The attraction of baseball games in a small-size league: are the effects of outcome uncertainties really important?

Jane, Wen-Jhan ; Kuo, Nai-Fong ; Wu, Jyun-Yi 等

Introduction

Previous research has indicated that one of the missions in professional sports has been to achieve greater uncertainty. Sports leagues have consistently justified restrictions on competition as being needed to promote outcome uncertainty, thereby benefiting the consumer by providing more attractive games. This kind of uncertainty includes a competitive balance (hereafter, CB) and game uncertainty (hereafter, GU), which are key factors in the demand function (Borland & Macdonald, 2003). The former describes the degree of uncertainty in a league which is comprised of members that are relatively competitive in terms of strength, and the latter refers to the degree of uncertainty which is made up of the relative capabilities of two teams that are competing to win a game.

Studies in sport economics have attempted to discern the effect of CB and other factors on league attendance. It is widely believed that sporting events will be more attractive and more entertaining should there be a greater degree of CB among the teams (Szymanski & Kesenne, 2004). If this were not so, it is believed that attendees would lose interest, and thus there would be significantly lower attendance at the games involved. The theory of CB in team sports was first proposed by Rottenberg (1956), who noted that "the nature of the industry is such that competitors must be of approximately equal 'size' if any are to be successful; this seems to be a unique attribute of professional sports" (p. 242). In cases where consumer demand depends to a large extent on inter-team competition, the necessary interactions across teams define the special nature of sports. Games with no balance of competition or contests among poorly matched competitors will eventually cause fan interest to wane and industry revenues to fall (Sanderson & Siegfried, 2003).

Forrest and Simmons (2002) define CB as a league structure which is characterized by relatively equal playing strength between league members. Michie and Oughton (2004) refer to balance between the sporting capabilities of teams in a league. A comprehensive classification of the definition of GU is proposed by Szymanski (2003). There are three types of GU in professional sports studies, and they are match uncertainty, seasonal uncertainty, and championship uncertainty. His research has documented (1) the relationship between CB and league attendance between seasons/years (e.g., championship uncertainty), (2) the relationship within a season/year (e.g., seasonal uncertainty), and (3) the relationship between GU and game-day attendance. However, the empirical evidence in this area seems far from unambiguous (see Szymanski, 2003, p. 1155).

Taiwan is one of the smallest countries to have had a professional baseball league. Its national baseball team is considered to be one of the strongest teams in the world. In Taiwan baseball retains a large following and remains the most popular team sport. Several Taiwanese players have enjoyed successful careers in Major League Baseball (hereafter, MLB) and Nippon Professional Baseball (hereafter, NPB). Including some evidence of game uncertainty in professional team sports and comparing the results with the MLB are important.

The three major purposes in this paper are as follows. First, the relationships between league-level and game-level uncertainties and game-day attendance are investigated. That is, the effect of CB among league-level teams and the effect of match uncertainty between two teams are included in the model. One technical difficulty in the analysis concerns the measurement of CB and GU, and so we employ some indices to measure the league-level and game-level uncertainties in a game while at the same time investigating game-day attendance.

Second, ordinary least squares (OLS) and censored normal (Tobit) regressions have been employed in previous research on this issue. Researchers seem to have assumed that the regressors only affect the location of the conditional mean. However, in the case of demand variables at sporting events, the shape of the distribution will be altered by different regressor values. The effect of outcome uncertainties on a high-quantile/box-office game and a low-quantile/unpopular game are different. It is therefore necessary to ask whether such a relationship changes for both the box-office and unpopular games.

Third, the ambiguity surrounding the hypothesis of outcome uncertainties still needs more empirical evidence in the literature. We focus on investigating the relationship between attendance and CB for different conditions/quantiles related to game-day attendance. As such, to fill this gap in the literature, we employ data from the Chinese Professional Baseball League (hereafter, CPBL) to examine these relationships.

Literature Review on Outcome Uncertainties and Attendance

Competitive balance is one of the key issues in sport economics. In recent years, economic studies of CB have been performed on a variety of sports, including baseball (Eckard, 2001; Schmidt & Berri, 2001; Humphreys, 2002; Meehan et al., 2007), European football (Falter & Perignon, 2000; Forrest & Simmons, 2002; Garcia & Rodriguez, 2002, 2007; Brandes & Franck, 2007), American college football (Price & San, 2003; Depken & Wilson, 2006; Eckard, 1998) and professional American football (Grier & Tollison, 1994). The nature of CB has been outlined and research has found that league attendance is positively influenced by an increase in CB.

In addition to the effect of CB in a league, GU between two teams is also important. It is likely that as two teams rigorously compete with each other, individual games become more attractive. There have been a number of studies that examine the effect of this uncertainty on sports attendance. In general, the literature on outcome uncertainty can be separated into studies looking at aggregate attendance in a year/season and those investigating attendance in specific games. The hypothesis of GU has been verified in various professional sports, and these include the Major League Baseball (Knowles, 1992; Rascher, 1999; Meehan et al., 2007), the European football (Jennett, 1984; Peel & Thomas, 1988; Buraimo & Simmons, 2008a, 2008b), the National Basketball Association (Rascher & Solmes, 2007), the National Hockey League (Jones & Ferguson, 1988), and the Rugby Union in New Zealand (Owen & Weatherston, 2004). As more appropriate data for measuring GU, for example, the odds in the betting market, have become available in recent decades, it has become possible to test the outcome uncertainty hypothesis on a game-by-game basis. However, the results are ambiguous (see Borland & MacDonald, 2003; Szymanski, 2003 for detailed references), and further empirical analysis is needed to clarify the figures.

Quantification of the CB of a league can be problematic (Utt & Fort, 2002; Mizak et al., 2005). Since the league structure provides competition, it is commonly suggested that the league should be treated as a single entity, rather than making the club the unit of analysis. Therefore, a standard technique is to calculate the percentage of matches that each club wins in a season and to use the standard deviation of this distribution, where each club has a perfectly balanced chance of winning each match (= an 0.5 probability of winning each match), to arrive at a single figure for the league (see Scully, 1989; Quirk & Fort, 1992; Humphreys, 2002; Zimbalist, 2002). The higher the index, the lower the degree of CB that is implied in a league. This index, which was first applied by Scully (1989), has been used in several studies to compare the closeness of win records within seasons in professional leagues. Moreover, the range of win percentages and the Hirschman-Herfindahl indexes in a season are also commonly used in the literature.

Indices of CB have not been applied to matchday attendance. Therefore, we have modified indices based to previous research to measure the degree of CB on a matchday. However, the measurement of CB has limitations (see Michie & Oughton, 2004 for a detailed discussion), and it will still be an important issue in sport economics in the future. (1) So we provide as many indices of CB as possible in order to investigate the robustness of our empirical results and to ensure the consistency of our main conclusions.

Empirical Methodology and Data Description

In this section we employ some indices to measure the CB for a league which provides outcome uncertainty in the league, and the GU which provides outcome uncertainty between rival teams. Then, the hypothesis of uncertainties that games with a high degree of league-level uncertainty and with a high degree of game-level uncertainty lead to high attendance at a game is investigated. Furthermore, the application of quantile regression can be used to explore the difference between the effects of attraction for different levels of outcome uncertainties on box-office games and low-attendance games.

Empirical Methodology

The concepts of the outcome uncertainties include the relatively equal playing strength between league members and the relative capabilities of two competing teams for winning in a game. The basic model of attendance demand for a match t between the host and guest teams is as shown in equation (1).

ATT = f(CB, AD, DD, S, X), (1)

where ATT represents the attendance. The independent variables include the measurement of competitive balance in a league (CB), the uncertainty of sporting competition between two teams (AD), the dummy for the host-guest winning percentage (DD), the sum of the two teams' winning percentage (S), and other control variables (X).

Teams compete with each other in order to win, and a professional baseball league typically uses the winning percentage to calculate a team's standing. In the case of a league-level competition among team members, CB is measured by the standard deviation of win percentages in a league at game t (CB_SD), the range of win percentages (CB_R) in a league at game t, and the Herfindahl-Hirschman index of win percentages (CB_HHI) in a league at game t. Therefore, the data on the winning percentage for every team at every game needs to be collected before these indices are calculated. The greater these indices are, the greater the degree of competitive imbalance in a league at time/game t will be. The calculation of HHI is, however, more complicated, and we describe the data process as follows. The share of cumulative wins for a team ([Share.sub.1] is calculated by the ith team's cumulative wins divided by the total number of games played in the league before game t. Therefore, the degree of CB for each team can be calculated by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where n is the number of teams within a league and [Share.sub.i] is the ith team's share of wins. The extent of CB is seriously biased because of the uncompleted games in the first couple of rounds, and so the games in the former rounds in the data must be dropped when the model is regressed.

For the game-level competition between two teams (m and n) in game t, ADWinr, DDWinr, and SWinr are calculated via winning percentages as two rivals meet for the last time before game t. ADWinr is the absolute value of the differential in the winning percentage for team m and team n in the latest game, and is used to measure the two rivals' game certainty before game t starts. DDWinr is the dummy of the host-guest winning percentage (host>guest=1, otherwise=0) for team m and team n in the latest game and we employ it to test the host team's winning effect on fans. SWinr is the sum of the two teams' winning percentages before game t and it is used to measure the quality of a game.

Other control variables include the characteristics of the host cities, stadiums, and teams. Besides, we also include the environmental factors and the game (Game) and year (Year) dummies. The former three characteristics include variables such as the household's average disposable income in the host city (Income), the population of the host city (Pop), the location of the stadium (Distance), the dummy for turf (Turf), the dummy for a public-viewing screen (Screen), the size of the field in square feet (Field), and the dummies for rival-team combinations (Pair). The latter variables include the dummy for the holiday (Holiday) and the rainfall (Rainfall).

To empirically assess the effects of CB and GU, we build up the following econometric model based on Equation (1):

ATT = C + F[beta] + X[gamma] + u, (2)

where C is the constant term, F=[CB, AD, DD, S] is the matrix of the sporting competition, X is a set of control variables, and u is the unobserved disturbance. A standard approach estimates the unknown parameters of equation (2) using the method of ordinary least squares (OLS). The OLS estimation is known to be the best linear unbiased estimator under well-defined conditions. However, the OLS approach only measures the "average" behavior of a conditional distribution. It can not provide enough information to describe the entire conditional distribution.

Quantile regression (QR) as introduced by Koenker and Bassett (1978) is a good approach to adopt at this point. This estimation permits us to estimate various quantile regressions on their conditional distribution, and it can provide richer information and enable us to obtain a more comprehensive and robust analysis. Therefore, we employ the QR to obtain a complete picture of the conditional distribution on attendance. Equation (2) can be re-written as:

ATT = C + F[[beta].sub.q.] + X[[gamma].sub.q] + [u.sub.q], (3)

where [[beta].sub.q] and [[gamma].sub.q] are matrices of coefficients on sporting competition and control variables which are associated with the q-th quantile, and [u.sub.q] is an unknown error term. It is assumed that [u.sub.q] satisfies the constraint, [Quant.sub.q]([u.sub.q]|F,X) = 0. To obtain the estimators of ([[beta].sub.q], [[gamma].sub.q]), given a particular value for q, we solve

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)

which can be shown in the form of a linear programming problem and is computationally straightforward. The special case q=0.5 is referred to as the median regression estimator. A more detailed discussion can be found in Koenker (2005).

Data Description

Our data contain information for six teams on over 1,860 individual matches in 15 stadiums within the period 2001-2007 in the CPBL. (2) There were 180 games for the seasons for the years 2001 and 2002 as each team played 90 games, and 300 games were scheduled as each team played 100 games for the seasons after 2003. The average number of attendees was 2,798.

The degree of sporting competition that included league-level CB and game uncertainties are calculated using previous definitions. Control variables including the characteristics of the host cities, stadiums, and teams are employed. All variables are collected from the Baseball Record Books, the official website of the CPBL, the Directorate-General of Budget, Accounting and Statistics (DGBAS), the URMAP, and the Central Weather Bureau. (3)

Sporting competitions will become attractive when the extent of the CB among the teams is high. Otherwise, fans lose interest and there is significantly lower attendance (Depken & Wilson, 2006). To attract potential competition in a game, the relationship between the lack of competitive balance in a league (CB_SD, CD_R, or HHI) and attendance is thus expected to be negative. Similarly, the coefficient of game certainty for two teams (ADWinr) is also expected to be negative. As to the coefficient of DDWin, it is expected to be positive because the host team's wins bring more host attendees. Moreover, fans are interested in high quality play, and so SWinr is expected to positively affect attendance.

Market size is usually included as a determinant of attendance, and we use the city population in which the game is played (Pop) as a proxy. Population data are available at various levels in the DGBAS, including the county, local authority, and ward. We construct our market size measure by using the smallest level. Winfree et al. (2004) have indicated that baseball is a normal good and that the income elasticity is inelastic (=0.175) for the MLB case. Thus, we would expect the coefficients of Income and Pop to be positively significant.

The variable Distance equals the distance in meters from the stadium to the nearest transportation hub. (4) Long transportation increases the cost for a game, and so it is expected to be negatively significant. Data for the other control variable, weather conditions, which is measured by the rainfall (Rainfall), have been collected from the Central Weather Bureau. (5) It is expected to negatively affect attendance in open-air stadiums.

Previous studies (Forrest & Simmons, 2002; Buraimo & Simmons, 2008a) use some classifications for revealing the Derby effect, and they have shown that these games tend to attract more attendees, ceteris paribus. In this study, we use the variables Pair_i, the dummies for a combination of two rivals, to capture matches of historical rivalry. (6) Compared to the abundant literature on European and American sports, the advantage of our setting is that it is more objective under the situation of no reference in the CPBL regarding historical rivalry. The statistics and the corresponding expectation of coefficients are listed in Table 1.

Empirical Results and Discussion

The results of the OLS and quantile regressions are presented in Table 2.7 We find that the OLS estimators and the QR estimators for different quantiles are quite different. Cameron and Trivedi (2009) indicate that the differences in the coefficients across quantiles are caused by the heteroskedastic errors. For this reason, we apply the Breusch-Pagan (1979) test to investigate the heteroskedasticity. These p-values of the test are 0.000, and they are listed in the bottom row of Tables 2, 3, and 4. The results support the conclusion that the QR method appropriately investigates the relationship between attendance and outcome uncertainties.

In terms of the sporting competition variables, the league-level (CB_SD) and game-level (ADWinr) uncertainties are significantly negatively related to attendance. As for the proxy of quality play (SWin), it is highly significant and positively related to attendance, and the effects are consistent in the regressions. For the effects of the host-city factors, the coefficients of income (Income) and population (Pop) are significantly positive. Other significant and consistent factors in the regressions are the provision of public-viewing screen facilities (Screen), the dummy for holidays (Holiday), Rainfall, and dummies for the rival-team combinations (Pair_i). (8)

Outcome Uncertainties for a League and a Game

Previous research suggests that balanced competition is an important factor. In the literature, however, there is no consistent conclusion in the empirical studies on game-day attendance. Our results support the hypotheses of outcome uncertainty. That is, both the unbalanced degrees of the league-level competition and the game-level certainty negatively affect the game-day attendance. On average, a 0.1% decrease in the standard deviation of winning percentages in a league brings 334 fans to a game, and a 1% decrease in the absolute value of the differential between the two rivals' winning percentages increases the number of fans at a game by 562, ceteris paribus. Moreover, fans also care about match quality. On average, two quality rivals who have an additional 0.1% of the total winning percentage bring about an increase of 233 in attendance, other things being equal. In these sporting competitions, the results correspond to our expectations.

Quality plays an important role in the demand for sports competitions. Fans are not only interested in uncertain games with close competition between two teams, but are also attracted by a league where the teams are evenly matched. Moreover, the effects of higher quantiles are greater than the lower ones for these factors. That is, both uncertainties and quality play have a larger effect when a box-office game is played. Regressions using alternative measures of competitive balance are included in Tables 3 and 4.9 To provide a better understanding of the effects for different quantiles, Figures 1, 2, and 3 display all the coefficients of the sporting competition variables for all quantiles.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

Host-Win Effect, Location, Derby Effect

As to the effect of a host-team win on attendance, it is insignificant and the result reflects the reality of Taiwanese baseball. Taiwan covers a land area of 35,280 square kilometers, which is relatively small in the world. The effect of location is thus less important in such a small geographic area with just 15 stadiums. In the absence of clear demarcations of market territories for the teams, plus the fact that fans do not entertain a strong sense of geographical division, the scheduling and assignment of game locations is done in such a way that the area factor does not distinguish the host team from the guest team. Rather, the host-or-guest designation is determined by equal odds in terms of taking turns playing the host or guest roles at a given location. This results in a totally different type of operation when compared to the MLB. Unlike teams that have their own stadium in their city, the localization of CPBL teams is not as strong as that of teams in the MLB. In effect, CPBL teams play in stadiums and cities which do not belong to any team. The evidence shows that attendance is not influenced by the appellation of the "titular" host team. This is mainly due to the small land area, the ease of travel, and the absence of a strong sense of geographical division among fans. The finding that the effect of distance is insignificant also echoes this point.

[FIGURE 3 OMITTED]

Historic rivalries are also an important factor for fans. For the Derby effect, 9 of 14 coefficients (Pair_i) are significantly positively related to attendance compared to the base combination. The top five coefficients of a paired game are Pair_2, Pair_3, Pair_4, Pair_5, and Pair_7, and only one team (Brother Elephants) is involved in all of them. Just like the effects of the New York Yankees in the MLB, Manchester United in European soccer, or the Giants in the NPB, there is a large effect, e.g., a 1,521 to 3,623 increase in audiences compared to the base game on average, when the Brother Elephants play in a CPBL game.

With respect to other significant coefficients, the positive coefficients of income and local population show that baseball is a normal good in relation to the consumers' expenditure and the market size has a positive effect on attendance. The income elasticity ranges from 0.398 to 0.426 in the semi-log model, and these estimations are higher than in the case of the MLB. (10) In addition, the provision of public-viewing screen facilities (Screen) and the dummy for holidays (Holiday) have a positive effect on attendance, while rainfall has a negative effect. Two positive effects of Screen and Holiday are magnified in a box-office game and these effects result in a popular game becoming more popular. Conversely, the rainfall reduces the number of fans at low-attendance games and makes an unpopular game even more unpopular.

From the cost and benefit view, the cost of an indoor stadium is much larger than the cost of public-viewing screens. However, the gap between the marginal effects of screen (509) and rainfall (-8) is huge as shown in Table 2. The policy implications of constructing a stadium facility in the short run is that the public-viewing screens are needed, but the indoor stadiums are not justified financially.

Conclusions

Unlike most research on the determinants of attendance, we include measures of CB in a league and an index for GU for two rivals at the same time in our quantile analysis. The results support the hypothesis of outcome uncertainties. More uncertainty in sporting competitions between two rivals in a game and more uncertainty regarding who will emerge as the champion among teams in a league can increase the fans' interest, and thus bring more fans to a game. The effects are especially enhanced in high box-office (high-quantile) games. An imbalance in competition reduces the number of fans at low-attendance games and leads to bigger losses in popular games. The robust regressions also support the hypothesis. In addition, our results support the view that the quality of a game is also an influential factor in game-day attendance, and the evidence of the Derby effect shows that there is a Brother-team effect on CPBL attendance.

The bandwagon effect can explain the results of the quantile regressions. That is, fans often attend and believe in high box-office games merely because many other fans attend and believe in the same things. Therefore, uncertainty strongly affects attendance, especially when more fans go to the field.

As Rottenberg (1956) suggested, an approximately equal size for each team is needed if any are to be successful. Therefore, the implementation of regulations to prevent big-market teams from using their financial advantage to buy success is important.

Institutional barriers that govern the limitations on the right to trade players and the team's expenditure on human resources have been implemented to different degrees in the league. In the long run, the policy implications of the uncertainty effect for the league are condensed as follows. On the one hand, in order to increase attendance, the league should consider more enforcement of existing rules, e.g., salary caps and draft rules, to increase the CB in the league. Restricted revenue sharing which is only used for investing in human resources is also a good way to accomplish this. On the other hand, increasing the number of potential competitors is important. Like the Premier League in England, which uses relegation and promotion of team(s) between first-tier and second-tier teams, an effective policy may include more second-tier teams in the CPBL to promote balanced competition.

In the short run, the policy implications of our findings provide an arrangement for game schedules for the league. Such a method involves creating some special games for the best two teams during the regular season. Generally speaking, the schedule cannot be changed once the season starts. Since the degree of league-level CB, the GU, and the game quality all affect game-day attendance, the special games that are inserted in the regular season should be determined based on these measures. Moreover, the results of the quantile regressions also indicate that the CB effect of the high quantile on attendance is larger than the lower one. Therefore, a highly balanced competition should be arranged in a bigger stadium. The revenue from box-office games should be able to totally cover the losses in low-quantile games. More specifically, the special games should be held on weekends every two or three weeks during the season. The top two teams at each point should compete with each other in these special games. As a result, attendance in the league will increase.

Compared to host-guest systems such as MLB, in the CPBL the insignificant coefficients of the host-team win and the distance reflect a different type of operation. The results of this study show that attendance is not affected by the titular host team, and the sense of belonging for fans of the host team is negligible. The findings also show that transportation costs do not seem to affect the fans' demand for game attendance. This is mainly due to the small geographical area and the absence of a strong sense of geographical division for fans in Taiwan.

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Endnotes

(1) The complexity of measuring CB is well summarized by Zimbalist (2003, p. 163). He indicated that, "In the end, it may be that the best measure of competitive balance is a multivariate index, that it is nonlinear or constrained, and/or that it differs league by league"

(2) The 15 stadiums included the Taipei City (Tienmou), Taipei County (Hsinchuang), Longtan, Hsinchu, Taichung, Douliou, Chiayi City, Chiayi County, Tainan, Kaohsiung City, Kaohsiung County (Cheng Ching Lake), Pingtung, Yilan, Hualien, and Taitung stadiums. We use the addresses of these stadiums to calculate the location of each stadium via a professional location system based on a Geographic Information System (GIS), i.e., the URMAP.

(3) The website of the CPBL is http://www.cpbl.com.tw/html/stadium.asp, the Directorate-General of Budget, Accounting and Statistics is http://61.60.106.82/pxweb/Dialog/statfile9.asp, the URMAP is http://www.urmap.com/, and the Central Weather Bureau is http://www.cwb.gov.tw/.

(4) The hubs include railway stations, subway stations, and highway interchanges. We use the system of the General Packet Radio Service (abbreviated as GPRS) location in the URMAP to calculate the shortest distance.

(5) For all stadiums, we choose the nearest weather station to obtain the information.

(6) There are six teams in the data, and the combination is C26=15. Therefore, we use 14 dummies to investigate the Derby effect.

(7) Censoring occurs when the number of tickets is sold out. Thus, in some research, the censored model is employed to deal with the empirical problem. We also consider this situation and apply a censored quantile regression proposed by Powell (1986). However, only two games reach the capacity of the stadium in the regression. Therefore, there is no need to consider the problem and we list the results for the QR in Table 2.

(8) i=2, 3, 4, 5, 6, 7, 12, 15, 21.

(9) Both of the p-values of the Breusch-Pagan test are 0.000 for Tables 3 and 4, respectively. The results support the conclusion that the QR method appropriately investigates the relationship between attendance and outcome uncertainties.

(10) The income elasticity is 0.175 for the MLB case (Winfree et al., 2004). Their explanation of the income inelasticity is that the consumers' leisure horizons widen when real incomes increase. The results of the estimation are provided by the author if needed.

Authors' Note

The authors would like to thank the editor and the anonymous referees for their helpful comments on the manuscript. All remaining errors are our own. Jane is grateful to the National Science Council for its financial support (NSC 98-2410-H-128 -016).

Wen-Jhan Jane [1], Nai-Fong Kuo [1], Jyun-Yi Wu [2], and Sheng-Tung Chen [3]

[1] Shih Hsin University

[2] National Central University

[3] Feng Chia University

Wen-Jhan Jane is an assistant professor in the Department of Economics. His current research focuses on the applied econometrics, especially the topics of peer effects, competitive balance, and wage theory in professional sports.

Nai-Fong Kuo is an associate professor in the Department of Finance. His research interests include the empirical finance, spatial econometrics, and applied general equilibrium.

Jyun-Yi Wu earned his doctorate in economics. His current research interests include empirical econometrics, time series analysis, and industrial economics.

Sheng-Tung Chen is an assistant professor in the Department of Public Finance. His research focuses on applied econometrics and public finance.

Table 1: Descriptive Statistics of the Data (n = 1860)

Variable Description Mean

ATT Number of attendees 2798.991

SD Standard deviation 0.165
 of win percentages
 in a league

R Range of win 0.414
 percentages in a
 league

HHI Hirschman-Herfindahl 3351.197
 indexes for
 competitive balance
 in a league

ADWinr Absolute value of 0.194
 differential between
 two teams' winning
 percentages before
 game t started

DDWinr Dummy of host-guest 0.46
 winning percentages
 before game t started
 (host>guest =1,
 otherwise=0)

SWinr Sum of two teams' 0.964
 winning percentage
 before game t started

Income Household's average 903530.6
 disposable income in
 city j in a year
 (NT Dollars)

Pop Population of host 1612421
 team (thousands)

Distance The distance to the 2864.154
 nearest transportation
 hub (meters)

Turf Dummy of turf (yes=1) 0.8278

Screen Dummy of public- 0.63
 viewing screen (yes=1)

Field The area of the field 132778.2
 ([feet.sup.2])
Rain Rainfall (millimeters) 3.295

Holiday Dummy of holiday 0.56
 (weekend =1)

Variable Std. Dev. Expectation

ATT 2170.456

SD 0.093 Negative

R 0.217 Negative

HHI 4554.196 Negative

ADWinr 0.196 Negative

DDWinr 0.498 Negative

SWinr 0.263 Positive

Income 162267.6 Positive

Pop 1245908 Positive

Distance 1140.883 Negative

Turf 0.378 ?

Screen 0.483 ?

Field 3565.973 ?

Rain 12.25 Negative

Holiday 0.496 Positive

Table 2: Estimation Results of OLS and Quantile Regressions (CB_SD)

ATT OLS

 25-th

 Coef. P>t Coef. P>t

CB_SD -3343.3 *** (0.002) -1219.6 * (0.100)
ADWinr -562.8 * (0.088) -361.8 * (0.096)
DDWinr -107.6 (0.168) -64.73 (0.216)
SWinr 2331.3 *** (0.000) 1675.3 *** (0.000)
Income 0.001 * (0.067) 0.001 *** (0.004)
Pop 0.000 * (0.015) 0.000 ** (0.035)
Distance -0.07 (0.335) -0.03 (0.461)
Field 0.003 (0.802) 0.008 (0.376)
Turf -5.55 (0.966) 28.59 (0.765)
Screen 509.3 *** (0.001) 186.5 ** (0.042)
Pair2 2517.2 *** (0.000) 1667.8 *** (0.000)
Pair3 3623.6 *** (0.000) 1996.2 *** (0.000)
Pair4 1521.8 *** (0.000) 1026.7 *** (0.000)
Pair5 2027.4 *** (0.000) 1131.3 *** (0.000)
Pair6 989.4 *** (0.000) 692.4 *** (0.000)
Pair7 2231.4 *** (0.000) 1440.7 *** (0.000)
Pair8 7.19 (0.968) 6.97 (0.962)
Pair10 -19.12 (0.915) 174.4 (0.238)
Pair12 534.1 *** (0.003) 372.4 ** (0.011)
Pair14 -12.11 (0.953) -15.78 (0.921)
Pair15 876.4 *** (0.000) 524.1 *** (0.001)
Pair20 -213.5 (0.195) -82.34 (0.590)
Pair21 918.5 *** (0.000) 614.9 *** (0.000)
Pair28 -224.1 (0.199) -132.03 (0.379)
Holiday 701.7 *** (0.000) 405.06 *** (0.000)
Rainfall -8.03 ** (0.022) -7.14 *** (0.000)
_cons -2460.3 (0.225) -2740.7 * (0.047)
Game Yes Yes Yes Yes
Year Yes Yes Yes Yes
(Pseudo)- 0.524 0.251
[R.sup.2]

Breusch-Pagan test 176.2 (0.00) ***

[H.sub.0]: [CB_SD.sub.25]
= [CB_SD.sub.50]=[CB_SD.sub.75] 3.45 (0.032)**

ATT Quantile

 50-th 75-th

 Coef. P>t Coef. P>t

CB_SD -2812.4 *** (0.001) -3770.0 ** (0.010)
ADWinr -502.8 ** (0.049) -531.5 (0.252)
DDWinr -99.54 * (0.090) -96.49 (0.339)
SWinr 2077.1 *** (0.000) 2020.1 *** (0.000)
Income 0.001 *** (0.004) 0.001 ** (0.023)
Pop 0 (0.323) 0.000 ** (0.037)
Distance -0.023 (0.621) -0.052 (0.528)
Field 0.021 * (0.052) 0.01 (0.565)
Turf -16.24 (0.881) 75.98 (0.682)
Screen 266.0 ** (0.011) 485.7 *** (0.007)
Pair2 2367.0 *** (0.000) 3058.5 *** (0.000)
Pair3 3003.5 *** (0.000) 5386.6 *** (0.000)
Pair4 1289.4 *** (0.000) 1679.7 *** (0.000)
Pair5 1705.0 *** (0.000) 2608.7 *** (0.000)
Pair6 875.1 *** (0.000) 1119.6 *** (0.000)
Pair7 2281.9 *** (0.000) 2769.8 *** (0.000)
Pair8 106.5 (0.509) 243.2 (0.376)
Pair10 92.98 (0.583) -14.99 (0.959)
Pair12 428.2 ** (0.010) 571.4 ** (0.043)
Pair14 183.4 (0.309) 15.66 (0.960)
Pair15 753.2 *** (0.000) 836.6 *** (0.008)
Pair20 -211.2 (0.228) -305.6 (0.308)
Pair21 764.2 *** (0.000) 959.5 *** (0.001)
Pair28 -200.3 (0.234) -220.1 (0.443)
Holiday 619.3 *** (0.000) 777.5 *** (0.000)
Rainfall -3.228 (0.143) -5.913 * (0.060)
_cons -4502.0 *** (0.004) -2960.1 (0.251)
Game Yes Yes Yes Yes
Year Yes Yes Yes Yes
(Pseudo)- 0.3 0.375
[R.sup.2]

Breusch-Pagan test 176.2 (0.00) ***

[H.sub.0]: [CB_SD.sub.25]
= [CB_SD.sub.50]=[CB_SD.sub.75]

Notes:

(a) *** denotes significance at the 1% level, ** denotes
significance at the 5% level, and * denotes significance
at the 10% level.

(b) Values in parentheses are the p-values.

Table 3: Estimation Results of OLS and Quantile Regressions (CR_R)

ATT OLS

 25-th

 Coef. P>t Coef. P>t

CB_R -1422.6 *** (0.001) -521.6 * (0.053)
ADWinr -548.4 * (0.094) -350.9 * (0.075)
DDWinr -108 (0.166) -64.72 (0.178)
SWinr 2336.0 *** (0.000) 1719.8 *** (0.000)
Income 0.001 * (0.064) 0.001 *** (0.004)
Pop 0.000 * (0.015) 0.000 ** (0.027)
Distance -0.068 (0.343) -0.038 (0.306)
Field 0.004 (0.758) 0.008 (0.338)
Turf -11.32 (0.931) 31.97 (0.716)
Screen 514.9 *** (0.001) 189.4 ** (0.025)
Pair2 2517.2 *** (0.000) 1667.3 *** (0.000)
Pair3 3632.0 *** (0.000) 2004.1 *** (0.000)
Pair4 1525.6 *** (0.000) 1037.6 *** (0.000)
Pair5 2018.4 *** (0.000) 1131.5 *** (0.000)
Pair6 991.1 *** (0.000) 693.8 *** (0.000)
Pair7 2229.9 *** (0.000) 1436.2 *** (0.000)
Pair8 0.751 (0.997) 0.289 (0.998)
Pair10 -12.38 (0.945) 159.4 (0.245)
Pair12 537.2 *** (0.003) 378.5 *** (0.005)
Pair14 -18.78 (0.928) -17.35 (0.905)
Pair15 874.1 *** (0.000) 546.9 *** (0.000)
Pair20 -218.3 (0.185) -83.86 (0.552)
Pair21 918.5 *** (0.000) 606.1 *** (0.000)
Pair28 -213.6 (0.220) -126.7 (0.352)
Holiday 699.9 *** (0.000) 407.7 *** (0.000)
Rainfall -8.01 ** (0.022) -5.87 *** (0.000)
_cons -2579.4 (0.201) -2732.2 ** (0.030)
Game Yes Yes Yes Yes
Year Yes Yes Yes Yes
(Pseudo)- 0.524 0.252
[R.sup.2]

Breusch-Pagan test177.4(0.000) ***

[H.sub.0]: [CB_R.sub.25] 5.66
= [CB_R.sub.50]=[CB_R.sub.75] (0.003) ***

ATT Quantile

 50-th 75-th

 Coef. P>t Coef. P>t

CB_R -991.0 *** (0.002) -2010.8 *** (0.000)
ADWinr -547.7 ** (0.023) -452.7 (0.206)
DDWinr -98.87 * (0.075) -94.19 (0.227)
SWinr 2120.5 *** (0.000) 2147.3 *** (0.000)
Income 0.001 *** (0.003) 0.001 ** (0.014)
Pop 0.000 *** (0.281) 0.000 ** (0.018)
Distance -0.026 (0.559) -0.073 (0.270)
Field 0.020 ** (0.047) 0.01 (0.462)
Turf -31.75 (0.758) 37.22 (0.797)
Screen 278.9 *** (0.005) 522.5 *** (0.000)
Pair2 2385.2 *** (0.000) 2988.3 *** (0.000)
Pair3 3050.7 *** (0.000) 5328.0 *** (0.000)
Pair4 1329.4 *** (0.000) 1637.7 *** (0.000)
Pair5 1756.9 *** (0.000) 2532.3 *** (0.000)
Pair6 888.6 *** (0.000) 1149.5 *** (0.000)
Pair7 2332.7 *** (0.000) 2703.3 *** (0.000)
Pair8 134.9 (0.374) 181.2 (0.395)
Pair10 101.5 (0.525) -23.42 (0.919)
Pair12 470.6 *** (0.003) 524.4 ** (0.017)
Pair14 224 (0.190) -17.62 (0.942)
Pair15 779.8 *** (0.000) 860.3 *** (0.000)
Pair20 -183.7 (0.265) -275.1 (0.228)
Pair21 787.9 *** (0.000) 904.4 *** (0.000)
Pair28 -152.5 (0.338) -233.7 (0.297)
Holiday 602.3 *** (0.000) 732.7 *** (0.000)
Rainfall -3.29 (0.114) -4.93 * (0.064)
_cons -4496.6 *** (0.002) -2741.1 (0.171)
Game Yes Yes Yes Yes
Year Yes Yes Yes Yes
(Pseudo)- 0.3 0.376
[R.sup.2]

Breusch-Pagan test177.4(0.000) ***

[H.sub.0]: [CB_R.sub.25]
= [CB_R.sub.50]=[CB_R.sub.75]

Notes:

(a) *** denotes significance at the 1% level, ** denotes
significance at the 5% level, and * denotes significance
at the 10% level.

(b) Values in parentheses are the p-values.

Table 4: Estimation Results of the OLS and Quantile
Regressions (HHI)

ATT OLS

 25-th

 Coef. P>t Coef. P>t

HHI -0.006 (0.618) 0.004 (0.513)
ADWinr -876.4 *** (0.006) -491.6 *** (0.004)
DDWinr -102.8 (0.191) -75.04 * (0.082)
SWinr 2313.1 *** (0.000) 1651.4 *** (0.000)
Income 0.001 ** (0.049) 0.001 *** (0.001)
Pop 0.000 *** (0.009) 0.000 ** (0.011)
Distance -0.059 (0.414) -0.031 (0.350)
Field 0.003 (0.832) 0.004 (0.586)
Turf -5.27 (0.968) 62.53 (0.417)
Screen 514.1 *** (0.001) 175.7 ** (0.018)
Pair2 2514.2 *** (0.000) 1696.8 *** (0.000)
Pair3 3620.9 *** (0.000) 1988.6 *** (0.000)
Pair4 1511.8 *** (0.000) 1005.0 *** (0.000)
Pair5 2035.8 *** (0.000) 1146.5 *** (0.000)
Pair6 985.1 *** (0.000) 721.0 *** (0.000)
Pair7 2260.2 *** (0.000) 1497.7 *** (0.000)
Pair8 2.99 (0.987) 6.5 (0.956)
Pair10 -13.24 (0.941) 169.3 (0.163)
Pair12 534.9 *** (0.003) 364.5 *** (0.002)
Pair14 -8.03 (0.969) -70.43 (0.586)
Pair15 893.2 *** (0.000) 571.7 *** (0.000)
Pair20 -196.4 (0.230) -57 (0.650)
Pair21 950.2 *** (0.000) 570.7 *** (0.000)
Pair28 -234 (0.182) -119.5 (0.318)
Holiday 698.7 *** (0.000) 411.8 *** (0.000)
Rainfall -7.84 ** (0.028) -7.44 *** (0.000)
_cons -2847.1 (0.156) -2336.5 ** (0.037)
Game Yes Yes Yes Yes
Year Yes Yes Yes Yes
(Pseudo)- 0.521 0.252
[R.sup.2]

Breusch-Pagan test 177.4 (0.00) *** 0.730
[H.sub.0]: (0.483)
= [HHI.sub.50] = [HHI.sub.75]

ATT Quantile

 50-th 75-th

 Coef. P>t Coef. P>t

HHI 0.005 (0.542) -0.02 (0.108)
ADWinr -647.9 *** (0.007) -665.6 * (0.063)
DDWinr -102.2 * (0.078) -114 (0.173)
SWinr 2035.5 *** (0.000) 2090.8 *** (0.000)
Income 0.001 *** (0.000) 0.001 ** (0.029)
Pop 0 (0.330) 0.000 *** (0.007)
Distance -0.001 (0.977) -0.018 (0.787)
Field 0.021 ** (0.041) 0.007 (0.633)
Turf -89.02 (0.405) 21.96 (0.885)
Screen 295.7 *** (0.004) 475.7 *** (0.001)
Pair2 2226.0 *** (0.000) 3020.6 *** (0.000)
Pair3 3132.1 *** (0.000) 5475.6 *** (0.000)
Pair4 1299.6 *** (0.000) 1745.5 *** (0.000)
Pair5 1784.4 *** (0.000) 2655.3 *** (0.000)
Pair6 857.7 *** (0.000) 1131.6 *** (0.000)
Pair7 2368.1 *** (0.000) 3055.7 *** (0.000)
Pair8 77.12 (0.625) 325.8 (0.151)
Pair10 62.07 (0.709) -83.04 (0.734)
Pair12 530.1 *** (0.001) 616.8 *** (0.008)
Pair14 196.4 (0.269) 11.94 (0.963)
Pair15 779.5 *** (0.000) 959.8 *** (0.000)
Pair20 -149.7 (0.382) -290.2 (0.235)
Pair21 839.9 *** (0.000) 1045.3 *** (0.000)
Pair28 -168.3 (0.310) -260.7 (0.271)
Holiday 593.6 *** (0.000) 729.2 *** (0.000)
Rainfall -2.65 (0.221) -5.45 ** (0.029)
_cons -5205.4 *** (0.001) -2813.2 (0.188)
Game Yes Yes Yes Yes
Year Yes Yes Yes Yes
(Pseudo)- 0.298 0.374
[R.sup.2]

Breusch-Pagan test 177.4 (0.00) ***
[H.sub.0]:
= [HHI.sub.50] = [HHI.sub.75]

Notes:

(a) *** denotes significance at the 1% level, ** denotes
significance at the 5% level, and * denotes significance
at the 10% level.

(b) The values in parentheses are the p-values.