Author: David T. Yi

Corresponding Author:
David T. Yi
Department of Economics
Xavier University
3800 Victory Parkway
Cincinnati, Ohio 45207
Email: [email protected]
Phone: 513-745-2933.

David Yi is Chair and Associate Professor of Economics at Xavier University in Cincinnati Ohio.

The Home Court Advantage: Evidence from Men’s College Basketball

ABSTRACT
The home court advantage in team sports is a well-established phenomenon whose true causes are not yet fully known despite the varying range of theories. In this paper, the researcher employs a stochastic production frontier model and explains the home court advantage phenomenon as an efficiency-enhancing phenomenon. Home teams, when supported by the home team’s crowd, play better with enhanced game efficiency. It is not simply playing aggressively at home or the familiarity of the home court that gives the home teams advantage over visiting teams, but rather the home court atmosphere enhances the home teams to play up to their potential.

Keywords: Home Court Advantage, Game Efficiency, Technical-Efficiency

INTRODUCTION
The home-court advantage in team sports is a well-established phenomenon. According to an ESPN article (2012), the typical home-court advantage in most National College Athletic Association (NCAA) Division-I men’s basketball games is around four points. A Sports Blog (SB) Nation article (2011), projected that an average National Basketball Association (NBA) team would have won 10.11% more games if it were allowed to play all of its contests at home, based on the team’s scores over the past three years. Such advantage could transform a 41-win team into a 45-win team. Although not an enormous improvement, it might just be enough to advance a team into the playoffs. According to Courneya and Carron (1992) and Nevill and Holder (1999), home teams win more than 50% of their games at home. Simply put, teams win more when played at home.

If the home court advantage in sports is indeed real, what is the cause of such phenomenon? Over the years, researchers have identified numerous sources. Many believe crowd, travel distance and site familiarity to be the most significant factors (Edwards et al., 1979, Edwards and Archambault, 1989, Bray and Widmeyer, 2000, and Smith, 2005). According to Bray and Widmeyer (2000), athletes believe home crowd support and a familiarity of the home court to have the most influence on their performance. Agnew and Carron (1994), Smith (2003) and Smith (2005), state that the chance of home team victory rises as crowd density increases. Similarly, Nevill and Holder (1999) find that ‘‘crowd factor appears to be the most fruitful and likely dominant cause of the home advantage.’’ Along with the three sources mentioned above, some researchers also point out psychological factor as an underlying explanation for the home court advantage phenomenon (Bray& Widmeyer, 2000). For example, Bray, Jones, and Owen (2002) found that athletes are more self-confident and report a higher self-efficacy before a home game, and that players may also be less anxious in front of a home crowd. Thout, Kavouras, and Kenefick (1998) have found through study, of players’ state of anxiety in basketball games, that players’ cognitive and somatic anxiety levels are higher, and self-confidence levels are lower for away games when compared to home games. Literatures in home court advantage also show that the boosted self-confidence level for home teams often results in home teams simply playing more aggressively. A seminar work of Schwartz and Barsky (1977) showed that home teams take more shots, score more field goals and points than they do playing in front of a hostile crowd. Another study by Varca (1980) used examples of the Southeastern Conference (SEC) college basketball teams for the 1977-1978 season to show that teams tend to play more aggressively at home; therefore, they grab more rebounds, have more blocked shots and more steals. In addition, Carmichael and Thomas (2005) showed some evidence in their study of English premiership football teams that attack play is more important and productive in terms of goals for the home team, whereas defensive play is more important for away teams; hence, demonstrating that perhaps being aggressive pays off for the home teams. So what causes home teams to play more aggressively?

In an article published in the Business Insider (2014), the former National Football League (NFL) football player Fran Tarkenton stated that a smile or even a nod up and down from his coach Bud Grant walking off the field made him walk 10 feet taller and a whole lot straighter. In the article, Fran Tarkenton highlighted the importance of intrinsic recognition as a form of positive reinforcement on boosting player confidence, and ultimately, game productivity/efficiency. Indeed, in organizational management literature, the psychological effect of intrinsic recognition as a form of positive reinforcement and employee productivity is well established. According to the well-known psychologist and behaviorist B.F. Skinner (1963), positive reinforcement -both intrinsically and extrinsically- is positively linked with the performance of employees. According to Wei and Yazdanifard (2014), positive reinforcement such as intrinsic reward is highly effective in strengthening and increasing behaviors. When employees obtain acknowledgement from managers or supervisors as a result of their job well done, they feel appreciated and have a sense of belonging to the company (Shiraz, Rashid and Riaz, 2011). Gohari et al (2013) found that this type of positive reinforcement in the form of intrinsic recognition is highly valued by staff and it is very likely that they will strive to perform better.

In this paper, the researcher sets out to investigate the determinants of the home court advantage as an efficiency-enhancing phenomenon. Considering the effect of game location (e.g. home vs. away), travel distance, and home crowd density, The researcher shows that, all else being equal, a higher home crowd density makes home teams more efficient. This finding then suggests that the home court advantage is a home crowd based phenomenon, in which the home court atmosphere (measured by home crowd density) creates the intrinsic recognition (e.g. a nod up and down) for home teams, and therefore enhances their game efficiency.

METHODOLOGY
In sports economics literature, researchers often treat team performance as a production process in which teams convert measurable performance inputs into game output (win/loss or points scored) to measure how well teams play up to their potential (Zak et al., 1979, Chatterjee et al., 1994, Carmichael and Thomas, 2005, Hardley et al., 2000, Dawson et al., 2000a, Dawson et al., 2000b, Hofler and Payne, 1997, Hofler and Payne, 2006, and Rimler et al., 2010). Among them, Zak et al. (1979), Hofler and Payne (1997, 2006) and Dawson et al. (2000a,b) measure how well teams play up to their potential by measuring productive efficiency. The efficiency of this process, i.e. how well the input mix is converted into output, is then measured by the extent to which inputs perform relative to their potential. Methodologically, this paper is in-line with these studies and the focus of this paper is to identify home-game related variables that determine game efficiency.
In order to examine the effect of playing at home on game efficiency, the researcher uses three specific measures: Location, Travel Distance (for the away team) and Home Court Atmosphere. The Location variable is an indicator variable that takes two values, home or away. Home Court Atmosphere is a continuous variable that takes a value between 0 and 1. Home Court Atmosphere is measured as home court density, which is calculated by taking a ratio between the number of actual attendance and arena capacity. The researcher uses the home court density as a proxy for home crowd support that indicates the atmosphere of the home court.

Following Hofler and Payne (2006) and Bishop and Brand (2003), the researcher adopts an inefficiency effects model developed by Battesse and Coelli (1995) to examine the effect of the home court advantage on game efficiency using the Atlantic-10 (A-10) men’s college basketball setting. Note that, in principle, the game efficiency that we measure is not the same as a team’s win efficiency as measured under Hofler and Payne (2006). This is because we use points scored as a dependent variable whereas Hofler and Payne use the number of wins as a dependent variable. Although high scoring is positively correlated with winning, scoring high points does not necessarily translate into winning. One must score higher than the opponent. In particular, due to data availability, we employ a cross-section version of the time-varying inefficiency model of Battese and Coelli (1995). Oczkowski and Sharma (2005) and Bishop and Brand (2003) also employed the cross-section version of the time-varying inefficiency model suggested by Battese and Coelli (1995).

In general, the production process in which firms transform their inputs into outputs can be represented by

Formula 1 (1)

where represents an organization’s potential output, is a vector of inputs which affect the output level, is an unknown parameter vector to be estimated and is a random disturbance term with a mean of zero. As outlined by Aigner, Lovell and Schmidt (1977), and Meeusen and van den Broeck (1977), under the specification in equation (1), any deviation from the stochastic frontier is solely due to statistical noise and such noise cannot be attributed to the production process. To cope with this issue, Aigner, Lovell and Schmidt (1977), and Meeusen and van den Broeck (1977) propose adding a non-negative disturbance term that is organization-specific. According to Aigner, Lovell and Schmidt (1977), the non-negative disturbance term reflects the fact that each organization’s output must be on or below its frontier given by equation (1), and any deviation is the result of factors that can be controlled by the organization such as technical and economic inefficiency. Therefore, the production process is specified as

(2)

where is a disturbance term which is assumed to be normally, independently and identically distributed with a zero mean and variance . Furthermore, the Battese and Coelli (1995) specification assumes that the one-sided disturbance term , which is assumed to account for technical inefficiency in the production, is independently distributed as truncations at zero of the distribution. In the cross section case

. (3)

is a row vector of variables that may affect the efficiency of an organization and is a column vector of parameters to be estimated. This specification allows a simultaneous estimation of both the frontier production in equation (2) and the inefficiency determinants model in equation (3) where the inefficiency determinants are specified as a function of factors aforementioned.

As noted above, given the data availability, the analysis of cross-section study is applied in order to examine the influence of home-related variables on game efficiency. At the most general level, a non-homogeneous translog production function of the following form is employed5:
, (5)

where is a natural logarithm of point scored by team i. independent variables consist of the two-point field goal percentage, three-point field goal percentage, free throw shooting percentage, offensive rebounds, defensive rebounds, personal fouls, assists, turnovers, blocked shots and steals. The estimation of production functions to measure the relationship between team output (points scored) and performance inputs has been undertaken by many researchers (Hofler and Payne 2006). In the study of professional basketball in the United States (U.S.), Zak, Huang and Siegfried (1979) used a ratio of the final scores and various ratios of percentage performance inputs (e.g. field goal percentage/field goal percentage of the other team). Hofler and Payne (1997, 2006) used the actual number of wins as a dependent variable and used various ratios of percentage performance inputs as independent variables in their study of the efficiency of professional basketball teams in the U.S. Chatterjee et al. (1994), Carmichael and Thomas (2005), Hardley et al. (2000), Dawson et al. (2000a), and Dawson et al. (2000b) use similar approach in their studies of measuring team performances in various types of sports.

The inefficiency effect is estimated using the following specification:

. (6)

As discussed earlier in regards to the factors affecting efficiency, we have 3 main Home Court Advantage variables: Location, Travel Distance, and Home Court Atmosphere (measured by Home Court Density). Location is measured with a 1/-1 Home/Not Home identifier. Home Court Atmosphere is an interaction of a ratio between attendance and arena capacity and Home/Not Home identifier.

DATA
The dataset used in our analysis contains 246 basketball games played by the A-10 men’s basketball teams during the 2005-2006 season conference games. Table 1 presents aggregate descriptive statistics for home and away teams. Interestingly, the home teams performed better in all categories during the 2005-2006 season. For example, each home team averaged almost 5 more points per game. The home team also shot 1.3%, 1.7%, and 4.1% better from a 2-point range, behind the arc, and behind the line, respectively.

Home teams had a tendency to secure the ball better as well. Offensive and defensive rebounding, assists, turnovers, blocks, and steals favored the home team relative to the away team. There does appear to be significant variation in the average differentials of each statistic; hence, one cannot conclude that the home teams performed significantly better than their opponents.

Table 2 reports home team arena capacity for A-10 schools and average percent capacities for each school. Schools such as St. Joseph, Xavier, Dayton and George Washington filled their arena with an above 90% attendance level on average whereas Duquesne, Richmond and Temple struggled to fill their arena with, on average, a lower than 50% attendance level.

Table 3 presents correlations between the independent variables and points scored by the teams. Notably, it is not two-point and three-point shooting percentages that have the strongest correlation with points scored at 0.4756 and 0.4261, respectively; assists have the strongest correlation (0.6438) with scored points, though they are strongly correlated with shooting percentage. This leads us to the argument that passing the ball well to create easier (high-percentage) shots generates points on the scoreboard. Referring to Table 4, we see that 6 out of 8 teams with winning percentages above 50% outperformed their opponents in assists. Of the 6 teams with less than a 50% winning percentage, only 3 teams outperformed in assists.

RESULTS
In order to ascertain the validity of the stochastic frontier approach and determine the appropriate specification of the production function, various hypothesis tests are conducted. Results from the generalized likelihood-ratio (LR) statistics are presented in Table 4.

First, given the assumption of the translog stochastic frontier model in equation (5), the null hypothesis that the points production follows a Cobb-Douglas production function ( is rejected at a 1% level indicating that the Cobb-Douglas production function is not an adequate specification. Second, the null hypothesis of the no technical inefficiency effects ( is rejected at a 1% level. Therefore, given the specification of the translog stochastic frontier model, to assume that teams are fully technically efficient is not an adequate representation of team level game efficiency. Lastly, the null hypothesis that all determinants are jointly zero ( is rejected at a 1% level. This implies that the technical inefficiency effects cannot be regarded as having the same truncated-normal distribution. These results reject simplification of the proposed model given by equations (5) and (6).

The estimation results of the full model in equations (5) and (6) are presented in Table 5. As we have discussed, equations (5) and (6) are estimated simultaneously using the maximum likelihood estimation technique. As expected, the stochastic frontier results show that the ratios associated with shooting accuracy such as 2-point and 3-point shooting percentages have a positive contribution to points scored. For example, a 10% increase in 2-point shooting percentage increases points scored by about 2.8%. This means a team that puts 60 points on the scoreboard with a 2-point shooting percentage of 40% can add an additional 1.6 points (so 1 or 2 more points) on the scoreboard if it improves its 2-point shooting percentage by 10%. Offensive and Defensive Rebounds also have a positive impact on points scored since rebounds enhance the chance to score more. Assists represent ball handling skills and teamwork. On the other hand, as expected, Personal Fouls and Turnovers have a negative effect on points scored. The estimated coefficients for the ratio of Blocks and Steals, which are proxies for defensive intensity, have the right signs but are shown to be insignificant in terms of their contributions on points scored.

The results of equation (6), which provide the estimates for the determinants of team level game efficiency, are presented under Inefficiency in Table 5. It shows the results when home related variables (Location, Travel Distance and Home Court Atmosphere) are considered in the inefficiency equation.

When each of the home-related variables is tested alone (model 2, 3 and 4), only Travel Distance and Home Court Atmosphere are shown to be significant and Location is shown to be not significant. As expected, Travel Distance has a negative effect on game efficiency, and Home Court Atmosphere has a positive effect on game efficiency. For example, a 10 % increase in Home Court Atmosphere increases points scored, on average, by 5.7%. This means a team that puts 60 points on the scoreboard with a half-filled arena can add additional 3.4 points (so 3 or 4 more points) on the scoreboard if it fills the arena by 10% more. Note that since the second equation in the model (equation (6)) measures the inefficiency effects, a positive sign in front of an estimated determinant’s parameter indicates that the particular parameter causes the efficiency to decrease. On the other hand, a negative sign in front of an estimated determinant’s parameter indicates that the particular parameter causes the efficiency to increase. When the home-related variables are tested together (Model 1 in Table 5), only Home Court Atmosphere is shown to have a significant effect on game efficiency. Therefore it appears that, among the three home-related variables, Home Court Atmosphere is the key determinant for game efficiency. The effect of Home Court Atmosphere is also greater when Home Court Atmosphere is tested together with Location and Travel Distance. For example, a 10% increase in Home Court Atmosphere increases points scored, on average, by 13.3%. This means a team that puts 60 points on the scoreboard with a half-filled arena can add an additional 8 points on the scoreboard if it fills the arena by 10% more. The effect of Home Court Atmosphere seems rather large. Nevertheless, the results indicate the significance of home crowd support on the aggressiveness and effectiveness of home teams. More importantly, the results indicate that the game location by itself does not improve game efficiency, hence does not create the home court advantage. What appears to matter more is the Home Court Atmosphere in which the home crowd encourages home team players to play to their potential by feeding the home team positive intrinsic recognition.

CONCLUSION
By examining the determinants of technical efficiency of college basketball teams, The researcher has explained the home-court advantage phenomenon as an efficiency phenomenon and identified the Home Court Atmosphere (measured by home crowd density), among all home-related factors, as the leading source of the home court advantage. The researcher showed that home teams, when supported by the home team’s crowd, play better with enhanced game efficiency. It is not simply playing aggressively at home or the familiarity of the home court that gives the home teams advantage over visiting teams as previous studies suggested, but rather the home court atmosphere – providing positive intrinsic recognition- that enhances the home teams to play up to their potential. Indeed, the result of this paper supports the idea that having a supportive and encouraging audience motivates the athletes to perform better.

APPLICATIONS IN SPORT
The results of this paper suggests that sports program directors and coaches have an incentive to develop ways to get the crowd into the game. Even with a small home crowd, as long as the home team crowd is fired up, that energy can be fed into the players and enhance their game efficiency. A small but rowdy crowd may be more beneficial than a large but silent crowd.

ACKNOWLEDGMENTS
None

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