The estimated rents of a top-flight men's college hockey player.

Kahane, Leo H.

Introduction

It is no secret that college athletics has become big business. A simple look at recent financial data illustrates this point. For example, data collected by the U.S. Department of Education's Office of Postsecondary Education, under the Equity in Athletics Disclosure Act (EADA), shows that 2008 athletics revenues from the National Collegiate Athletic Association (NCAA) Division I schools was approximately $4.4 billion, more than half of which came from football (see Table 1). For the period from 2004 to 2008, the real growth in revenues amounted to 30.6%, while growth in expenditures was 27.6%. The NCAA itself has become a sizeable economic entity. The 2008-2009 annual report of the NCAA reported a total operation revenue of $661 million. The late NCAA President Myles Brand earned $1.72 million a year in salary and benefits during 2008 (Perry, 2010). Adding to this is the spiraling salaries paid to coaches at top NCAA schools. According to data reported by USA Today (2010), of the 110 Football Bowl Subdivision (FBS) coaches for which data were available, 56 had total salaries (excluding bonuses) of $1 million or more in 2009 compared to just five coaches in 1999. Pete Carroll of the University of Southern California had a reported total salary of approximately $4.4 million. The average total salary for all 110 coaches was approximately $1.3 million (USA Today, 2010). As for college hockey coach salaries, data were not readily available, but the University of New Hampshire's men's hockey coach, Dick Umile, was reported to have earned $382,000 in salary and deferred income in 2008, making him the highest paid state worker that year (The Associated Press, 2009).

The business of college sports, however, would not exist without one key component: the student-athlete. Yet because of NCAA eligibility rules, student-athletes are not allowed to be compensated for their athletic skills beyond a possible athletic scholarship (plus minor expenses). The NCAA also restricts the ability of students to move between colleges. These restrictions imposed by the NCAA have led economists to describe the institution as being a classic example of a cartel. For example, Fleisher, Goff, and Tollison (1992) wrote, "... economists generally view the NCAA as a cartel. They hold this view because the NCAA has historically devised rules to restrict output (the number of games played), and to restrict competition for inputs (student-athletes)" (p. 5). This characterization of the NCAA implies that student-athletes generate economic rents that are eventually distributed to various stake holders, including coaches, athletic directors, other college administrators, and the NCAA itself. (1) A question that arises is just how much revenue does a top college athlete generate? Several studies, which we discuss in detail below, have attempted to answer this question for college basketball and football. This paper adds to the extant literature in two ways. First, it considers the marginal revenue product (MRP) of top men's college ice hockey players, a sport yet to be analyzed. Second, unlike previous studies that employed a single cross-section of data, we utilized a panel dataset that not only increased the sample size but allowed for better control of college-specific attributes that may have affected the MRP generated by top college athletes as well.

Empirical results, presented in detail below, showed that top-flight college hockey players generate between $131,000 and $165,000 in added revenues to schools. The NCAA reports that the average value of an athletic scholarship for 2008 is between $14,000 for in-state public schools to $32,000 for private schools (National Collegiate Athletic Association, 2010). This implies that a premium college hockey player generates rents in excess of $100,000 per year for the typical institution.

Related Research

Brown was the first to estimate the MRP of a college athlete in his 1993 paper, which computed the value generated by a premium college football player. He took the basic approach to modeling a team's revenues as a function of the size of the local market, the quality of the team, the quality of the team's opponents, and a measure of the number of premium college football players on the team. The latter variable was proxied by computing the number of players on the team who were eventually selected in the National Football League's rookie draft. (2) Using data for NCAA Division I-A football teams, (3) Brown finds that a premium college football player generated approximately $500,000 in revenues for their team. (4) In a related paper, Brown (1994) took the same approach but applied it to men's NCAA Division I college basketball. His findings showed that top-level college basketball players generated annual economic revenues in the range of about $871,000 to $1.28 million.

Turning to women's college athletics, Brown and Jewell (2006) investigated the MRP of the top 10 college basketball conference players who were eventually drafted by a team in the Women's National Basketball Association (WNBA). Their findings show that the typical college team earned approximately $241,000 from the play of a future WNBA draftee. (5)

Data Description and Model

In the three aforementioned papers, a single cross-section of data was used to estimate the MRP of premium college athletes, resulting in samples as small as 39 observations (Brown, 1993) and 46 observations (Brown, 1994). (6) The present study employed a panel dataset that covered four men's college hockey seasons (2005-2008) and produced a sample size of 172 observations. The data employed were for NCAA Division I college hockey teams. There are six conferences that make up Division I hockey: the Atlantic Hockey Association (AHA), the Central Collegiate Hockey Association (CCHA), College Hockey America (CHA), the Eastern College Athletic Conference (ECAC), the Hockey East Association (HEA), and the Western Collegiate Hockey Association (WCHA). Two of these conferences, however, represent substantially lesser quality hockey. As shown in Table 2, the AHA and CHA have never won, or been the runner-up in, the NCAA Division I college championship, going as far back as 1978. In addition, for the period covered by the dataset (2005-2008), no college players on the teams in these conferences were drafted by National Hockey League (NHL) teams. Therefore, only the top four conferences--CCHA, ECAC, HEA, and WCHA--were included in our analysis. (7)

Within these four conferences, the revenues generated from hockey differed substantially. As seen in Figure 1, the WCHA generated the greatest revenues per game among the four conferences in 2008--the mean value totaled more than $156,000 compared to the ECAC with a mean value of approximately $76,000 per game, (the lowest value). As for the importance of hockey revenues overall, Figure 2 shows a box plot of the proportion of total men's sports revenues accounted for by men's hockey. As is evident from the graph, there is considerable variation both within and between conferences. (8) The HEA exhibits the smallest dispersion of relative revenues--as measured by the interquartile range, shown in the graph as the height of the gray box--while the CCHA has the largest dispersion. Of the four conferences, the WCHA men's hockey teams had the highest proportion with a median value of 19.7% of total men's sports revenues. In comparison, the CCHA hockey programs accounted for a median value of only 7.3% of total revenues for all men's sports. The dominance of the WCHA in both revenues per game and relative hockey revenues (also reflected in Table 2) was driven by several college hockey powerhouses in the league, such as the University of Wisconsin, the University of Denver, the University of Minnesota, and the University of North Dakota. Collectively this group won 14 of the 31 national championships during the period from 1978 to 2008. (9)

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

In order to estimate the value of a top-flight college hockey player, we used the following model:

[y.sub.it]=[[alpha].sub.i]+[[gamma].sub.t]+[beta][x.sub.it]+[[epsilon].sub.it] (1)

The dependent variable, [y.sub.it], is real revenues per game (in 2008 dollars) for team i in season t. The vector [x.sub.it] contains a set of covariates that are expected to explain team revenues per game, [beta] is vector of parameters to be estimated, and is an idiosyncratic error term. The variable [[alpha].sub.i] is a vector of individual effects, and [[gamma].sub.t] is a vector of year dummies.

The key variable of interest included in [x.sub.it] is the measure that represents the number of premium hockey players on a team. We took the approach of Brown (e.g., 1993, 1994, 2011) and computed the number of players on a college hockey team who were eventually drafted by an NHL team. (10) One complication that potentially obscured the effects of a premium hockey player on team revenues was the visibility of the player. That is, a future NHL draftee may only play a few games on a college hockey team before leaving to play professional hockey. In that case, it is unlikely that the few games played by such a player would have an appreciable impact on team revenues. In order to control for such cases, the number of NHL draftees we computed was limited to college players that played at least 20 games for their college team. (11) As reported in the descriptive statistics provided in Table 3 a, the average Division I college hockey team had approximately one premium player; the maximum on a team was 5 premium players.

As to whether there was significant variation both within and between teams, Table 3b provides a breakdown of the standard deviation into the within and between components for both team revenues and the number of NHL draftees. As can be seen in Table 3b, most of the variation occurs between teams, yet there is considerable variation within teams (especially for the number of NHL draftees). This further emphasizes the usefulness of the panel data estimation in identifying the effects of premier hockey players on team revenues.

We included a number of control variables in [x.sub.it] which were expected to affect team revenues. One was the size of the student population. It was assumed that, all else equal, colleges with larger student populations would earn greater hockey revenues. (12) Another measure contained in [x.sub.it] was a measure of team quality. To measure team quality, data were collected for college hockey team rankings polls: one produced by USA Today (http://www.usatoday.com/sports/college/hockey/usatmen.htm) and the other by U.S. College Hockey Online (USCHO; http://www.uscho.com/rankings/). The top 15 ranked teams from each poll were given a score of 15 if they were the number one ranked team, 14 for the number two ranked team, and so on. The average of the two scores--taken from the USA Today poll and the USCHO poll--was computed and used to construct the variable team rank. Other things equal, it was expected that the greater the value the team quality (as proxied by team rank), the greater the revenues the team would earn. (13)

Lastly, included in [x.sub.it] are a set of dummy variables for conference membership. This was intended to control for the possibility that revenues might differ across conferences due perhaps in part to regional differences in the quality of play, interest in the sport, and the desire to attend hockey games.

Estimation Approach and Results

The dataset employed to estimate the model shown in Equation 1 contains four seasons of data for 43 teams, which belong to the four conferences noted earlier. This resulted in a total sample size of 172 observations. With regard to estimation methodology, several issues arose. First, as noted by Brown (e.g., 1993, 1994, 2011) the number of NHL draftees may be endogenous as schools with larger revenues may be able to attract and recruit higher skilled college hockey players. In order to test for this possibility, a Hausman test was employed. The results did not support endogeniety. (14)

A second issue regarding methodology was whether a fixed- or random-effects regression was appropriate. A Hausman test for these two competing approaches supported the use of the more efficient random-effects estimation. (15) For completeness, results from the fixed- and random-effects estimations were presented. (16)

Lastly, a normality test for the distribution of the log of real revenues per game did not support normality. (17) In such cases, use of least-squares estimation methods could create problems for inference tests based on the usual standard errors and t statistics. To address this possible problem, pooled quantile regressions were estimated with bootstrapped standard errors. (18) Estimation results appear in Table 4.

Comparing the fixed- and random-effects results shown in Table 4, it was evident that, with the exception of student population, the regressions produced very similar estimated coefficients. Given the greater efficiency of the random-effects model, we focused on those results. The key variable, number of NHL draftees, had a positive estimated coefficient, which was significant at the 5% level. Given that the dependent variable was in natural logs, the estimated coefficient implied that an increase in one future NHL draftee increased team revenues per game by an estimated 7%, all else equal. In terms of dollars, using the mean value for real revenues per game (shown in Table 3a) translated to an additional $7,285 per game, or approximately $131,000 over a typical season. (19)

The estimated coefficients of the control variables have the predicted signs. The coefficient to student population was positive and significant at the 5% level and suggested that an additional 1,000 students was expected to increase real revenues per game by approximately 1.6%, all else equal. Concerning team quality, team rank had an estimated coefficient that was positive and significant at the 1% level. The results implied that an improvement in the rankings by one place would boost revenues by about 1.6%, other things equal. The coefficients to the year dummies were positive and increased in magnitude over time; however, they were significant only for 2007 and 2008. This suggested that, compared to the base year of 2005, revenues had generally been growing for the typical team during these last 2 years. Lastly, the conference dummies suggested that teams in the WCHA, HEA, and ECAC conferences tend to earn greater revenues per game in comparison to the base case of the CCHA. This conforms to the earlier analysis of Table 2 and Figures 1 and 2 and likely reflects a greater regional interest in hockey for these teams.

Regarding the quantile regression results, Table 4 presents the estimates for the 25th, 50th, and 75th quantiles. Of the three quantiles estimated, only the 50th quantile (median) regression produced a statistically significant coefficient for the number of NHL draftees; thus, we focused on these results. All of the coefficients in this regression had the same sign as those in the random-effects regression. The estimated coefficient for the number of NHL draftees was positive and significant at the 5% level. Given that, in this regression, the dependent variable was real revenues per game (in thousands), the results suggested that one additional future NHL draftee was expected to increase team revenues per game by $9,161 or by approximately $165,000 over a typical 18 home game schedule. The estimated coefficients in the year dummies and student population variables were not statistically significant. Team rank, however, was positive and significant at the 1% level. Its estimated coefficient suggested that an improvement by one place would increase team revenues per game by approximately $4,600, all else equal. Finally, as with the random-effects estimates, HEA, ECAC, and WCHA conference teams tend to earn greater revenues per game than the CCHA.

Conclusion

The empirical results reported in this paper estimated the MRP of an elite college hockey player to be in the range of approximately $131,000 to $165,000. While these estimated MRPs pale in comparison to those of elite college football and basketball players, they were much greater than the estimated value ($14,000 to $32,000) of an athletic scholarship noted earlier; they yielded a net gain to the college. Furthermore, these gains were multiplied for teams with more than one elite hockey player. For example, in 2006, the University of Michigan had five players on the team who were eventually drafted by the NHL. Based on the estimates reported above, these players collectively would have boosted real team revenues by an impressive sum of an estimated $655,000 to $825,000 for the University.

Concerning the direction of future research on this topic, several ideas arise. One obvious improvement would be to increase the sample size. While this study works with a sample that is larger than previous studies, even larger samples are certainly possible. (20)

A second extension has to do with the revenue data used in this study. The revenue data used in the analysis was a combination of various hockey revenue sources. The EADA survey form that teams fill out asks for total revenues, which may include "... revenues from appearance guarantees and options, an athletic conference, tournament or bowl games, concessions, contributions from alumni and others, institutional support, program advertising and sales, radio and television, royalties, signage and other sponsorships, sport camps, state or other government support, student activity fees, ticket and luxury box sales, and any other revenues attributable to intercollegiate athletic activities" (https://surveys.ope.ed.gov/athletics/PrintFormsView.aspx?id=2). To the extent that premier hockey players do not directly impact certain categories of hockey revenues (e.g., institutional support or student fees), this might have lead to biased estimates for the revenue effects of premier hockey players in the regressions included in this study. A better approach would be to follow Brown (2011) and utilize a more detailed breakdown of team revenues so as to allow for a more refined estimate of the MRP of premium college hockey players. Unfortunately, to date, such data are not publically available.

A third extension might be to consider the substitutability between sports within schools. That is, is it the case the schools with large football programs tend to have reduced attendance and revenues for their hockey programs? While the conference dummies included in this present analysis may partially control for this possibility, a more thorough investigation into this issue is possible.

Lastly, another possibility for future research has to do with the argument that elite college athletes, because they often generate net positive revenues for colleges, are exploited and perhaps should receive payments beyond the limited sums allowed under NCAA rules. Such a paper, which would have more of a policy focus than the present one, might first begin by summarizing the collective findings of this and similar papers on just how much revenue elite college athletes generate for their institution. (21)

References

Brown, R. W. (1993). An estimate of the rent generated by a premium college football player. Economic Inquiry, 31, 671-684.

Brown, R. W. (1994). Measuring cartel rents in the college basketball player recruitment market. Applied Economics, 26, 27-34.

Brown, R. W. (2011). Research note: Estimates of college football player rents. Journal of Sports Economics, 12, 200-212.

Brown, R. W., & Jewell, R. T. (2006). The marginal revenue product of a women's college basketball player. Industrial Relations, 45(1), 96-101.

Fleisher, A. A., III, Goff, B. L., & Tollison, R. D. (1992). The National Collegiate Athletic Association: A study in cartel behavior. Chicago, IL: The University of Chicago Press.

Koenker, R. (2005). Quantile regression. Cambridge, UK: Cambridge University Press.

Koenker, R., & Hallock, K. (2001). Quantile regression. Journal of Economic Perspectives, 15, 143-156. National Collegiate Athletic Association. (2010). Behind the blue disk: FBS athletic revenues and expenses. Retrieved December 17, 2010, from http://www.ncaa.org/wps/wcm/connect/public/NCAA/Resources/Behind+the+Blue+Disk/Behind+the+Blue+Disk++FBS+Athletic+Re venues+and+Expenses

Perry, N. (2010). UW President Mark Emmert leaving to head NCAA. The Seattle Times. Retrieved June 4, 2010, from http://seattletimes.nwsource.com/html/localnews/2011716909_emmert28m.html

The Associated Press. (2009). UNif hockey coach is highest paid. Retrieved January 5, 2011, from http://www.concordmonitor.com/article/unh-hockey-coach-is-highest-paid

USA Today. (2009). Analyzing salaries for Football Bowl Subdivision coaches. Retrieved October 21, 2010, from http://www.usatoday.com/sports/college/football/2009-coaches-contractsdatabase.htm

Endnotes

(1) Revenues generated may also be used by colleges to cross-subsidize other non- or low-revenue sports.

(2) Brown (1993) works with data from the 1988-1989 college football season. The number of premium college football players is computed by adding up the number of players on a given team who were drafted in either the 1989, 1990, or 1991 NFL rookie drafts.

(3) In 2006, the NCAA Division I-A was renamed the FBS.

(4) In a follow-up paper, Brown (2011) makes use of less aggregated data to refine his earlier estimated MRP of college football players. His new results suggest that future NFL-draftees generate in excess of $1.1 million in added revenues.

(5) Brown and Jewell (2006) also estimate the MRP of future WNBA draftees using a quantile regression methodology. The results show that the added revenue from a premium women's college basketball player varies greatly over the conditional revenues distribution, with gains ranging from about $38,000 at the 20th quantile to about $400,000 at the 80th quantile for revenues.

(6) Brown and Jewell (2006) use 112 observations. Brown (2011) uses 86 observations in his analysis.

(7) Wayne State University dropped their men's Division I ice hockey program in 2007 and, as a result, is not included in the dataset.

(8) The one outlier shown in Figure 2 is for Colorado College where the men's hockey program accounted for approximately 58% of all men's sports revenues in 2008.

(9) In addition, the CCHA is the home for several large universities known for their football programs. For example, the CCHA includes football powerhouses Ohio State University, University of Michigan, and the University of Notre Dame. The presence of these large football programs may reduce the relative importance of their men's hockey programs.

(10) In the dataset employed, all college hockey players drafted by the NHL were drafted by the time they finished their second year of college hockey play.

(11) There were a total of six players that did not achieve the 20 game minimum requirement. Regressions using all NHL draftees, regardless of the number of games they played for their college team, produced similar estimated coefficients but with slightly weaker significance levels for the number of draftees measure.

(12) Brown (1993, 1994, 2011) and Brown and Jewell (2006) controlled for market size differences by employing various measures of local population. Assuming that population measures for the periods covered by the present analysis are unlikely to differ significantly, the variables in a should capture population differences across teams' markets.

(13) Brown (1993, 1994, 2011) and Brown and Jewell (2006) included a measure of a team's opponents' quality as a covariate. The measure had mixed results in terms of statistical significance across these studies. A measure of a team's opponents' ranking was included in the present regression model. It was not found to be statistically significant and was thus dropped from the model, leaving the remaining coefficients little changed.

(14) A Hausman test for a simple fixed-effect, versus a two-stage IV regression, produced a Chisquared statistic of 0.68 and a corresponding p-value of 0.995. The added instruments used in the first-stage regression were the local county population and the school's Academic Progress Rate. The latter is a measure computed by the NCAA designed to show a school's success at moving student athletes towards graduation.

(15) The Hausman test for fixed- versus random-effects models produced a chi-squared statistic of 8.95 and a corresponding p value of .256.

(16) A mixed regression, which includes both random and fixed effects, was also estimated using Stata's xtmixed command. The estimated coefficients were virtually identical, both in size and significance, to those for the random effects estimates and thus are not reported.

(17) Stata's sktest, which tests for normality by jointly considering the measure of skewness and kurtosis, rejected the null hypothesis of normality at the 4% level of significance.

(18) See Koenker and Hallock (2001) for a discussion of how quantile regression is better suited to handle problems of nonnormality of the dependent variable. Unfortunately, including fixed effects for quantile regression is problematic (see Koenker, 2005).

(19) The average number of home games per season for the sample is approximately 18.

(20) The key variable, number of NHL draftees, is the impediment as its calculation is very labor intensive.

(21) For an interesting discussion of the topic of paying college athletes see The New York Times article, "March Money Madness" (March 18, 2008). Retrieved January 4, 2011, from http://roomfordebate.blogs.nytimes.com/2009/03/18/march-money-madness/

Author's Note

I would like to thank two anonymous referees for providing valuable comments on an earlier draft. I would also like to thank Belinda Eugster for valuable research assistance. An earlier draft of this paper was presented at the 86th Western Economics Association International Conference, June 29-July 3, 2011, San Diego, California.

Leo Kahane is an associate professor of economics at Providence College. His research interests include sports economics, international economics, and political economy. He is also the editor of the Journal of Sports Economics.

Leo H. Kahane [1] [1] Providence College Table 1. Revenues and Expenditures in Division I College Sports, 2004 and 2008 2004 2008 Revenues Total $2,970,008,906 $4,420,820,371 Football $1,813,247,801 $2,708,417,275 Basketball (Men's) $542,127,054 $795,651,053 Hockey (Men's) $43,686,032 $55,034,079 Expenses Total $2,373,035,226 $3,453,039,409 Football $1,180,835,249 $1,746,703,182 Basketball (Men's) $542,127,054 $795,651,053 Hockey (Men's) $43,686,032 $55,034,079 Athletic student aid Total $1,181,841,219 $1,592,122,148 Percent of revenues 39.8 36.0 Recruiting expenses Total $105,027,454 $138,712,346 Percent of revenues 3.5 3.1 Percent Percent real growth growth Revenues Total 48.8 30.6 Football 49.4 31.0 Basketball (Men's) 38.2 21.2 Hockey (Men's) 24.3 9.0 Expenses Total 45.5 27.6 Football 47.9 29.8 Basketball (Men's) 46.8 28.7 Hockey (Men's) 26.0 10.5 Athletic student aid Total 34.7 18.2 Percent of revenues Recruiting expenses Total 32.1 15.9 Percent of revenues Source. U.S. Department of Education, Equity in Athletics Disclosure Act (http://ope.ed. gov/ athletics.aspx) Note. Real growth computed by converting 2004 figures into 2008 dollars using the consumer price index. Table 2. Division I College Hockey Conferences and Championships from 1978 to 2008 Conference Championships Runners-up Athletic Hockey Association (AHA) 0 0 Central Collegiate Hockey 9 4 Association (CCHA) College Hockey America (CHA) 0 0 Eastern College Athletic 2 4 Conference (ECAC) Hockey East Association (HEA) 6 14 Western Collegiate Hockey 14 9 Association (WCHA) Table 3a. Descriptive Statistics (n = 172) Standard Variable Mean deviation Minimum Maximum Real revenues 102613.1 61605.1 13919.8 340663.0 per game Number of NHL 0.983 1.167 0 5 draftees Student population 10.540 8.370 1.773 36.616 (in thousands) Central Collegiate 0.279 0.450 0 1 Hockey Association (CCHA) Eastern College 0.256 0.438 0 1 Athletic Conference (ECAC) Hockey East 0.233 0.424 0 1 Association (HEA) Western Collegiate 0.233 0.424 0 1 Hockey Association (WCHA) Team rank 2.782 4.488 0 15 Note. Revenue and student population data were obtained from the U.S. Department of Education's Equity in Athletics Act website (http://ope.ed.gov/athletics/index.aspx). The number of NHL draftees was computed using data from The Internet Hockey Database (http://www.hockeydb.com). Team rank was computed from sources noted in the main text. Table 3b. Breakdown of Between and Within Standard Deviations Standard Variable Mean deviation Observations Real revenues Overall 102,613 61605.1 n = 172 per game Between 59444.9 n = 43 Within 17985.6 t= 4 Number of NHL Overall 0.983 1.167 n = 172 draftees Between 0.972 n = 43 Within 0.659 t= 4 Table 4. Estimated Revenues for Division I College Hockey Programs Fixed-effects Random-effects Variables Ln(Real Ln(Real revenues revenues per game) per game) Number of NHL draftees 0.0693 0.0710 ** (0.050) (0.034) Year 2006 0.0964 0.0945 (0.063) (0.064) Year 2007 0.2042 ** 0.2030 *** (0.081) (0.067) Year 2008 0.2317 ** 0.2313 *** (0.100) (0.069) ECAC 0.3172 * (0.179) HEA 0.6506 *** (0.170) WCHA 0.8166 *** (0.169) Student population -0.0019 0.0158 ** (in thousands) (0.042) (0.008) Team rank 0.0080 0.0163 ** (0.008) (0.007) Constant 11.1670 *** 10.5343 *** (0.432) (0.171) Observation 172 172 R-squared overall/pseudo 0.092 0.432 Quantile Variables regression q = 25 q = 50 q = 75 Number of NHL draftees -3.913 9.161 ** 4.680 (5.502) (4.153) (6.889) Year 2006 10.473 10.656 7.907 (10.275) (11.049) (15.120) Year 2007 10.547 11.699 19.610 (10.320) (11.957) (16.184) Year 2008 14.117 17.839 9.249 (11.183) (12.116) (16.184) ECAC 9.659 19.860 * 31.871 ** (15.453) (11.874) (14.581) HEA 47.041 *** 49.104 *** 58.799 *** (15.060) (10.242) (16.347) WCHA 51.162 *** 60.296 *** 82.860 *** (16.129) (13.631) (21.907) Student population 0.477 0.402 2.940 ** (in thousands) (0.705) (0.863) (1.260) Team rank 4.598 *** 4.592 *** 5.273 *** (1.352) (1.306) (1.716) Constant 23.914 32.542 ** 31.637 (19.527) (16.179) (20.646) Observation 172 172 172 R-squared overall/pseudo 0.224 0.262 0.366 Note. *** p < .01, ** p < .05, * p < .1. Robust standard errors in parentheses for fixed and random effects. Boot-strapped standard errors for quantile regressions (1,000 replications).