796 1.645367 0 26 Height 1558 72.58665 2.092867 67 78 Weight 1558 199.1958 14.39049 165 245 Draft1 1558 0.3510911 0.4774646 0 1 Draft2 1558 0.161104 0.3677449 0 1 Draft4 1558 0.3966624 0.4893619 0 1 Undrafted 1558 0.0815148 0.2737119 0 1 Points 1558 0.4877504 0.3025222 0 2.3 Shots 1558 1.618409 0.7470591 0.0769231 4.828571 Hits 1558 0.0373388 0.1428845 0 1.409091 PIM 1558 0.6386647 0.4898713 0 4.386364

D C 2368 1100239 1153262 125000 1.05E+007 GP 2368 0.7079273 0.2590023 0.1341463 1.02439 TOI 2368 13.22093 9.164947 0 30.6 Rookie 2368 0.2149493 0.410874 0 1 Veteran 2368 0.3699324 0.4828881 0 1 AllStar 2368 0.5190034 1.806801 0 16 Cup 2368 0.2474662 0.6230961 0 6 Trophy 2368 0.0836149 0.5230004 0 6 Height 2368 73.89231 1.792056 68 81 Weight 2368 210.353 13.41847 165 258 Draft1 2368 0.3086993 0.4620543 0 1 Draft2 2368 0.1490709 0.3562336 0 1 Draft4 2368 0.4349662 0.4958573 0 1 Undrafted 2368 0.0747466 0.2630376 0 1 Points 2368 0.2584853 0.1821753 0 1.288889 Shots 2368 1.223859 0.657858 0 4.756098 Hits 2368 0.0530158 0.1940564 0 2.6 PIM 2368 0.977638 0.670669 0 5.487805

L C 1455 914028.4 1095923 120530 1.10E+007 GP 1455 0.7080302 0.2629093 0.1341463 1.0625 TOI 1455 9.236575 6.739453 0 25.53333 Rookie 1455 0.2542955 0.4356142 0 1

Veteran 1455 0.3408935 0.4741726 0 1 AllStar 1455 0.2845361 0.9903947 0 8 Cup 1455 0.2364261 0.59841 0 5 Trophy 1455 0.0329897 0.2071894 0 2 Height 1455 73.13746 2.090541 67 80 Weight 1455 206.0179 16.64591 161 260 Draft1 1455 0.2254296 0.4180086 0 1 Draft2 1455 0.1408935 0.3480312 0 1 Draft4 1455 0.5058419 0.5001378 0 1 Undrafted 1455 0.0982818 0.2977976 0 1 Points 1455 0.3703793 0.2505246 0 1.434783 Shots 1455 1.474188 0.7705732 0.0769231 5.231707 Hits 1455 0.0431931 0.1600321 0 1.746032 PIM 1455 1.04603 1.03309 0 8.052631

R C 1463 1191697 1462838 99270 1.10E+007 GP 1463 0.7344786 0.2561341 0.1341463 1.036585 TOI 1463 9.653896 7.42451 0 26.86667 Rookie 1463 0.2447027 0.4300578 0 1 Veteran 1463 0.3205742 0.4668569 0 1 AllStar 1463 0.6596036 1.671456 0 12 Cup 1463 0.3157895 0.7388502 0 6 Trophy 1463 0.0922761 0.456405 0 6 Height 1463 72.47915 1.82907 66 78 Weight 1463 203.0677 14.14988 170 245 Draft1 1463 0.2727273 0.4455141 0 1 Draft2 1463 0.1244019 0.3301524 0 1 Draft4 1463 0.5215311 0.499707 0 1 Undrafted 1463 0.0813397 0.2734496 0 1 Points 1463 0.4493272 0.2925639 0 1.817073 Shots 1463 1.748316 0.9229916 0 5.2 Hits 1463 0.0416845 0.1545111 0 1.367347 PIM 1463 0.9900987 0.9381089 0 7.461538

Total C 6844 1139813 1364901 99270 1.70E+007 GP 6844 0.7217496 0.2595439 0.1341463 1.0625 TOI 6844 11.06982 8.13785 0 30.6 Rookie 6844 0.242256 0.4284797 0 1 Veteran 6844 0.3465809 0.4759156 0 1 AllStar 6844 0.5639977 1.738198 0 16 Cup 6844 0.2660725 0.6813181 0 6 Trophy 6844 0.1062244 0.8767188 0 26 Height 6844 73.13252 2.027244 66 81 Weight 6844 205.3342 15.15074 161 260 Draft1 6844 0.2929573 0.4551523 0 1 Draft2 6844 0.1447984 0.3519231 0 1

Draft4 6844 0.4598188 0.4984193 0 1 Undrafted 6844 0.0827002 0.2754486 0 1 Points 6844 0.3752595 0.2696366 0 2.3 Shots 6844 1.479005 0.7920375 0 5.231707 Hits 6844 0.0449365 0.1680835 0 2.6 PIM 6844 0.9176761 0.8053417 0 8.052631

Table 2: Summary Statistics from (1) for Post-Cap Seasons

Position Variable N Mean Std. Dev. Min. Max.

C C 1878 2023611 1965873 78000 9500000 GP 1878 0.7520149 0.2647278 0.1341463 1.02439 TOI 1878 14.46284 4.163886 0 24.28333 Rookie 1878 0.2896699 0.4537299 0 1 Veteran 1878 0.3301384 0.470388 0 1 AllStar 1878 0.5628328 1.416864 0 13 Cup 1878 0.2390841 0.5708471 0 4 Trophy 1878 0.1192758 0.6006932 0 13 Height 1878 72.75399 2.057297 67 79 Weight 1878 199.4329 13.6423 160 245 Draft1 1878 0.3892439 0.4877087 0 1 Draft2 1878 0.1751864 0.3802277 0 1 Draft4 1878 0.3391906 0.4735607 0 1 Undrafted 1878 0.1112886 0.314573 0 1 Points 1878 0.45158 0.2865444 0 1.681818 Shots 1878 1.685085 0.7399831 0.1111111 4.536585 Hits 1878 0.9991161 0.6696726 0 4.46875 PIM 1878 0.5484265 0.4228521 0 4.071429

D C 2488 2042252 1693637 135000 9000000 GP 2488 0.7233597 0.2571485 0.1341463 1.02439 TOI 2488 18.53445 4.583371 0 29.4 Rookie 2488 0.2299035 0.4208552 0 1 Veteran 2488 0.3798232 0.4854403 0 1 AllStar 2488 0.4674437 1.233392 0 12 Cup 2488 0.1973473 0.5358489 0 4 Trophy 2488 0.0574759 0.4469352 0 8 Height 2488 73.77291 2.073508 68 81 Weight 2488 209.1688 14.87848 170 260 Draft1 2488 0.3155145 0.4648139 0 1 Draft2 2488 0.1442926 0.3514568 0 1 Draft4 2488 0.4469453 0.4972772 0 1 Undrafted 2488 0.1322347 0.3388139 0 1 Points 2488 0.2825508 0.17737 0 1.085714 Shots 2488 1.230451 0.6046969 0.0666667 4.647059 Hits 2488 1.269631 0.7025822 0 4.264706 PIM 2488 0.7056665 0.4565031 0 3.933333

L C 1405 1860448 1754627 73000 9538462 GP 1405 0.7310958 0.2679563 0.1341463 1.02439 TOI 1405 13.39266 4.435875 0 23.1 Rookie 1405 0.2384342 0.4262777 0 1

Veteran 1405 0.3437722 0.4751353 0 1 AllStar 1405 0.4213523 1.024125 0 8 Cup 1405 0.2341637 0.5955438 0 4 Trophy 1405 0.0754448 0.3976452 0 5 Height 1405 73.03772 2.076699 65 80 Weight 1405 206.094 16.70286 157 265 Draft1 1405 0.347331 0.4762915 0 1 Draft2 1405 0.144484 0.351705 0 1 Draft4 1405 0.3900356 0.4879316 0 1 Undrafted 1405 0.1231317 0.3287053 0 1 Points 1405 0.4182405 0.2781552 0 1.513889 Shots 1405 1.71356 0.8865215 0 6.683544 Hits 1405 1.281019 0.7582092 0 4.897436 PIM 1405 0.8072297 0.7227946 0 5.928571

R C 1439 1880347 1712679 115000 9240000 GP 1439 0.7438837 0.2557255 0.1341463 1.012195 TOI 1439 13.62018 4.451072 0 24.73333 Rookie 1439 0.2265462 0.418742 0 1 Veteran 1439 0.3829048 0.4862644 0 1 AllStar 1439 0.6594858 1.717769 0 12 Cup 1439 0.2612926 0.5883394 0 4 Trophy 1439 0.1042391 0.5875174 0 6 Height 1439 72.82418 1.91773 67 78 Weight 1439 203.6324 15.71217 167 255 Draft1 1439 0.3182766 0.4659694 0 1 Draft2 1439 0.1223072 0.3277541 0 1 Draft4 1439 0.4996525 0.5001737 0 1 Undrafted 1439 0.1299514 0.3363668 0 1 Points 1439 0.4335981 0.2774856 0 1.5 Shots 1439 1.810976 0.8633916 0.0285714 4.487805 Hits 1439 1.181679 0.7372321 0 4.564103 PIM 1439 0.7707888 0.6756465 0 5.526316

Total C 7210 1969655 1785216 73000 9538462 GP 7210 0.7364274 0.2612016 0.1341463 1.02439 TOI 7210 15.49113 4.957274 0 29.4 Rookie 7210 0.2464632 0.4309813 0 1 Veteran 7210 0.3604716 0.4801706 0 1 AllStar 7210 0.5216366 1.359253 0 13 Cup 7210 0.2281553 0.5679863 0 4 Trophy 7210 0.0864078 0.5129977 0 13 Height 7210 73.1749 2.087238 65 81 Weight 7210 204.9287 15.59099 157 265 Draft1 7210 0.3414702 0.4742357 0 1 Draft2 7210 0.1479889 0.3551136 0 1

Draft4 7210 0.4183079 0.4933155 0 1 Undrafted 7210 0.1245492 0.33023 0 1 Points 7210 0.3831663 0.2609973 0 1.681818 Shots 7210 1.558876 0.793223 0 6.683544 Hits 7210 1.183835 0.7215998 0 4.897436 PIM 7210 0.6974988 0.5661143 0 5.928571

Table 3: Regression Results from (1) for the 1994-1995 NHL Season

(1) (2) (3) (4) VARIABLES Compensation Compensation Compensation Compensation (Centers) (Left Wingers) (Right Wingers) (Defensemen)

GP 54,147 146,059 105,937 303,722** (176,634) (133,104) (223,304) (125,769) o.TOI - - - -

Rookie 20,922 -7,511 -35,516 -90,700 (110,388) (77,785) (104,127) (78,187) Veteran -11,760 60,492 99,865 104,041 (113,081) (77,246) (112,487) (67,404) AllStar 165,536*** 110,031** 222,794*** 277,690*** (37,158) (46,725) (50,095) (32,015) Cup 190,493** 37,478 -144,046** -89,779** (77,072) (47,789) (60,012) (43,547) Trophy 130,683*** -38,072 381,259** -279,329*** (26,572) (339,950) (158,212) (79,318) Height -22,070 4,661 34,756 21,245 (33,510) (24,200) (32,873) (20,965) Weight 9,006* 2,044 -1,453 1,810 (4,710) (3,288) (4,472) (2,926) Draft1 6,041 276,989** 75,407 146,736 (155,803) (120,674) (182,721) (108,613) Draft2 -262,362 43,205 -110,606 -43,476 (175,556) (127,592) (195,082) (118,808) Draft4 -125,068 60,814 -69,113 -60,187 (143,821) (111,913) (168,764) (106,112) Undrafted -61,990 19,286 -94,374 176,434 (162,974) (94,805) (175,546) (116,040) Points 1.020e+06*** 76,390 2,041 -228,284 (236,133) (238,320) (291,702) (236,298) Shots -29,429 217,666*** 268,314*** 215,100*** (97,693) (75,154) (94,451) (64,117) o.Hits - - - -

PIM -43,941 18,950 62,053* -984.4 (71,437) (29,863) (36,878) (33,731) Constant -44,028 -912,743 -2.280e+06 -1.927e+06 (1.858e+06) (1.433e+06) (1.913e+06) (1.268e+06)

Observations 150 132 139 224 R-squared 0.740 0.482 0.567 0.582 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 4: Regression Results from (1) for the 2014-2015 NHL Season

(1) (2) (3) (4) VARIABLES Compensation Compensation Compensation Compensation (Centers) (Left Wingers) (Right Wingers) (Defensemen)

GP -254,851 -263,453 43,001 1.134e+06*** (458,193) (468,846) (473,063) (335,620) TOI 72,834** 148,561*** 244,951*** 49,835*** (29,524) (52,646) (62,689) (18,505) Rookie -1.131e+06*** -640,565** -1.098e+06*** -948,190*** (228,539) (265,658) (279,143) (196,543) Veteran 643,316*** 921,653*** 668,231*** 938,797*** (222,575) (248,715) (255,020) (183,986) AllStar 806,816*** 312,425** 260,000** 614,613*** (118,644) (130,885) (125,106) (93,033) Cup 127,817 14,239 92,352 39,685 (165,695) (172,888) (187,361) (150,074) Trophy -182,015 206,654 -208,615 51,326 (182,828) (249,198) (225,998) (287,355) Height -38,574 18,426 58,270 -61,793 (69,551) (75,219) (77,924) (54,071) Weight -4,052 15,439 -9,781 10,538 (9,993) (10,324) (10,956) (8,227) Draft1 -68,248 -335,931 -66,849 623,758** (311,881) (380,871) (501,844) (278,529) Draft2 -362,396 -549,662 -516,486 463,984 (334,112) (405,025) (539,281) (316,561) Draft4 -341,267 -792,799** -546,608 233,572 (337,603) (365,613) (495,909) (281,839) Undrafted -693,767** -445,134 364,414 -349,122 (349,797) (350,931) (335,030) (239,370) Points 1.917e+06*** 1.029e+06 301,744 1.929e+06** (725,451) (864,145) (906,296) (772,744) Shots 389,761* 663,399*** 282,978 257,652 (221,027) (233,451) (285,694) (207,360) Hits -169,102 93,465 107,592 -101,303 (136,450) (150,706) (150,741) (117,261) PIM 420,180 -8,563 309,275 259,805 (333,324) (263,699) (206,270) (236,674) Constant 3.824e+06 -5.392e+06 -4.104e+06 1.589e+06 (3.863e+06) (4.421e+06) (4.418e+06) (3.113e+06)

Observation s 202 132 136 252 R-squared 0.736 0.731 0.670 0.684 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 5: Summary Statistics for Justified and Unjustified Compensation for Pre-Cap Seasons

Position Variable N Mean Std. Dev. Min. Max.

C JustifiedC 1576 1349115 1464562 -702240.7 9401224 UnjustifiedC 1576 -0.0004858 877160.3 -4017675 9284242

D JustifiedC 2376 1097008 998787.7 -597663.6 9087228 UnjustifiedC 2376 0.0005277 575371.2 -2841892 4012042

L JustifiedC 1467 908490.5 858848.1 -946623.1 7398712 UnjustifiedC 1467 -0.0003648 676817 -3613849 5718410

R JustifiedC 1468 1188064 1313175 -669580.5 1.07E+007 UnjustifiedC 1468 0.0002554 641902 -3846121 4077753

Total JustifiedC 6887 11339 52 1175414 -946623.1 1.07E+007 UnjustifiedC 6887 0.0000476 689542.3 -4017675 9284242

Table 6: Summary Statistics for Justified and Unjustified Compensation for Post-Cap Seasons

Position Variable N Mean Std. Dev. Min. Max.

C Justifie dC 1895 2014551 1677911 -1158664 8956106 UnjustifiedC 1895 -0.0025808 1016057 -4851898 4561602

D JustifiedC 2510 2035150 1379039 -1199356 8168745 UnjustifiedC 2510 0.0000747 978340.5 -3885944 4086344

L JustifiedC 1417 1852694 1531049 -890572.3 1.05E+007 UnjustifiedC 1417 0.0009263 851688 -3104165 4342233

R JustifiedC 1447 1877396 1406730 -1917399 9297259 UnjustifiedC 1447 -0.0005939 973774.2 -4309960 3533406

Total JustifiedC 7269 1962809 1498968 -1917399 1.05E+007 UnjustifiedC 7269 -0.0005847 964068.2 -4851898 4561602

Table 7: Summary Statistics from (3) for Pre-Cap Seasons

Position Variable N Mean Std. Dev. Min. Max.

C WinningPerc 279 0.448351 0.0992879 0.1875 0.7560976 Rev 88 6.47E+007 1.75E+007 3.90E+007 1.13E+008 Pos 279 0.9718982 0.5079799 0.1289702 3.236469 σ 279 0.8352581 0.5640449 0.1262071 4.167297 Gini 279 0.3884145 0.1252459 0.0626102 0.6884626

D WinningPerc 279 0.448351 0.0992879 0.1875 0.7560976 Rev 88 6.47E+007 1.75E+007 3.90E+007 1.13E+008 Pos 279 0.9981991 0.372385 0.3270263 2.195424 σ 279 0.8981145 0.3896933 0.3189551 2.753688 Gini 279 0.3590511 0.093233 0.1066416 0.6253845

L WinningPerc 279 0.448351 0.0992879 0.1875 0.7560976 Rev 88 6.47E+007 1.75E+007 3.90E+007 1.13E+008 Pos 279 0.9177744 0.5109515 0.0286274 2.678437 σ 277 0.8363944 0.505738 0.1444065 2.946686 Gini 278 0.3097531 0.129952 0 0.6341181

R WinningPerc 279 0.448351 0.0992879 0.1875 0.7560976 Rev 88 6.47E+007 1.75E+007 3.90E+007 1.13E+008 Pos 279 0.9338495 0.5201186 0.0696968 2.472832 σ 278 0.8590194 0.4736018 0.0141375 2.438438 Gini 279 0.3623189 0.1236736 0 0.6573796

Total WinningPerc 1116 0.448351 0.0991543 0.1875 0.7560976 Rev 352 6.47E+007 1.75E+007 3.90E+007 1.13E+008 Pos 1116 0.9554303 0.4821304 0.0286274 3.236469 σ 1113 0.8572323 0.4873469 0.0141375 4.167297 Gini 1115 0.3549249 0.122098 0 0.6884626

Table 8: Summary Statistics from (3) for Post-Cap Seasons

Position Variable N Mean Std. Dev. Min. Max.

C WinningPerc 300 0.5590193 0.0864644 0.3170732 0.8020833 Rev 300 9.99E+007 3.16E+007 5.60E+007 2.29E+008 Pos 300 0.9695433 0.3211966 0.2187385 1.851985 σ 300 0.9194575 0.3888123 0.0442709 2.297594 Gini 300 0.3956077 0.0962861 0.0610497 0.5770561

D WinningPerc 300 0.5590193 0.0864644 0.3170732 0.8020833 Rev 300 9.99E+007 3.16E+007 5.60E+007 2.29E+008 Pos 300 0.9938451 0.2306383 0.2908523 1.757567 σ 300 0.9646395 0.2997134 0.3382564 1.999432 Gini 300 0.3814836 0.0654372 0.1236674 0.5478098

L WinningPerc 300 0.5590193 0.0864644 0.3170732 0.8020833 Rev 300 9.99E+007 3.16E+007 5.60E+007 2.29E+008 Pos 300 0.9320134 0.4108397 0.0538739 2.161522 σ 299 0.9241073 0.4492601 0.0757201 3.020163 Gini 300 0.3455349 0.1143337 0 0.5863947

R WinningPerc 300 0.5590193 0.0864644 0.3170732 0.8020833 Rev 300 9.99E+007 3.16E+007 5.60E+007 2.29E+008 Pos 300 0.9281859 0.3841125 0.0566621 2.155935 σ 297 0.9250407 0.42448 0.1790339 3.141366 Gini 300 0.3529138 0.1125851 0 0.5982229

Total WinningPerc 1200 0.5590193 0.0863561 0.3170732 0.8020833 Rev 1200 9.99E+007 3.16E+007 5.60E+007 2.29E+008 Pos 1200 0.9558969 0.3444116 0.0538739 2.161522 σ 1196 0.9333397 0.394458 0.0442709 3.141366 Gini 1200 0.368885 0.1010901 0 0.5982229

Table 9: Regression Results from (3) for Pre-Cap Seasons

(1) (2) (3) (4) (5) (6) (7) (8) VARIABLES WinningPerc WinningPerc WinningPerc WinningPerc WinningPerc WinningPerc WinningPerc WinningPerc (Left (Left (Right (Right (Centers) (Centers) Wingers) Wingers) Wingers) Wingers) (Defensemen) (Defensemen)

Gini 0.201*** 0.0318 0.0216 -0.0583 0.0636 -0.0967* 0.273*** 0.0353 (0.0461) (0.0519) (0.0459) (0.0625) (0.0481) (0.0554) (0.0618) (0.0647) σ 0.00416 -0.00439 0.00425 -0.0211 (0.0119) (0.0147) (0.0135) (0.0168) Pos 0.0718*** 0.0311* 0.0734*** 0.132*** (0.0148) (0.0162) (0.0144) (0.0179) Owner -0.0221 -0.0259 -0.0193 -0.0163 (0.0167) (0.0187) (0.0172) (0.0160) GM 0.0109 0.00564 0.00578 0.0111 (0.0139) (0.0153) (0.0143) (0.0134) Coach -0.0489*** -0.0505*** -0.0518*** -0.0494*** (0.0110) (0.0121) (0.0116) (0.0107) Constant 0.370*** 0.383*** 0.442*** 0.463*** 0.425*** 0.433*** 0.350*** 0.343*** (0.0188) (0.0179) (0.0154) (0.0168) (0.0184) (0.0183) (0.0229) (0.0218)

Observations 279 279 278 276 279 278 279 279 R-squared 0.064 0.238 0.001 0.085 0.006 0.187 0.066 0.288 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 10: Regression Results from (3) for Pre-Cap Seasons

(1) (2) (3) (4) (5) (6) (7) (8) VARIABLES Revenue Revenue Revenue Revenue Revenue Revenue Revenue Revenue (Left (Left (Right (Right (Centers) (Centers) Wingers) Wingers) Wingers) Wingers) (Defensemen) (Defensemen)

Gini 0.758*** 0.281 0.0342 -0.728** 0.660*** 0.00207 0.516* -0.430 (0.217) (0.248) (0.210) (0.317) (0.206) (0.253) (0.299) (0.300) σ 0.121** 0.0416 0.141** -0.0256 (0.0490) (0.0722) (0.0664) (0.0863) Pos 0.141* 0.191** 0.169** 0.448*** (0.0739) (0.0865) (0.0648) (0.0831) Owner -0.0864 -0.0959 -0.0740 -0.0541 (0.0690) (0.0808) (0.0705) (0.0675) GM 0.0251 0.0218 0.0370 0.0610 (0.0624) (0.0720) (0.0644) (0.0615) Coach 0.0976* 0.0467 0.0208 0.0219 (0.0508) (0.0577) (0.0522) (0.0493) Constant 0.702*** 0.616*** 0.990*** 0.997*** 0.768*** 0.721*** 0.812*** 0.720*** (0.0894) (0.0893) (0.0688) (0.0751) (0.0772) (0.0777) (0.112) (0.0982)

Observations 88 88 88 88 88 88 88 88 R-squared 0.124 0.324 0.000 0.125 0.107 0.300 0.033 0.374 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 11: Regression Results from (3) for Post-Cap Seasons

Gini 0.0953* -0.0454 0.0500 0.0313 0.0338 -0.0178 0.0165 -0.152** (0.0517) (0.0585) (0.0437) (0.0506) (0.0444) (0.0519) (0.0765) (0.0722) σ -0.00401 -0.00822 -0.00111 0.0270* (0.0126) (0.0114) (0.0118) (0.0163) Pos 0.0788*** 0.0152 0.0407*** 0.138*** (0.0172) (0.0137) (0.0147) (0.0209) Owner -0.0305* -0.0323* -0.0419** -0.0321* (0.0181) (0.0187) (0.0187) (0.0171) GM -0.0181 -0.0245* -0.0178 -0.0265** (0.0130) (0.0136) (0.0133) (0.0123) Coach -0.0373*** -0.0437*** -0.0452*** -0.0375*** (0.0101) (0.0104) (0.0102) (0.00952) Constant 0.521*** 0.522*** 0.542*** 0.562*** 0.547*** 0.548*** 0.553*** 0.473*** (0.0211) (0.0216) (0.0159) (0.0173) (0.0165) (0.0185) (0.0296) (0.0294)

Observations 300 300 300 299 300 297 300 300 R-squared 0.011 0.161 0.004 0.101 0.002 0.129 0.000 0.245 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 12: Regression Results from (3) for Post-Cap Seasons

Gini 0.329** 0.0352 0.113 -0.000160 0.278** 0.391** 0.304 -0.225 (0.152) (0.183) (0.129) (0.155) (0.130) (0.159) (0.225) (0.220) σ 0.0121 0.00506 -0.0374 0.0705 (0.0393) (0.0349) (0.0360) (0.0498) Pos 0.147*** 0.0675 0.0117 0.439*** (0.0538) (0.0421) (0.0452) (0.0636) Owner -0.104* -0.118** -0.128** -0.109** (0.0567) (0.0573) (0.0574) (0.0520) GM 0.0459 0.0371 0.0419 0.0299 (0.0408) (0.0417) (0.0409) (0.0375) Coach -0.00999 -0.0244 -0.0199 -0.00453 (0.0315) (0.0318) (0.0314) (0.0290) Constant 0.870*** 0.836*** 0.961*** 0.943*** 0.902*** 0.891*** 0.884*** 0.587*** (0.0619) (0.0677) (0.0469) (0.0531) (0.0482) (0.0567) (0.0871) (0.0896)

Observations 300 300 300 299 300 297 300 300 R-squared 0.015 0.054 0.003 0.028 0.015 0.047 0.006 0.192 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

Table 13: Summary Statistics and Regression Results from (4)

Cap Variable Mean

0 GiniWinningPer c 0.1216083 1 GiniWinningPerc 0.085286

Total GiniWinningPerc 0.1027884

(1) VARIABLES GiniWinningPerc

Cap -0.0363*** -0.000539 Constant 0.122*** -0.000388

Observations 2,316 R-squared 0.662 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1