Filling the Stands

Factors Determining NBA and WNBA Attendance

Margaret Cronin Advisor: Dr. Vladamir Kontorovich Senior Thesis Economics Department Haverford College April 2011

Abstract

This study identifies differences between the market characteristics, relative performance, characteristics of play, and substitutes for the NBA and WNBA and, specifically, how those differences impact attendance for these leagues and the teams within them. It does so by examining the statistical and economic significance of factors driving attendance at professional basketball games. An OLS model, censored normal model, and fixed effects model estimate the magnitude of these factors’ impacts on attendance for different teams and leagues. In so doing I open the door to expand the current sports economics literature, specifically pertaining to attendance at professional sporting events, to include women’s sports beyond their current role: an assumed extension of their male counterparts’ findings.

Acknowledgements

I would like to thank my advisor, Professor Vladamir Kontorovich for all of his helpful guidance, feedback, and suggestions during this project. I would also like to thank the entire Haverford College Economics Department for all they taught me over the past four years.

I’d also like to thank my friends and teammates for all they did to make sure I kept my spirits up in the process, without which I would never have succeeded in getting this far.

Finally, I would like to thank my family for their love and support and especially my parents, who gave me every opportunity to learn. Without them I wouldn’t understand economics or basketball and this project wouldn’t have stood a chance.

Table of Contents

I. Introduction ...... 5

II. Literature Review...... 7

III. Methods ...... 11

IV. Data...... 16

V. Results...... 19

Combined...... 19

Chow Test...... 21

NBA Results...... 23

WNBA Results ...... 25

VI. Implications, Conclusions, and Future Research...... 26

VII. References ...... 28

VIII. Appendix...... 30

I. Introduction

The 2010 NBA (National Basketball Association) Championship winning Los Angeles

Lakers had an average per game attendance of 18,997 while the WNBA (Women’s National

Basketball Association) champions in the same year, the Seattle Storm, averaged a mere 8,322 fans at each of their games. Often it is assumed that attendance at professional sporting events is directly related to a team’s success on the court or field. However, both of these teams achieved

(approximately) the same amount of success in the same season at the same sport. Yet, the

Lakers averaged over 10,000 more fans per game than the Storm. This paper examines the factors that impact attendance in professional basketball. By identifying differences between teams in the NBA and WNBA I will uncover why some teams have greater attendance than others and, ultimately, why the NBA has greater attendance than the WNBA.

Lower attendance (combined with lower ticket prices) in the WNBA results in less revenue for these teams than their male counterparts. Aside from the direct effect on revenue, attendance is also indicative of a team’s fan base and demand for that team in general, both of which are positively related to revenues.

Why should anyone, aside from basketball fans, care about increasing the WNBA’s revenue? While higher revenues may allow for higher quality facilities and players; improving the quality of the product overall, this doesn’t seem like an important economic goal in itself.

Professional sports, however, are big businesses with major impacts on their communities.

Teams touch many different parts of the economy, by charging admission, advertising in stadiums, and seeking government subsidies for stadiums and events (Fort 2006 pp.2-4). Cities subsidize stadiums and the stadium neighbors face the costs that come with externalities associated with professional sporting events; the costs associated with increased security,

parking, and transportation required as a result of that stadium. Thus, the importance of finding out what value comes from a professional sports team is paramount, not only for the team and its enthusiasts, but also for anyone in a community that has, or is considering having, a team.

In addition to the business end of sports economics, there also seems to be an obvious link to gender discrimination in the labor market. If consumers are choosing NBA games over

WNBA games merely because WNBA games are played by women, this is an obvious case of discrimination. This raises certain ethical and, thanks to laws like the Title IX, legal questions.

However, in an economic sense, these differences are merely differences in preferences.

Economic theory can often be used to identify discrimination, but typically only in situations where a disparity in pay coincides with equal production. In the case of the NBA and WNBA this kind of discrimination cannot be determined. Since players of different genders do not play against each other their production cannot be compared. Just as a consumer may, for unknown reasons, prefer red cars to blue cars a consumer may prefer men’s basketball to women’s basketball. This preference may or may not be justified, but economically that justification is irrelevant. Just because discrimination cannot be proven through economic analysis does not mean it doesn’t exist. For now, however, the legal, ethical, social, and moral implications of sexist preferences will be ignored for the sake of focusing on the economic implications of NBA and WNBA attendance.

II. Literature Review

Although the National Basketball Association (NBA) and Women’s National Basketball

Association (WNBA) both play professional basketball some argue that these two sports are the same in name only. As Jonathan V. Last writes:

Most sports are defined by a unique physical parameter. In baseball, for example, it's the ninety feet between bases. In basketball, it's the ten-foot rim. Within these confines, people play different species of a sport. A bunch of 5'10" men--or women--don't play a lower quality of basketball than the men in the NBA, they play an entirely different game. (Last)

Last represents popular opinion based on casual observation. Women, he and many others note, play a different version of basketball than men and the men’s version is simply more entertaining. KimMarie McGoldrick and Lisa Voeks take a more analytic approach to find these differences in their 2005 paper, “’We Got Game!’: An Analysis of Win/Loss Probability and

Efficiency Differences Between the NBA and WNBA.” In their paper McGoldrick and Voeks describe how the two leagues differ by the characteristics of their play (what kind of shots they are making and taking, number of fouls, steals, turnovers, and points) as well as how different characteristics impact game outcomes for the two leagues. They also note a number of less quantifiable differences, such as the length of the shot clock and game. Some differences, such as length of game and season, they incorporate into their data for more accurate comparison (this proved equally helpful in my study). Finally, they use a stochastic frontier model to predict the maximum potential performance of teams in the league. By comparing actual performance to this predicted performance they uncover how efficient teams are. Teams that perform closer to predicted performance are more efficient. They conclude that, in addition to differences in the type of game they play (the men’s game is generally more aggressive) WNBA teams are less efficient than NBA teams. They note this may be due to the fact that the WNBA, and thus all of

its teams, is newer than the NBA and its teams, so its teams have not yet been able to build team chemistry which improves efficiency. These differences do not alone explain attendance differences, but they do raise the idea that there may be differences between the two leagues

(besides the gender of the players) that draw more fans to NBA games than WNBA games.

If Last, McGoldrick, and Voeks are correct than there are some important implications for WNBA teams trying to improve their attendance. If men’s basketball and women’s basketball are such different games, then one of two scenarios is occurring: the WNBA and

NBA are different goods and their demands are modeled by completely different information or women’s and men’s teams are different but demand for both is determined by the same model and, thus, WNBA teams that more closely resemble NBA teams will face greater demand than those that are less similar to NBA teams.

These models are based off of those in the previous literature that examine the factors impacting attendance at sporting events. Simon Rottenberg in his 1956 article, “The Baseball

Players’ Labor Market” describes attendance as “a function of the general level of income, the price of admission to baseball games relative to the prices of recreational substitutes, and the goodness of substitutes" (Rottenberg 246). He goes on to further explain this function:

Attendance at the games of any given team is a positive function of the size of the population of the territory in which the team has the monopoly right to play; the size and convenience of location of the ball park; and the average rank standing of the team during the season in the competition of its league. It is a negative function of the goodness of leisure-time substitutes for baseball in the area and of the dispersion of percentages of games won by the teams in the league. (Rottenberg 246)

His work argued (quite intuitively) that baseball teams in larger markets (more populated cities) make more money than those in smaller markets (less populated cities), teams that win more make more money than teams that win less, and teams make more money when there are less

quality substitutes in the area for use of leisure time and money. Rodney Fort’s 2005 article,

“The Golden Anniversary of ‘The Baseball Player’s Labor Market’’’ comments that these factors are still key in determining demand for sports events today. Thus, it seems any model for sporting event demand must hinge on these five basic elements: population, income, quality, substitutes, and price.

While originally this attendance model was used for baseball it has been expanded for use in analyzing the impact of assorted factors related to demand in a number of sports since then. In a later paper, which Rodney Fort wrote with Jason A. Winfree, they use this attendance model to analyze the impact of the NHL lockout in 2004-2005 on junior and minor league hockey attendance. Their study looked at the impact of changes in a substitute on attendance. They found NHL fans to be hockey fans in general, as the elimination of NHL games led to increased attendance at minor and junior league hockey games.

In their study “When is the Honeymoon Over?” John C. Leadley and Zenon X. Zygmont look more specifically at determinants of attendance in the NBA. Their study extended the use of such attendance models to the NBA, using attendance as a dependent variable and general admission ticket prices, local unemployment rates, variables for team and arena age (as their study was meant to measure the honeymoon effect, which is the expected increase in attendance for the novelty of a new team or arena), winning percentage, lagged winning percentage, games behind at the end of the season, and arena seating capacity as independent variables. They confirmed a honeymoon effect in demand in the NBA comparable to that of Major League

Baseball but smaller in terms of actual attendance due to capacity constraints present in the NBA that are not present in baseball. They found this effect begins to diminish in the fifth year and is essentially gone by the tenth.

James J. Zhang, Dale G. Pease, Stanley C. Hui, and Thomas J. Michaud’s article,

“Variables Affecting the Spectator Decision to Attend NBA Games,” looked at factors related to

NBA game attendance more generally. In their attempt to develop a Spectator Decision Making

Inventory they found factors related to game promotion (advertising, publicity, discounts, and other promotions), the home team (team performance and presence of superstars), and the opposing team (team performance and presence of superstars) positively related to how many games one attends in the current season; schedule convenience positively related to how many games one attended in the previous season; and the home team positively related to the number of seasons in which one has attended games. They also found differences in the effects of these factors related to age, economic status, ethnicity, education level, and occupation.

Although women’s teams face the lowest attendance in professional sports, the current literature on attendance and what influences it is dominated by men’s sports. This paper will expand these studies to women’s professional sports and especially what makes the model for women’s sports different from men’s. Thus, it will provide insight for the WNBA that has previously only been available tangentially from research about the NBA. Additionally, differences discovered between the NBA and WNBA will likely reveal differences in attendance for men and women’s sports more generally. Thus, this paper will be useful for the successful future of not just the WNBA but also other professional women’s sports leagues (such as

Women’s Professional Soccer and National Professional Fastpitch).

III. Methods1

This research starts with a basic OLS method of estimation used to create a model that predicts demand for attending professional basketball games based on a number of likely factors.

The factors examined are reflective or indicative of the determinants of demand indicated by

Rottenberg: substitutes, income, population, and quality. There are, however, a few ways in which my model differs from Rotternberg’s. While Rottenberg’s model included quality only in terms of how many games a team wins (i.e. winning percentage) I consider quality in terms of quality of entertainment (i.e. how much fun is it to watch the team; how close are games, how many turnovers or fouls cause the game to stop, etc.) many of which are suggested in past literature. Rottenberg’s model also includes price as a determinant of demand. However, price should not be included in a demand function; it should instead be determined by the interaction of supply and demand. Because arenas have a fixed capacity, there is a fixed supply of basketball (see Figure 1) which limits the amount of demand that can be met. Thus, if a team can increase its demand, with a fixed supply, it can also increase its price (see Figure 2). Instead of including price I choose to, instead, use a censored normal regression to estimate the model in addition to the basic OLS method of estimation because fifty-seven (out of 536) observations had an average attendance equal to their stadium capacity.2

1 More information about the data used in this model, how it is measured, and where it was obtained from can be found in the following section (“Data”) and Appendix A. 2 Notably, all of these observations were NBA teams and typically were teams that had been very successful in the previous year. While censored observations do not represent a very large part of the sample, it represents a very specific type of observation, and to not account for the censoring would be detrimental to this study. 11

Rottenberg’s Model:

Demand for a sporting event = β0 + β1(substitutes) + β2(income) + β3(population) + β4(quality) + β5(price)

My Model:

Demand for a sporting event = β0 + β1(substitutes) + β2(income) + β3(population) + β4(quality of play) + β5(quality of entertainment) + β6(gender)

β1(Substitutes) = β11 (In-state Division I College teams (of the same gender)) + β12(other NBA/WNBA teams) + β13(WNBA/NBA teams) + β14(MLB, NHL, and NFL teams)

Income = the deflated average annual salary of the team’s Metropolitan Statistical Area

β3 (Population) = β31(the population of the team’s Metropolitan Statistical Area) + β32(Whether the team has moved to a new city)

β4 (Quality of play) = β41(Winning percentage) + β42(Whether that team made the playoffs in the current year) + β43(Whether that team went to the championship game in the current year) + β44(Whether that team won a championship in the current year) + β45(Whether that team made the playoffs in the previous year ) + β46(Whether that team went to the championship game in the previous year) + β47(Whether that team won a championship in the previous year)

β5(Quality of Entertainment) = β51(Pace) + β52(3 pointers) + β53(free throws) + β54(points scored) + β55(rebounds) + β56(assists) + β57(steals) + β58(blocks) + β59(turnovers) + β510(fouls) + β511(all stars) + β512(point differential) + β513(Whether the team has a new name)

Figure 1

Figure 2

A censored normal regression, similar to the OLS model, identifies a regression line or line of best fit by which one can predict the dependent variable’s quantity, given the quantities of the independent variables. The censored normal regression has the advantage, however, of

accounting for an limit in the dependent variable (in this case, an upper limit is set on demand by the capacity of the arena). In the OLS model the squared residuals are minimized to find an intercept and slope from which the regression line can be constructed (Wooldridge 30-32). The censored regression uses a “maximum likelihood estimation, a general method for obtaining parameter estimates and performing statistical inference on the estimates” (Hallahan 1). The censored regression uses a probability density function to estimate the probability that the value has been censored and to make a best guess, using these probabilities and the values that are available, at what the value would have been had it not been censored. Thus, it is able to estimate values greater than the greatest value given.

Because the data is panel data, I use fixed effects analysis in addition to the OLS and censored normal regressions. This analysis will separate the effects of organizational differences between different teams. Thus, residual error that correlates with a particular team is controlled for and identified as a difference between teams rather than a difference between two independent observations. This is both an advantage and disadvantage for fixed effects analysis.

By using fixed effects analysis the results indicate what a team can do to improve its attendance, not just theoretically speaking why it has lower attendance than another team. However, if a team wants to implement something it has never tried before, it cannot determine the effects using fixed effects. Additionally, fixed effects does not indicate what causes differences between individual teams.. Finally, it was not possible to account for censored observations in the fixed effects analysis, so the fixed effects analysis faces similar issues to the OLS estimation.

It is for these reasons the combination of the OLS model, the censored normal, and the fixed effects analysis are all used together to draw conclusions about which factors are most influential in determining professional basketball demand and attendance. However, it is to be noted that,

as will be apparent in looking at the results, the censored regressions and the OLS regressions were not drastically different from each other. Thus, I will continue with the analysis using only the censored regression and fixed effects analysis since, as explained above, the censored normal estimate is likely (even if only slightly) more accurate than the OLS estimation due to its unique way of incorporating censored results.

IV. Data

This study uses a panel data set that has 536 observations; 364 NBA observations and

172 WNBA observations3 in the United States4 following thirty NBA and eighteen WNBA teams over the course of thirteen seasons, from 1997 until 2009.5 It is an unbalanced panel data set, as some teams have entered and left both leagues since 1997.

The dependent variable6 in this project is the log of average per game attendance. Thus, impacts of factors in the model are interpreted as percent changes in attendance. Independent variables that determine demand, as previously mentioned, fall into one of four categories: substitutes, population, income, and quality. Population and average income are expected to have a positive effect on attendance because cities with more people will also likely have more people at sporting events they host. Additionally, if the residents of a city have greater income they have more money to spend on goods, including tickets to sporting events. Thus, increased income in an area is expected to increase attendance at sporting events in that area. Substitutes, on the other hand, are expected to have a negative impact on attendance, as fans have a limited income and are likely choosing between two different sporting events. Substitutes include the number of other teams participating in the same city in the same league (how many other

WNBA/NBA teams are there?), the same sport in a different league (Is there a WNBA team in the same city as an NBA team or vice versa?), the same sport at a different level (How many

3 However, due to missing variables the models only represent 366 observations, 255 NBA and 111 WNBA 4 While there are NBA teams in Canada, Canadian observations were dropped to make the study United States-specific to ensure comparable market data. 5 Although the NBA has been around since 1947, the WNBA originated in 1997. Thus, starting the data in 1997 allows for reasonably comparable data for both leagues. 6 Detailed Descriptions of variables as well as their sources can be found in Appendix A. 16

Division I college teams are in that state?), and different major professional sports (How many

MLB, NFL, and NHL teams are there in that city?).

Quality is significantly more complex, but is also important in determining attendance.

As mentioned earlier, quality (in my model) is not merely measured in terms of winning percentage (although that is a part of quality and is expected to have a positive impact on attendance). Other factors related to the quality of the team (in terms of talent) are whether or not the team makes the playoffs and whether it goes to or wins a championship in that year, all of which are expected to positively correlate with attendance. These add to what winning percentage offers by allowing one to examine the impacts of different milestones of success on attendance. While winning percentage assumes the same increase in attendance in response to any increased performance. Playoff and championship variables, on the other hand, provide an idea of jumps in attendance for reaching certain success milestones.

However, quality of entertainment matters just as much, if not more than, quality of athletic performance. A team that wins every game by 100 points is a high quality basketball team but is not necessarily high quality entertainment and thus it will not necessarily attract many fans, nor is a team that often shuts down the other team defensively but without providing much in the way of exciting scoring. Thus, additional qualities that I expected to make a team more entertaining (when controlling for quality of play) and thus increase attendance are greater pace (an estimate of the number of possessions per 48 minutes by a team, indicating a faster game in which that team has possession of the ball more often) more points scored, lower differences between points scored for and against that team, more three-pointers, more free throws, more blocks, and more steals. Additionally, the number of players on a team voted to the all star team is indicative of how many “super stars” are on that team. Since super stars (by

their definition) are fan favorites, I believe they attract fans, and thus, more all stars will result in greater attendance for a team. Factors I predicted to result in less entertaining games, and thus lower attendance when controlling for winning percentage, are more rebounds, more fouls, more assists, and more turnovers. These characteristics of play are likely to help a team win but typically slow down a game and are, thus, not as exciting or fun to watch as faster-paced, higher scoring game strategies. All statistical data is per forty-eight minute game to control for differences in season and game length between the different leagues and different seasons.

Lag variables are also indicators of quality to fans. A higher winning percentage, a playoff or championship appearance, or a championship in the previous year will likely have a positive effect on the present season’s attendance. This is because fans often buy tickets before the season or very early in the season when they do not yet know how the team will perform in the current season. Their best guess at how the team will perform is how it performed the year before. Additionally, dummy variables indicating if a team has moved to a new city or has a new name are included. Although these changes should not change the basketball play at all, they change the market and interest around the team. These two changes are a kind of marketing tool.

They promote the team and attract fans by drawing attention to the team in news and other avenues.

Attendance also has a time trend; some years attendance is higher across the board than others. Thus, because the observations span thirteen years the model also controls for the year of the observation. Finally, basketball game attendance is constrained by the capacity of the arena.

For this reason a final statistic is used to indicate the percentage of arena capacity filled. This statistic is used to identify observations in which the demand model was constrained by the supply and to allow for censored modeling.

V. Results7

Combined Results

The combined censored normal regressions indicated, not surprisingly, that the most significant8 factor in determining attendance at a professional basketball game is the gender of the players (since the gender of a team is constant, gender was dropped in the fixed effects model). A WNBA team is predicted, by the censored normal model, to have 70.9% lower attendance than an NBA team with the same performance in that year and the year before, the same characteristics of play, with the same population, income, and substitutes. This, unfortunately, indicates that there is little WNBA teams can do to catch up to their male counterparts. More scoring, faster paced games, relocation, and having all stars may have some impact, but the WNBA’s greatest weakness is that it is a league of women and, it seems, fans prefer men’s basketball to women’s.

Similarly uncontrollable (unless a team relocates), but significant, factors included population and income. According to the censored normal regression a 1% increase in the population of the team’s Metropolitan Statistical Area is expected to cause a 6.15% increase in average single home game attendance for a professional basketball team, all else held constant.

A 1% increase in deflated average salary predicts a 35.65% increase in average single home game attendance, all else held constant, according to fixed effects analysis. However, additional

NBA and WNBA substitutes counteract this effect. Each additional team is expected to cause

10.15% decline in average single home game attendance for other teams in the same league (this is the relationship between two or more NBA teams in an area or two or more WNBA teams in

7 Detailed results for combined, NBA, and WNBA OLS, censored, and fixed effects models can be found in appendices B-J. 8 Significance, here and in all future references, indicates at least a 5% level of significance. 19

an area) according to the censored normal regression and an 8.62% decline for a team in the same city playing in the other league (this is the relationship between and NBA and WNBA team in the same city) according to fixed effects analysis. Joint statistical testing indicates an even more significant impact when basketball substitutes (both professional leagues and Division I college teams) are considered as a group.

After these characteristics of the local market the most powerful drivers (or detractors) of average single home game attendance are the relative success of the team. Winning percentage and a playoff appearance in the previous year are both expected to increase a team’s average single home game attendance. A one percentage point increase in winning percentage is expected to increase attendance by between .20% (fixed effects) and .36% (censored normal regression), ceterus paribus. This indicates that winning one more game is expected to increase attendance by between .24% and .43%, ceterus paribus. Additionally, going to the playoffs in the previous year is expected to increase attendance by between 4.68% (fixed effects) and 6.56%

(censored normal), ceterus paribus. If the previous year’s winning percentage, championship appearance, and championship victory are also included the effect is expected to be even greater and more significant than a playoff appearance alone (although this is evident because of joint statistical testing, and thus the magnitude is not clear).

All of the findings so far seem fairly intuitive and consistent with the findings of

Rottenberg and other sports economists. However, the significance of characteristics of play (as an indicator of entertainment quality) on attendance is new to this study and should, according to popular media and societal opinion, explain the differences between NBA and WNBA attendance. According to the censored normal regression an additional assist per forty-eight minute game is expected to decrease average single home game attendance by 1.36%, ceterus

paribus. This negative impact of selfless (but boring) play is also evident in the censored normal regression which predicts a decline of 1.16% for each additional assist per forty-eight minute game, ceterus paribus. The fixed effects model also predicts a .4% increase for every additional point scored in a game (holding all else constant, including winning percentage and point differential) and a 1.73% increase for each additional All Star added to the roster. All of the models also indicate points, free throws, and three pointers are jointly significant yet the source and impact of this significance is not clear. Thus, as predicted, attendance is impacted not only by the quality of play but also by the quality of entertainment; as indicated by specific characteristics of play.

Chow Test

As the above results showed, gender had a tremendous impact on attendance. However, in addition to the shift gender caused in the model, it also seemed possible that a completely different model would be, not only appropriate but also, necessary for the two leagues. In Figure

3 (below), for example, a distinct separation of a group of higher attendance teams and lower attendance teams (likely NBA and WNBA teams, respectively) is clear. However, it also seems that these two groups have a different trend with respect to winning percentage (and likely other characteristics as well).

Figure 3 A Chow Test can test this hypothesis. By modeling the male and female data separately the sum of squared residuals will likely decrease. In other words, the predicted values will be closer to the actual values. However, while the squared residuals will decrease with separate models, the smaller sample size will also sacrifice degrees of freedom. The Chow Test will determine if more is gained from the separate, more accurate models, with less degrees of freedom.

[SSRC-(SSRM+SSRF)]/SSRM+SSRF F= ------k/[n-2k]

The Chow Test (Dougherty 2006) tests the significance of an F-statistic found by the formula above. SSR is the sum of squared residuals (with C, M, and F designating combined, female, and male respectively) while k indicates the degrees of freedom for the combined model and n-2k indicates the degrees of freedom remaining with the separate models. By finding all of these numbers we determine that the F-statistic is 2.486. With 27 numerator degrees of freedom

and 308 denominator degrees of freedom the critical value is less than 1.950 (which is the critical value at 24 degrees of freedom in the numerator and 120 degrees of freedom in the denominator) but greater than 1.696 (which is the critical value with 30 degrees of freedom in the numerator and infinite degrees of freedom in the denominator) for significance at the 1% level (StatSoft,

Inc. 2011). Since 2.486 is greater than 1.950, the Chow Test is significant at the 1% level and, thus, separate models are appropriate.

NBA Results

Factors impacting NBA attendance are quite similar to those impacting professional basketball attendance in the combined model. Once again, an increase in population predicts an increase in average home game attendance in the censored normal regression, predicting a 6.31% increase in attendance for a 1% increase in population, ceterus paribus. Somewhat strangely, the fixed effects impact is predicted to be a 40.63% decrease in attendance for a 1% increase in population, ceterus paribus. Because this model looks at changes within organizations and the populations do not typically change drastically over time it is likely this result can be attributed to a few observations which changed locations to cities with greater population but less demand for NBA games. This seems especially possible considering the positive correlation between year and attendance. The censored regression predicts a .85% increase in attendance per year while fixed effects predicts a per year increase of 1.05%, both holding all else constant.

Population tends to increase over time and when it does, its result may have been attributed to a time trend rather than a population change except in the instances (just described) in which the organization relocates.

Once again, performance seems to heavily impact attendance, with the censored normal regression predicting a .56% increase in attendance for a one percentage point increase in

winning percentage (all else held constant) and a 5.25% increase in the present year’s attendance for a trip to the playoffs in the previous year (again, all else held constant). For the fixed effects model these predicted impacts are .28% and 4.48%, respectively. However, as with the combined model, substitutes (specifically, WNBA teams) detract from attendance, predicting a

4.08% decrease in attendance for each additional WNBA team in the same city according to the censored normal model, ceterus paribus. Using the fixed effects model that impact increases to

8.24%.. Interestingly, having more all stars, while positively contributing to attendance in the combined model, is expected to cause a 2.377% decrease in attendance at NBA games, ceterus paribus. This is a surprising result, which I can only explain by teams assuming a greater super star premium on their ticket prices than actually exists, and because of it this the decline in demand is reflective of an inappropriate increase in price (which was not included in the model for reasons explained in the “Methods” section).

Also, like in the combined model, characteristics of play (or how the teams play in order to win) had a significant impact on attendance. In the separate models there were even more significant playing characteristics for NBA teams. The censored normal model predicted a

0.59% increase in attendance for an additional point scored per forty-eight minute game and a

1.2% decline in attendance for an additional assist per forty-eight minute game, holding all else constant in each case. The fixed effects model changed only the predicted magnitudes of these factors to 0.67% and 1.17%, respectively. The fixed effects model also estimated an increase in attendance associated with more blocks and hit free throws (1.71% and 1.00%, ceterus paribus, respectively) and decrease associated with rebounds (0.87%, ceterus paribus). Both models indicated an additional joint significance for previous year’s performance (winning percentage, playoff appearance, championship appearance, and championship victory in the previous year)

and the combination of points, free throws, and three-pointers, both of which are likely positive but the magnitude is not clear. There was also a joint effect from rebounds and assists, which again has an unclear effect, but is likely negative. The NBA model seems to be in line with both my expectations and the expectations from the literature.

WNBA Results

The WNBA, on the other hand only showed significance with the time trend, playoffs, and previous year’s performance. The censored normal regression predicts a 3.75% decrease in attendance every year (ceterus paribus). The fixed effects model similarly shows a 2.76% predicted decline in attendance every year (ceterus airbus). Thus it seems the time trend for the

WNBA is actually the reverse of the NBA, indicating that while NBA games are increasing in popularity and demand, WNBA games are decreasing. However, the effect of playoffs is similarly a positive one, going to the playoffs is predicted to increase a team’s attendance by

13.77%, all else held constant, according to the censored normal model and 9.05%, all else held constant , according to the fixed effects model. There is also a joint positive significance

(although the magnitude and source are not clear) from the previous year’s performance.

Unfortunately, these were the only factors with any kind of statistical significance in the WNBA model.

VI. Implications, Conclusions, and Future Research

As previously mentioned this study is meant to determine what factors are responsible for the difference in attendance between the NBA and WNBA and to expand the current research, which identifies key factors that determine attendance at professional sporting events to include women’s professional sporting events. A common misconception about the WNBA, and women’s sports in general, is that they are inferior to their male counterparts and thus will continue to be consumed in lower quantities until they become more like the men. This study indicates, however, that playing basketball more like men does not bring more fans to WNBA games. WNBA teams, similar to their NBA counterparts, can expect an increase in attendance for improved performance relative to the other teams in the league. However, in contrast to

NBA teams, the characteristics of play WNBA teams used to succeed do not have a significant impact on attendance.

The implications of these findings are key to future research of women’s professional sports. The results reveal that demand for NBA basketball and WNBA basketball cannot be predicted by the same model. While the NBA results were as predicted by my model (which was based on past sports economics models, originally designed by Rottenberg), the same model produced significantly less useful results for the WNBA. Thus, it seems that NBA and WNBA games are not simply the same good of different qualities. The lack of significance for factors that have proven to be significant in men’s sports, and specifically basketball, indicate women’s professional sports, and specifically basketball, are demanded based on different criteria than their male counterparts. For the WNBA, it seems that rather than becoming more like men’s basketball, women’s basketball needs to, instead, determine what factors drive their attendance

in order to make decisions that will put them in the best position for increased attendance rather than continuing to rely on an NBA model, which is not relevant to the WNBA.

However, it is left to future researchers to discover what these factors are. Regrettably, this study did not reveal many factors driving WNBA attendance. A limitation in this study was its reliance on male dominated-models. All of my models were based off of those previously used for men’s professional sports. Future researchers will need to further examine why fans are at WNBA games (or women’s professional sporting events more generally) in order to fully develop their model. My study shows that men’s sports are not the appropriate place to start research for women’s sports, future research will need to determine what that best place to start is.

VII. References

The Association for Professional Basketball Research. (2008). NBA/ABA Home Attendance Totals. Retrieved from http://www.apbr.org/attendance.html Basketball-reference.com. (2011). Retrieved from http://www.basketball-reference.com Dougherty, C. (2006). Chow Test. Economics, London School of Economics, London, England. Retrieved from econ.lse.ac.uk/ie/ieppt/series2/C5D6.pps ESPN. (2011). NBA Attendance Report - 2009. Retrieved from http://espn.go.com/nba/attendance/_/year/2009 Fort, Rodney D. (2005). The golden anniversary of ‘‘the baseball player’s labor market.’’ Journal of Sports Economics. Retrieved from http://jse.sagepub.com/content/6/4/347 Fort, Rodney D. (2006). Sports Economics. Upper Saddle River, NJ: Pearson Education, Inc. Hallhan, C. The Tobit Model: An Example of Maximium Likelihood Estimation with SAS/IML. Retrieved from http://www2.sas.com/proceedings/sugi22/STATS/PAPER293.PDF Inside Arenas (2011). Retrieved from http://insidearenas.com Last, J.V. (2002 May 10). Why white (and other) women can’t jump. The Weekly Standard. Retrieved from http://www.weeklystandard.com/content/Public/Articles/000/000/001/200ofapa.asp Leadley, John C. and Zenon X. Zygmont (2005). When is the honeymoon over? National Basketball Association Attendance 1971-2000. Journal of Sports Economics. Retrieved from http://jse.sagepub.com/content/6/2/203 McGoldrick, KimMarie and Lisa Voeks (2005). “We Got Game!”: An Analysis of Win/Loss Probability and Efficiency Differences Between the NBA and WNBA. Journal of Sports Economics. Retrieved from http://jse.sagepub.com/content/6/1/5 "NBA All-Star Game Rosters." NBA All Star. N.p., 2011. Web. 27 Mar 2011. . NBA Media Ventures (2011). NBA.com. Retrieved from http://www.nba.com NFL Enterprises, LLC (2011). NHL.com. Retrived from http://www.nfl.com NHL Enterprises, L.P. (2011). NHL.comˆ. Retrieved from http://www.nhl.com MLB Advanced Media, L.P. (2011). MLB.com Retrieved from http://www.mlb.com Rottenberg, Simon (1956). The baseball players’ labor market. Journal of Political Economy. Retrieved from http://www.jstor.org/stable/1825886 StatSoft, Inc. (2011). Electronic Statistics Textbook. Tulsa, OK: StatSoft. WEB: http://www.statsoft.com/textbook/. 28

WNBA Enterprises, LLC. (2011). WNBA.com. Retrieved from http://www.wnba.com Winfree (2008). Fan substitutation and the 2004-05 NHL lockout. Journal of Sports Economics. Retrived from http://jse.sagepub.com/content/9/4/425 Women's Basketball Online, . (2010). Season by Season WNBA Attendance. Retrieved from http://womensbasketballonline.com/wnba/attendance/sbsatten.pdf Wooldridge, Jeffrey M. (2009). Introductory Econometrics. Mason, OH: South-Western Cengage Learning. UCLA Academic Technology Services, . (2011). Stata data analysis examples, tobit analysis. Retrieved from http://www.ats.ucla.edu/stat/stata/dae/tobit.htm U.S. Bureau of Labor Statistics. (1997-2010). Quarterly Census of Employment and Wages. U.S. Census Bureau. (1990-2010). Population Estimates. USA Basketball, Inc. (2001). Rules Retrieved from http://www.usabasketball.com/rules/rules.html Zhang, J. J., Pease, D. G., Hui, S. C., & Michaud, T. J. (1995).Variables affecting the spectator decision to attend NBA games. Sport Marketing Quarterly, 4(4), 29-39.

VIII. Appendix

Appendix A. Variables

Name Description Source avgattend Average home attendance ESPN.com Calculated by dividing total home attendance The Association for by number of home games Professional Basketball Research Women’s Basketball Online lavgattend Natural Log of avgattend Formula= ln(avgattend) org Name of Organization Basketball-Reference.com orgcode Unique numerical code for each different organization Pop Population of the team’s MSA United State Census AvgAnSal Average Annual Salary of MSA Bureau of Labor Statistics Year Year of play Basketball-Reference.com Female 1=female, 0=male Basketball-Reference.com Playoff 1=team made playoffs, 0=team did not make Basketball-Reference.com playoffs Ship 1=team played in the championship game, Basketball-Reference.com 0=team did not play in the championship game Champ 1=team won the league 0=team did not win Basketball-Reference.com the league wpcnt Winning Percentage Basketball-Reference.com Formula= games won/games played Pace Estimate of number of possessions per 48 Basketball-Reference.com minute game. Formula= (Team possessions + Opponent Possessions)/ ((2* Minutes Played by the team)/5) Threes Three pointers made per 48 minute game Basketball-Reference.com FreeThrows Free throws made per 48 minute game Basketball-Reference.com PtsFor Points scored by the team per 48 minute Basketball-Reference.com game PtsAgainst Points cored by opponents per 48 minute Basketball-Reference.com game rebounds Rebounds per 48 minute game Basketball-Reference.com Assist Assists per 48 minute game Basketball-Reference.com Steals Steals per 48 minute game Basketball-Reference.com Blocks Blocks per 48 minute game Basketball-Reference.com Turnovers Turnover per 48 minute game Basketball-Reference.com Fouls Fouls per 48 minute game Basketball-Reference.com ALLSTAR Number of players on the team’s roster voted Allstarnba.com 30

to the All Star Game WNBA.com NewName 1= A team with a new name, 0=A team with Basketball-Reference.com the same name as last season NewCity 1= A team located in a new city, 0=A team Basketball-Reference.com that remained in the same city as last year ptdiff Average difference between team and Formula=Points scored by the opponent scoring team per 48 minute game – Points scored against the team per 48 minute game SubSame Number of other teams in the same league Basketball-Reference.com and same MSA SubOthBball Number of teams in the other professional Basketball-Reference.com basketball league in the same MSA SubOtherSport Number of MLB, NHL, and NFL teams in MLB.com, NHL.com, and the MSA NFL.com SubCollege Number of Division I college basketball NCAA.org teams of the same gender in the same state playoff_1 1=team made playoffs, 0=team did not make Basketball-Reference.com playoffs (in the previous season) ship_1 1=team played in the championship game, Basketball-Reference.com 0=team did not play in the championship game (in the previous season) champ_1 1=team won the league 0=team did not win Basketball-Reference.com the league (in the previous season) wpcnt_1 Winning Percentage (in the previous season) Basketball-Reference.com Formula= games won/games played ArenaCap Arena Capactiy InsideArenas.com AttPctCap Average percent of capacity filled Formula= avgattend/ArenaCap Censored 1=AttPctCap==1, 0=AttPctCap<1 lengthgame Minutes in a Game USA Basketball Rules of the Game lengthseason Games in a Season BasketballReference.com lpop Natural loge of population Formula = ln(pop) lsal Natural log of average annual salary Formula = ln(avgansal) CPI Consumer Price Index for that MSA9 in that BLS year dsal Deflated average annual salary Formula = avgansal/CPI ldsal Natural log of deflated annual salary Formula = ln(dsal)

9 CPIs were not available for the following MSAs and so the average CPI for cities of their approximate size and region (given in parenthesis where A indicates a population greater than 1.5 million and B/C indicates a population between 50,000 and 1.5 million) were used instead: Charlotte (South B/C), Indianapolis (Midwest A), Connecticut (Northeast B/C), New Orleans (South B/C), Oklahoma City (Midwest A), Orlando (South B/C in 97 and A in 98-09), Phoenix (West A), San Antonio (South A), Sacramento (West A), and Salt Lake City (West B/C). 31

Appendix B. Combined OLS Results

Joint Significance Tests

( 1 ) pl a y o f f _ 1 = 0 ( 2 ) sh i p _ 1 = 0 ( 1 ) pt s f o r = 0 ( 3 ) ch a m p _ 1 = 0 ( 2 ) fr e e t h r o w s = 0 ( 4 ) wp c n t _ 1 = 0 ( 3 ) th r e e s = 0

F ( 4 , 3 3 5 ) = 6. 6 8 F ( 3 , 3 3 5 ) = 3. 2 5 P r o b > F = 0 . 0 0 0 0 P r o b > F = 0 . 0 2 1 9

( 1 ) pl a y o f f = 0 ( 1 ) su b o t h b b a l l = 0 ( 2 ) sh i p = 0 ( 1 ) st e a l s = 0 ( 2 ) su b c o l l e g e = 0 ( 3 ) ch a m p = 0 ( 2 ) bl o c k s = 0

F ( 2 , 3 3 5 ) = 0. 7 8 F ( 3 , 3 3 5 ) = 0. 3 2 F ( 2 , 3 3 5 ) = 0. 6 2 P r o b > F = 0 . 4 5 8 1 P r o b > F = 0 . 8 1 3 7 P r o b > F = 0 . 5 3 7 8

( 1 ) tu r n o v e r s = 0 ( 1 ) ne w n a m e = 0 ( 1 ) re b o u n d s = 0 ( 2 ) fo u l s = 0 ( 2 ) ne w c i t y = 0 ( 2 ) as s i s t = 0

F ( 2 , 3 3 5 ) = 0. 1 8 F ( 2 , 3 3 5 ) = 2. 5 3 F ( 2 , 3 3 5 ) = 3. 8 0 P r o b > F = 0 . 8 3 5 3 P r o b > F = 0 . 0 8 1 4 P r o b > F = 0 . 0 2 3 4

Appendix C. Combined Censored Normal Results

Joint Significance Tests

( 1 ) [m o d e l ] p l a y o f f _ 1 = 0 ( 2 ) [m o d e l ] s h i p _ 1 = 0 ( 1 ) [m o d e l ] p t s f o r = 0 ( 1 ) [m o d e l ] s u b s a m e = 0 ( 3 ) [m o d e l ] c h a m p _ 1 = 0 ( 2 ) [m o d e l ] f r e e t h r o w s = 0 ( 2 ) [m o d e l ] s u b o t h b b a l l = 0 ( 4 ) [m o d e l ] w p c n t _ 1 = 0 ( 3 ) [m o d e l ] t h r e e s = 0 ( 3 ) [m o d e l ] s u b c o l l e g e = 0

F ( 4 , 3 3 6 ) = 8. 3 2 F ( 3 , 3 3 6 ) = 3. 1 1 F ( 3 , 3 3 6 ) = 4. 3 9 P r o b > F = 0 . 0 0 0 0 P r o b > F = 0 . 0 2 6 4 P r o b > F = 0 . 0 0 4 8

( 1 ) [m o d e l ] p l a y o f f = 0 ( 2 ) [m o d e l ] s h i p = 0 ( 1 ) [m o d e l ] s t e a l s = 0 ( 1 ) [m o d e l ] t u r n o v e r s = 0 ( 3 ) [m o d e l ] c h a m p = 0 ( 2 ) [m o d e l ] b l o c k s = 0 ( 2 ) [m o d e l ] f o u l s = 0

F ( 3 , 3 3 6 ) = 0. 3 3 F ( 2 , 3 3 6 ) = 0. 5 4 F ( 2 , 3 3 6 ) = 0. 6 2 P r o b > F = 0 . 8 0 6 5 P r o b > F = 0 . 5 8 3 0 P r o b > F = 0 . 5 3 9 2

( 1 ) [m o d e l ] n e w n a m e = 0 ( 1 ) [m o d e l ] r e b o u n d s = 0 ( 2 ) [m o d e l ] n e w c i t y = 0 ( 2 ) [m o d e l ] a s s i s t = 0

F ( 2 , 3 3 6 ) = 2. 7 7 F ( 2 , 3 3 6 ) = 4. 4 1 P r o b > F = 0 . 0 6 4 4 P r o b > F = 0 . 0 1 2 8

Appendix D Combined Fixed Effects Results

Joint Significance Tests

( 1 ) pl a y o f f _ 1 = 0 ( 2 ) sh i p _ 1 = 0 ( 1 ) pt s f o r = 0 ( 1 ) pl a y o f f = 0 ( 3 ) ch a m p _ 1 = 0 ( 2 ) fr e e t h r o w s = 0 ( 2 ) sh i p = 0 ( 4 ) wp c n t _ 1 = 0 ( 3 ) th r e e s = 0 ( 3 ) ch a m p = 0

F ( 4 , 2 9 1 ) = 6. 6 5 F ( 3 , 2 9 1 ) = 4. 0 5 F ( 3 , 2 9 1 ) = 0. 2 6 P r o b > F = 0 . 0 0 0 0 P r o b > F = 0 . 0 0 7 7 P r o b > F = 0 . 8 5 3 3

( 1 ) st e a l s = 0 ( 1 ) tu r n o v e r s = 0 ( 1 ) ne w n a m e = 0 ( 2 ) bl o c k s = 0 ( 2 ) fo u l s = 0 ( 2 ) ne w c i t y = 0

F ( 2 , 2 9 1 ) = 1. 5 7 F ( 2 , 2 9 1 ) = 0. 0 6 F ( 2 , 2 9 1 ) = 1. 2 6 P r o b > F = 0 . 2 0 8 9 P r o b > F = 0 . 9 4 4 5 P r o b > F = 0 . 2 8 6 2

( 1 ) re b o u n d s = 0 ( 2 ) as s i s t = 0

F ( 2 , 2 9 1 ) = 7. 2 6 P r o b > F = 0 . 0 0 0 8

Appendix E. NBA OLS Results

Joint Significance Tests

( 1 ) pl a y o f f _ 1 = 0 ( 2 ) sh i p _ 1 = 0 ( 1 ) pt s f o r = 0 ( 1 ) su b o t h b b a l l = 0 ( 3 ) ch a m p _ 1 = 0 ( 2 ) fr e e t h r o w s = 0 ( 2 ) su b o t h e r s p o r t = 0 ( 4 ) wp c n t _ 1 = 0 ( 3 ) th r e e s = 0 ( 3 ) su b c o l l e g e = 0

F ( 4 , 2 2 5 ) = 3. 1 1 F ( 3 , 2 2 5 ) = 3. 3 7 F ( 3 , 2 2 5 ) = 2. 6 9 P r o b > F = 0 . 0 1 6 3 P r o b > F = 0 . 0 1 9 3 P r o b > F = 0 . 0 4 7 3

( 1 ) pl a y o f f = 0 ( 2 ) sh i p = 0 ( 1 ) st e a l s = 0 ( 1 ) tu r n o v e r s = 0 ( 3 ) ch a m p = 0 ( 2 ) bl o c k s = 0 ( 2 ) fo u l s = 0

F ( 3 , 2 2 5 ) = 0. 7 5 F ( 2 , 2 2 5 ) = 0. 5 1 F ( 2 , 2 2 5 ) = 0. 5 1 P r o b > F = 0 . 5 2 6 0 P r o b > F = 0 . 5 9 9 7 P r o b > F = 0 . 6 0 2 7

( 1 ) ne w n a m e = 0 ( 1 ) re b o u n d s = 0 ( 2 ) ne w c i t y = 0 ( 2 ) as s i s t = 0

F ( 2 , 2 2 5 ) = 2. 2 6 F ( 2 , 2 2 5 ) = 4. 0 2 P r o b > F = 0 . 1 0 6 6 P r o b > F = 0 . 0 1 9 3

Appendix F. NBA Censored Normal Results

Joint Significance Tests

( 1 ) [m o d e l ] p l a y o f f _ 1 = 0 ( 2 ) [m o d e l ] s h i p _ 1 = 0 ( 1 ) [m o d e l ] p t s f o r = 0 ( 1 ) [m o d e l ] s u b o t h b b a l l = 0 ( 3 ) [m o d e l ] c h a m p _ 1 = 0 ( 2 ) [m o d e l ] f r e e t h r o w s = 0 ( 2 ) [m o d e l ] s u b o t h e r s p o r t = 0 ( 4 ) [m o d e l ] w p c n t _ 1 = 0 ( 3 ) [m o d e l ] t h r e e s = 0 ( 3 ) [m o d e l ] s u b c o l l e g e = 0

F ( 4 , 2 2 6 ) = 4. 8 9 F ( 3 , 2 2 6 ) = 3. 2 4 F ( 3 , 2 2 6 ) = 2. 4 0 P r o b > F = 0 . 0 0 0 9 P r o b > F = 0 . 0 2 2 9 P r o b > F = 0 . 0 6 9 0

F ( 3 , 2 2 6 ) = 1. 2 8 F ( 2 , 2 2 6 ) = 0. 4 3 F ( 2 , 2 2 6 ) = 1. 0 4 P r o b > F = 0 . 2 8 1 4 P r o b > F = 0 . 6 5 1 9 P r o b > F = 0 . 3 5 3 5

( 1 ) [m o d e l ] n e w n a m e = 0 ( 1 ) [m o d e l ] r e b o u n d s = 0 ( 2 ) [m o d e l ] n e w c i t y = 0 ( 2 ) [m o d e l ] a s s i s t = 0

F ( 2 , 2 2 6 ) = 2. 4 8 F ( 2 , 2 2 6 ) = 4. 4 4 P r o b > F = 0 . 0 8 5 9 P r o b > F = 0 . 0 1 2 9

Appendix H. NBA Fixed Effects Results

Joint Significance Tests

( 1 ) pl a y o f f _ 1 = 0 ( 2 ) sh i p _ 1 = 0 ( 1 ) pt s f o r = 0 ( 3 ) ch a m p _ 1 = 0 ( 2 ) fr e e t h r o w s = 0 ( 1 ) su b o t h e r s p o r t = 0 ( 4 ) wp c n t _ 1 = 0 ( 3 ) th r e e s = 0 ( 2 ) su b c o l l e g e = 0

F ( 4 , 1 9 9 ) = 6. 7 6 F ( 3 , 1 9 9 ) = 7. 2 5 F ( 2 , 1 9 9 ) = 2. 4 9 P r o b > F = 0 . 0 0 0 0 P r o b > F = 0 . 0 0 0 1 P r o b > F = 0 . 0 8 5 5

( 1 ) pl a y o f f = 0 ( 2 ) sh i p = 0 ( 1 ) st e a l s = 0 ( 1 ) tu r n o v e r s = 0 ( 3 ) ch a m p = 0 ( 2 ) bl o c k s = 0 ( 2 ) fo u l s = 0

F ( 3 , 1 9 9 ) = 0. 1 7 F ( 2 , 1 9 9 ) = 5. 1 5 F ( 2 , 1 9 9 ) = 0. 6 5 P r o b > F = 0 . 9 1 4 4 P r o b > F = 0 . 0 0 6 6 P r o b > F = 0 . 5 2 1 0

( 1 ) ne w n a m e = 0 ( 2 ) ne w c i t y = 0 ( 1 ) re b o u n d s = 0 C o n s t r a i n t 1 d r o p p e d ( 2 ) as s i s t = 0

F ( 1 , 1 9 9 ) = 1. 2 1 F ( 2 , 1 9 9 ) = 10 . 1 8 P r o b > F = 0 . 2 7 2 3 P r o b > F = 0. 0 0 0 1

Appendix I WNBA OLS Results

Joint Significance Tests

( 1 ) pl a y o f f _ 1 = 0 ( 1 ) su b s a m e = 0 ( 2 ) sh i p _ 1 = 0 ( 1 ) pt s f o r = 0 ( 2 ) su b o t h b b a l l = 0 ( 3 ) ch a m p _ 1 = 0 ( 2 ) fr e e t h r o w s = 0 ( 3 ) su b c o l l e g e = 0 ( 4 ) wp c n t _ 1 = 0 ( 3 ) th r e e s = 0 C o n s t r a i n t 1 d r o p p e d

F ( 4 , 8 3 ) = 2. 8 6 F ( 3 , 8 3 ) = 0. 6 2 F ( 2 , 8 3 ) = 0. 1 0 P r o b > F = 0 . 0 2 8 4 P r o b > F = 0 . 6 0 4 7 P r o b > F = 0 . 9 0 2 0

( 1 ) wp c n t = 0 ( 2 ) pl a y o f f = 0 ( 3 ) sh i p = 0 ( 1 ) st e a l s = 0 ( 1 ) tu r n o v e r s = 0 ( 4 ) ch a m p = 0 ( 2 ) bl o c k s = 0 ( 2 ) fo u l s = 0

F ( 4 , 8 3 ) = 1. 7 4 F ( 2 , 8 3 ) = 0. 8 9 F ( 2 , 8 3 ) = 0. 3 4 P r o b > F = 0 . 1 4 9 1 P r o b > F = 0 . 4 1 5 6 P r o b > F = 0 . 7 1 2 8

( 1 ) ne w n a m e = 0 ( 2 ) ne w c i t y = 0 ( 1 ) re b o u n d s = 0 C o n s t r a i n t 2 d r o p p e d ( 2 ) as s i s t = 0

F ( 1 , 8 3 ) = 0. 2 5 F ( 2 , 8 3 ) = 1. 1 2 P r o b > F = 0 . 6 1 8 2 P r o b > F = 0 . 3 2 9 9

Appendix I WNBA Censored Normal Results

Joint Significance Tests

( 1 ) [m o d e l ] p l a y o f f _ 1 = 0 ( 2 ) [m o d e l ] s h i p _ 1 = 0 ( 1 ) [m o d e l ] p t s f o r = 0 ( 3 ) [m o d e l ] c h a m p _ 1 = 0 ( 2 ) [m o d e l ] f r e e t h r o w s = 0 ( 1 ) [m o d e l ] s u b o t h b b a l l = 0 ( 4 ) [m o d e l ] w p c n t _ 1 = 0 ( 3 ) [m o d e l ] t h r e e s = 0 ( 2 ) [m o d e l ] s u b c o l l e g e = 0

F ( 4 , 8 4 ) = 3. 8 2 F ( 3 , 8 4 ) = 0. 8 3 F ( 2 , 8 4 ) = 0. 1 4 P r o b > F = 0 . 0 0 6 6 P r o b > F = 0 . 4 8 2 2 P r o b > F = 0 . 8 7 1 2

( 1 ) [m o d e l ] w p c n t = 0 ( 2 ) [m o d e l ] p l a y o f f = 0 ( 3 ) [m o d e l ] s h i p = 0 ( 1 ) [m o d e l ] s t e a l s = 0 ( 1 ) [m o d e l ] t u r n o v e r s = 0 ( 4 ) [m o d e l ] c h a m p = 0 ( 2 ) [m o d e l ] b l o c k s = 0 ( 2 ) [m o d e l ] f o u l s = 0

F ( 4 , 8 4 ) = 2. 3 3 F ( 2 , 8 4 ) = 1. 1 9 F ( 2 , 8 4 ) = 0. 4 5 P r o b > F = 0 . 0 6 3 0 P r o b > F = 0 . 3 1 0 2 P r o b > F = 0 . 6 3 6 2

( 1 ) [m o d e l ] r e b o u n d s = 0 ( 2 ) [m o d e l ] a s s i s t = 0

F ( 2 , 8 4 ) = 1. 5 0 P r o b > F = 0 . 2 2 8 4

Appendix J. WNBA Fixed Effects Results

Joint Significance Tests

F ( 4 , 6 7 ) = 3. 6 1 F ( 3 , 6 7 ) = 1. 1 8 F ( 3 , 6 7 ) = 1. 5 2 P r o b > F = 0 . 0 1 0 0 P r o b > F = 0 . 3 2 2 7 P r o b > F = 0 . 2 1 8 0

( 1 ) ne w n a m e = 0 ( 1 ) st e a l s = 0 ( 1 ) tu r n o v e r s = 0 ( 2 ) ne w c i t y = 0 ( 2 ) bl o c k s = 0 ( 2 ) fo u l s = 0 C o n s t r a i n t 2 d r o p p e d

F ( 2 , 6 7 ) = 1. 4 2 F ( 2 , 6 7 ) = 1. 4 2 F ( 1 , 6 7 ) = 0. 0 6 P r o b > F = 0 . 2 4 9 4 P r o b > F = 0 . 2 5 0 0 P r o b > F = 0 . 8 0 5 3

( 1 ) re b o u n d s = 0 ( 2 ) as s i s t = 0

F ( 2 , 6 7 ) = 1. 3 7 P r o b > F = 0 . 2 6 0 5