Retaining Current Vs. Attracting New Golfers: Practices among the Class A Carolinas Professional Golf Association Membership

Abstract

Golf rounds declined in the U.S. from 2001 to 2004. The southeast region of the country has started to show increases in golf rounds. A possible explanation for this turn-around can be found in the theory of reasoned action. A survey among Professional Golf Association Class A Members in the Carolinas section of the PGA shows the utility of retaining current avid golfers is greater than the utility of attracting new golfers. Implications for managing golf clubs nationally are discussed.

Introduction

The golf industry in the U.S. has recently been stagnant or declining in the number of rounds of golf played annually. The National Golf Foundation (NGF) has reported a national decline from 2001 to 2004 of -4.5% (NGF, 2004). A similar trend (-4.3%) has been observed in the southeast region during that period. Some observers (Graves, 2006; Harrack, 2006) have suggested that concentrating on getting avid golfers to play more rounds is a better approach than trying to attract new golfers to a club.

More recently, the NGF (ngf.org, 2007) is reporting a national upturn in golf rounds of +0.8% with the southeast region showing a robust growth of +4.5%. The question of why the southeast region is doing so well is one of management priorities. The theory of reasoned action (Hawkins, Mothersbaugh, and Best, 2007) provides a framework for understanding how managers of business enterprises make decisions. Professional Golf Association (PGA) members who run golf club enterprises are no different than the chief executive officer of a Fortune 500 company in the decisions they need to make. A business manager needs to identify how to grow the business and make a profit. Operational goals have varying priority and utility in this effort, and golf club managers have intensified their commitment to growing rounds of golf (Staw, 1981).

Theory of Reasoned Action

The theory of reasoned action specifies the decision-making task confronting PGA members who manage golf clubs. Historically, psychologists (Baron, 2000), game theorists (Von Neuman and Morgenstern, 1972), sociologists (Homans, 1961), economists (Elster, 1986), and marketers (Johnson and White, 2004) have all embraced theory of reasoned action concepts.

The concepts embodied in the theory of reasoned action include: 1) bounded rationality (only a few evaluative criteria can be considered simultaneously implying limited capacity), 2) making trade-offs (applying the evaluative criteria to viable alternatives in a compensatory way), 3) the superior option is revealed as the one with the highest utility value to the business manager. Thus, the PGA member managing a golf club must decide what is important and which of those important goals will lead to the best business outcome.

The theory of reasoned action has a measurement methodology known as utility calculations (Baron, 2000). The basic concept, evaluative criteria, involves various dimensions, features, or benefits sought in attempts to solve a specific problem, such as reaching operational goals at a golf club. Managerial decisions involve an assessment of one or more evaluative criteria related to the potential benefits or costs that may result from a decision of which goals to pursue.

Thus, evaluative criteria are typically business activities associated with either benefits desired by managers or the costs they must incur. Depending upon the business situation, management evaluative criteria can differ in terms of type, number, and importance. Thus, a study of business management decision making involves an evaluation of both the importance of the business activity and the business performance resulting from specific criteria. Determining an evaluation of business activity options can be accomplished in two ways: 1) direct methods where PGA members are simply asked about the importance and satisfaction with performance concerning business activities they may use in a particular decision situation, and 2) indirect techniques, where it is assumed PGA members will not or cannot state their views on these issues. The approach taken here is direct assessment described below in the methodology.

The purpose of this project was to conduct a survey of PGA Class A professionals who manage golf course enterprises in the CPGA region to determine what their priorities are regarding operational goals they see as related to stimulating growth in rounds of golf played at their clubs.

Hypothesis

It is hypothesized that PGA Class A Members managing golf clubs in the CPGA will consider the utility of retaining current golfers to be larger than the utility of attracting new golfers.

Methodology

The Class A PGA members survey provided data concerning golf course management practices utilizing an e-mail recruitment and VOVICI (formerly WebSurveyor). The issues involved include:

1.    Making the questions easy to understand and answer;

2.    Measuring the relevant concepts such as importance and performance;

3.    Asking appropriate demographic questions;

4.    Having a relevant e-mail list;

5.    Having a short and effective invitation;

6.    Sending the e-mail invitation at an effective time; and

7.    Using follow-ups as necessary.

Faculty handled items one through four above and utilized WebSurveyor to create the survey instrument. The e-mail recruiting list came from the PGA; thus it was relatively fresh and accurate. Items five, six, and seven were handled by the students after instruction from faculty.

There were 72 students in two Retail Management classes who participated in fielding the PGA web survey. Each student had a list of approximately 20 PGA members to contact through e-mail. The first round of e-mail invitations produced few completed survey responses without an endorsement letter. The second round of e-mail invitations included an endorsement letter from the Secretary of the Carolinas Section of the PGA. In addition, a specific subject line was provided that said, “A Message from Karl Kimball, Secretary of the Carolinas Section of the PGA.” Students were also required to copy the Retail Management professor on all outgoing e-mails to keep track of their efforts so they could receive course credit and so the PGA respondents could receive a summary of the results after the responses were analyzed.

This approach to survey control ensured that e-mail invitations were sent out in a timely fashion, had an appropriate and inviting subject line, included an endorsement by an appropriate source, and offered an incentive for participation in the form of a summary of the results (Goodman, 2006). As a result, 107 completed surveys were available for analysis.

Measuring business managerial judgments of the importance of and satisfaction with performance on specific operational goals can include rank ordering scales, Semantic Differential scales, or Likert Scales. Likert Scales were used here.

Using a Likert Scale to measure importance and satisfaction with performance against operational goals in the theory of reasoned action applied to golf club management comes in the form of a calculated utility score. Here, utility is defined as the product of each operational goal’s rated importance score and its rated satisfaction with performance score measured on a Likert Scale. For this study, it is the importance and satisfaction score associated with retaining current golfers as well as attracting new golfers using the Importance and Satisfaction Likert Scales below.

Importance

5 = Extremely Important
4 = Somewhat Important
3 = Neutral
2 = Not Very Important
1 = Not Important At All

Satisfaction with Performance

5 = Very Satisfied
4 = Somewhat Satisfied
3 = Neutral
2 = Somewhat Dissatisfied
1 = Very Dissatisfied

In addition to measuring importance and satisfaction with performance concerning retaining and attracting golfers to the club, a series of demographic items were included in the survey such as type of course, golf population served, tenure of the course manager as a Class A Member, and the time at the current club spent by the Class A Member of the PGA.

Results

Sample Characteristics

The results of the demographic items appear below and indicate the survey produced a wide variety of clubs where the PGA members are located.

Type of Course: The majority of PGA members were at either private (34.7%) or semi-private courses (28.7%), with some at public courses (17.8%), resorts (11.9%), or other type of courses (6.9%).

Golfing Population Served: Almost half of the PGA members described their golfing population as mostly permanent residents (49.5%) with few serving either mostly out-of-town visitors or mostly part-time residents (6.9% each), while close to a third (30.7%) have a golfing population balanced among these three groups.

Tenure as a PGA Class A Member: Few PGA members in the survey have been in Class A for 5 years or less (8.9%) or between 6 and 10 years (14.9%). Almost half have been in Class A between 11 and 20 years (48.5%) and less than a third have been in Class A for more than 20 years (27.7%).

Time Served at Current Club: Over a third of these Class A members have been at their current club for either 2 to 5 years (37.6%) or more than 10 years (38.6%). A minority have been in place either 6 to 10 years (18.8%) or 1 year or less (5.0%).

Importance of Retaining Current Golfers and Attracting New Golfers

The results for the importance of reaching the operational goals of attracting new golfers and retaining current golfers appear in Table 1. PGA members rated both operational goals as extremely important.

Table 1: Means and Standard Deviations for Operational Goal Importance

Operational Goals Mean Response Standard Deviation
Attracting New Golfers 4.64 0.622
Retaining Current Golfers 4.80 0.531

Satisfaction with Performance in Retaining Current Golfers and Attracting New Golfers

Results for satisfaction with performance with operational goals appear in Table 2. PGA members were somewhat satisfied with performance against the two operational goals.

Table 2: Means and Standard Deviations for Satisfaction with Performance in Reaching Operational Goals

Operational Goals Mean Response Standard Deviation
Attracting New Golfers 4.10 0.572
Retaining Current Golfers 4.19 0.741

Utility of Retaining Current Golfers and Attracting New Golfers

Results for the calculated utility scores for the two operational goals appear in Table 3. A paired-t test was done on the mean responses for the two operational goals and indicates retaining current golfers has significantly higher utility to the PGA members compared to attracting new golfers (t [90] = -2.44, p <.02 two-tailed).

Table 3: Means and Standard Deviations for Utility in Reaching Operational Goals

Operational Goals Mean Response Standard Deviation
Attracting New Golfers 19.02 3.85
Retaining Current Golfers 20.09 4.32

A final issue concerns whether or not reaching these operational goals is producing an increase in rounds played and how that utility is realized and that increase is accomplished.

Change in Rounds Played

A series of survey items dealing with number of rounds played per year at the club was also included. These items included total number of rounds played, number of rounds at a discounted price, number of rounds as part of a golf and lodging package, and number of complementary rounds. Table 4 shows the change in number rounds reported by the PGA members.

Table 4: Percentage Reporting Changes in Rounds Played

Percentage Reporting Changes in Rounds Played Increasing Stable Declining
Number of Rounds Played Per Year 45.9% 42.9% 11.2%
Number of Rounds at a Discounted Price 24.4% 50.0% 25.6%
Number of Rounds as Part of Golf and Lodging Package 22.8% 63.3% 13.9%
Number of Complimentary Rounds Played 6.5% 76.3% 17.2%

The net percentage of PGA members reporting change in rounds played can be found by subtracting the percentage reporting a decline from the percentage reporting an increase in the number of rounds while ignoring those who are stable. Thirty-five percent of the PGA members reported net rounds are increasing. This increase was attributed to golf and lodging packages bringing more golfers to the course (+9%). In addition, declines in discounted (-1%) and complementary rounds (-11%) were reported. The figure below displays these results for the net percentage of PGA Class A Members reporting changes in net rounds played.

Net Percentage Reporting Change in Rounds Played
Conclusions and Implications:

Figure 1. Net Percentage Reporting Change in Rounds Played

Conclusions and Implications

Support for the hypothesis that CPGA Class A Members would show more utility for getting additional rounds from current golfers compared to attracting new golfers indicates they have solved the problem of declining rounds of golf in accordance with the theory of reasoned action. These club professionals realized that getting additional rounds of golf from golfers who patronize their clubs is more effective than trying to attract new golfers with discounted rounds and complementary rounds. Any costs associated with golf and lodging packages were more than compensated for by a substantial increase in rounds per year.

For the PGA membership to increase rounds nationally, the focus should be on retaining current avid golfers to increase rounds and get them to the club by offering golf and lodging packages and reducing discounted and complementary rounds to attract new golfers. Growth can be restored in this manner for golf rounds in the U.S.

References

Baron, J. (200). Thinking and Deciding, 3rd edition, Cambridge, UK: Cambridge University Press.

Elster, J. Ed. (1986). Rational Choice. Oxford, UK: Basil Blackwell.

Fishbein, M. and Ajzen, I. (1975). Belief, Attitude, Intention, and Behavior: An Introduction to Theory and Research. Reading, MA: Addison-Wesley.

Goodman, G.F. (2006). Five common email marketing mistakes. http:// www.Entrepreneur.com>

Graves, R. (2006), Golf Ranges Drives Profits: Today’s range is a practice center, learning center, clubfitting center, Etc. PGA Magazine, (August 1), 37-57.

Harack, T. (2006), Pushing forward: A proactive recruitment program can help stimulate stagnant membership roles, Golf Business, 12 (August), 26-27.

Hawkins, D., Mothersbaugh, D., and Best, R. (2007). Consumer Behavior: Building Marketing Strategy, 10th ed. Boston, MA: McGraw-Hill: Irwin.

Homans, G. (1961). Social Behaviour: Its Elementary Forms. London: Routledge and Kegan Paul.

Johnson, D., and White, J. (2004). A new integrated model of noncompensatory and compensatory decision strategies, Organizational Behavior and Human Decision Processes, 95, 1-19.

National Golf Foundation (2004), Rounds Played in the United States, 2004 Edition.

National Golf Foundation Press Release (2007), Rounds Played in the United States, 2007, <http://www.ngf.org/cgi/whonews.asp?storyid=191>

Staw, B.M. (1981). The escalation of commitment to a course of action. Academy of Management Review, 6, 577-587.

Von Neuman, J, and Morgenstern, O. (1972). Theory of Games and Economic Behavior, Princeton, NJ: Princeton University Press.

Show Me the Money! A Cross-Sport Comparative Study of Compensation for Independent Contractor Professional Athletes

Abstract:

Numerous pay equity studies have been conducted. Many have examined the compensation of professional athletes. However, few studies have compared athlete compensation across sports, which is the objective of this research. Focusing on independent contractor athletes, several analyses were performed to determine how one type of athlete’s (e.g., horse jockeys) earnings from competition (excluding sponsorships, appearance fees, etc.) compare to other types of contracted athletes, such as race car drivers, golfers, bull riders, tennis players, etc. Overall, this exploratory study sheds insight into how the different groups of athletes are paid, and, more importantly, provides a framework for future research that examines the compensation inputs (versus outputs) of each of these groups.

Introduction:

Salaries for professional athletes continue to escalate each year. From Alex Rodriguez’s record $252 million contract to David Beckham’s $50 million per year enticement to join the LA Galaxy soccer team, most sports fans believe that professional athletes, in general, are overpaid and not worth their salaries. Yet for the professional athlete, maximizing compensation is critical, given the short careers and health risks associated with professional sports. Thus, athletes and their agents often look to see what others within their sport are paid in an effort to negotiate for more money. Few, if any, have compared athlete compensation across sports. While a cross-sport comparison might not be necessary in team professional sports (e.g., MLB, NHL, NFL, NBA) given the strength of their collective bargaining agreements, independent contractor professional athletes (e.g., jockeys, bull riders, golfers, race car drivers) need this type of analysis. The purpose of this research is to compare independent contractor professional athlete salaries across sport using four perspectives: total payout to athletes per sport, percentage of winnings per sport, top individual earner by sport and mean earnings for the top 50 athletes in each sport. These perspectives will allow independent contractor professional athletes to better analyze the “fairness” or equity of compensation.

Background:

Ever since jockey Gary Birzer was paralyzed while racing in 2004, the jockeys’ guild and track owners have had an acrimonius relationship, to say the least. While much of the ongoing battle has centered on who should pay for the jockeys’ long-term disability coverage, the dispute has recently turned to jockey compensation. The jockeys believe they are underpaid, given the amount of overall purse money involved in the sport and the inherent health risks of racing horses. In contrast, the race tracks believe that the horse owners and trainers deserve the bulk of winnings, given their financial risk and knowledge. With the sides at a stalemate, Corey Johnsen, President of Lone Star Park at Grand Prairie and current President of the Thoroughbred Racing Associations (the trade organization for the tracks) commissioned this study. By collecting extensive data across a number of sports, Johnsen sought to provide a starting point for discussions between the tracks and the jockeys’ guild in an effort to resolve the dispute.

Review of Literature:

A number of management and economic researchers have investigated compensation equity or justice across many industries. While it is beyond the scope of this paper to cover all of this literature, this section highlights a few key citations.

Carrell and Dittrich (1978) were two of the first to provide a comprehensive look at pay equity. The authors looked at the components of pay equity, such as an individual’s perceived inputs and outputs. In addition, they examined how an individual adjusts performance when he or she perceives pay to be inequitable. Adding to the body of existing literature, Younts and Mueller (2001) measured the importance individuals place on compensation justice, in particular distributive justice (i.e., the outcomes or rewards received). Similarly, St-Onge (2000) extended the literature by evaluating the influence of several individual variables on pay-for-performance perceptions, specifically looking at actual pay-for-performance, trust in decision-makers, perceived procedural justice, outcome satisfaction and size. Using social equity theory, Sweeney and McFarlin (2005) found that an individual’s pay satisfaction was based on that individual’s wage comparisons with similar and dissimilar others.

Looking specifically at athlete compensation, the majority of previous studies have dealt with team sports, and, in particular, Major League Baseball, given its unique market structure and history (e.g., anti-trust exemption, owner collusion in the 1980s, etc.). For instance, Slottje, Hirschberg, Hayes, and Scully (1994) used Frontier estimation to measure wage differentials in Major League Baseball and discovered that free agency status significantly influenced wage inefficiency. Similarly, Scully (2004) examined the effects of free agency on compensation as a share of league revenue and the dispersion of compensation among players across the four major professional sports: MLB, NBA, NFL, and NHL. As expected, he concluded that both were higher when leagues permitted a free labor market. Looking more closely at one professional sport, NHL hockey, Idson and Kahane (2000) empirically investigated the effects of co-worker productivity by examining individual variables, such as height, weight, points scored, plus/minus ratios, star status, and team/coach variables, such as team revenues, coach’s tenure, and coach’s winning percentage in the league. They concluded that “estimates of the effects of individual attributes on compensation are upwardly biased when team effects are not taken into account in standard salary regressions” (p. 356). Lastly, Nero (2001) used multiple regression analysis to measure the salary effectiveness of independent contractor athletes in one sport: PGA tour golfers. In his study, he analyzed the impact of a pro golfer’s driving distance, fairways hit, putting average per green, and sand saves (i.e., the percentage of times a player uses at most two shots to score from a greenside sand trap) on earnings. He concluded that putting average had the greatest influence on a golfer’s earnings.

Analysis:

  1. To compare jockey compensation to other independent contractor professional athletes, eleven sports were chosen (see Table 1). Salary data was compiled using primary research, including telephone and face-to-face interviews with representatives from various sports and secondary research utilizing websites, sports journals, magazines, and newspapers.

Table 1: Independent Contractor Sports for Comparison

  1. Professional Rodeo Cowboys Association (PRCA)
  2. Professional Bull Riding (PBR)
  3. Women’s Professional Rodeo Association (WPRA)
  4. Professional Golfers’ Association of America (PGA)
  5. Ladies Professional Golf Association (LPGA)
  6. Association of Tennis Professionals (ATP)
  7. Women’s Tennis Association (WTA)
  8. National Association of Stock Car Racing (NASCAR)
  9. National Hot Rod Association (NHRA)
  10. Association of Volleyball Professionals (AVP)
  11. Union Cycliste International (UCI)

Results:

Total Payout per Sport

Table 2 reveals the total payouts (excluding additional income such as endorsements or appearance fees) for horse racing (NTRA: National Thoroughbred Racing Association) and the independent contractor athletes in eleven other sports in 2005 and 2004.

Table 2: Total Payout by Sport

Assn 2005 2004
NTRA $1,085,000,000 $1,092,100,000
PRCA $37,553,821 $18,881,001
PBR $5,615,563 $3,491,450
WPRA $5,000,000 $4,000,000
PGA $266,112,055 $256,740,000
LPGA $44,400,000 $42,075,000
ATP $90,287,231 $88,549,527
WTA $59,190,883 $56,614,168
UCI $85,050,000 $85,050,000
NASCAR $275,276,253 $264,210,961
NHRA $13,500,000 $12,600,000
AVP $3,500,000 $3,000,000
Totals $1,970,485,806 $1,927,312,107

As illustrated, the amount of money paid out (i.e., purse money) in horse racing far exceeds the other sports. In fact, the second and third ranked sports, NASCAR and PGA, have purses approximately 25% of those of the NTRA. However, when the payouts for jockeys-only (i.e., the percentage of the purse that is paid to the jockeys by the owners) is compared to the athletes in the eleven other sports, the amount is much less than the compensation paid to PGA golfers and NASCAR drivers (see Figure 1).

Figure 1
Figure 1
Percentage of Winnings Per Sport

Figure 2 provides another perspective of the data in Figure 1. When we analyzed the dollars paid to jockeys as a percentage of the total purses (payouts), we found that jockeys, on average, received 7.5% of the available purse. This is much lower than a number of the other sports. Figure 3 provides the breakdown of purse percentage for first, second, and third places. As shown, NTRA jockeys receive 6% of the available purse for winning a race and 1% and .55% for second and third places respectively. In contrast, PRCA and PBR athletes received at least 20% of the purse for a second place finish.

Figure 2
Figure 2

Figure 3
Figure 3
Note: NTRA represents just the jockey’s percentages

Top Individual Earner by Sport

While using one individual in each sport is not an accurate representation of all athletes within the sport, comparing the top earner provides a glimpse of the earning potential per sport. As Figure 4 reveals, the top jockey, John Velasquez did not earn as much as Tiger Woods (PGA), Roger Federer (ATP), Maria Sharapova (WTA), Annika Sorenstam (LPGA), or Tony Stewart (NASCAR). However, he still makes nearly $2 million per year in earnings.

Figure 4

Top 50 Earners by Sport

Given the drawbacks of looking at the top earner in each sport, the top 50 earners in each sport were compared (see Figure 5). As shown, the average salary of the top 50 jockeys ranks fifth and is approximately $500,000 per year.

Figure 5
Figure 5
Note: NTRA represents just the jockeys (excludes owners and trainers)

Conclusions, Limitations, and Future Research:

Although a very simplistic bivariate analysis was used, this research provides important information for both sides of the jockey compensation debate. From the perspective of the tracks, over $1 billion is paid out in purses each year, with millions going to the jockeys, making horse racing a very lucrative sport. In contrast, from the jockeys’ perspective, they only receive 6% of the purse earnings, if they win, and 7.5% overall. While both sides have their stance, this research should allow the two sides to come together and begin discussions on how to solve this labor dispute. For instance, there might be a way to re-distribute the earnings to allow the second and third place finishers to earn more.

As with any research, there are limitations to this study. For one, this analysis excludes additional monies that athletes receive outside of competing (e.g., appearance fees, endorsements, etc.). Secondly, this research was limited by the bivariate analysis.

In the future, researchers should comparatively examine the sponsorship/endorsement dollars that independent contractor professional athletes receive across the twelve sports. This would provide a more thorough comparison of the total compensation these athletes receive. In addition, more sophisticated statistical analyses are needed to compare athletes across sports via multiple regression analysis or related techniques. As Porter and Scully (1996) pointed out, an individual athlete’s performance is difficult to measure because it is “a serially repeated and rewarded event. Among the individuals competing in professional sports, the distribution of earnings is determined by the distribution of awards for performance, the distribution of talent (expected performance), and by work effort (the number of competitions undertaken)” (p. 149).

Hopefully, future researchers will be able to examine in more detail the pay equity of independent contractor professional athletes.

References:

Carrell, M. and J. Dittrich (1978). Equity theory: The recent literature, methodological considerations, and new directions, The Academy of Management Review, Vol. 3, 202.

Idson, T. and L. Kahane (2004). Teammate effects on pay, Applied Economics Letters, Vol. 11 (12), 731.

Nero, P. (2001). Relative salary efficiency of PGA tour golfers, American Economist, Vol.45 (2), 51.

Porter, P. and G. Scully (1996). The distribution of earnings and the rules of the game, Southern Economic Journal, Vol. 63 (1), 149.

Scully, G. (2004). Player salary share and the distribution of player earnings, Managerial and Decision Economics, Vol. 25 (2), 77.

Slottje, D., J. Hirschberg, K. Hayes and G. Scully (1994). A new method for detecting individual and group labor market discrimination, Journal of Econometrics, Vol. 61 (1), 43.

St-Onge, S. (2000). Variables influencing the perceived relationship between performance and pay in a merit pay environment, Journal of Business and Psychology, Vol. 14 (3), 459.

Sweeney, P. and D. McFarlin (2005). Wage comparisons with similar and dissimilar others, Journal of Occupational and Organizational Psychology, Vol. 78, 113.

Younts, C.W. and C. Mueller (2001). Justice processes: Specifying the mediating role of perceptions of distributive justice, American Sociological Review, Vol. 66 (1), 125.

Cross-Country Skiing USSA Points as a Predictor of Future Performance among Junior Skiers

Abstract:

Junior cross-country skiers’ performances prior to participation in the 2006 Junior Olympics were compared to their results in the 2006 Junior Olympics using USSA points as a measure of performance.  Junior class and division (team) were also included as independent variables.  Prior performance as determined by USSA points is a poor indicator of performance in the Junior Olympics.

Introduction:

Cross-country skiing times from different races, even those of the same length, are not comparable because the terrain is different for each race.  Furthermore, snow conditions may vary, even from hour to hour, on the same course.  Merely comparing times of skiers over similar distances is not an accurate comparative assessment of skiers’ abilities.  The United States Ski and Snowboard Association (USSA) points list was developed to allow comparison between skiers who may have entered several different races.  USSA points are awarded to registered cross-country skiers for participation in sanctioned ski races.  A lower value in USSA points indicates that a skier is a better, more competitive skier.  USSA points and similar International Ski Federation (FIS) points are used to help select the U.S. national teams, to seed racers in both mass and interval start races, and to monitor the progress of athletes in physiological studies (Bodensteiner & Metzger 2006; Staib, Im, Caldwell, & Rundell 2000).

The USSA formula that allocates points to skiers is based on race performance. It includes a number of variables that capture the relative ability of skiers in the race.  Who enters the race and how they place are used in determining the penalty.  Each race’s penalty is based upon the current USSA points of top finishers in the race.  The type of start or race and a minimum penalty also are used in the calculation of USSA and FIS points assigned to a skier’s race (Bodensteiner & Metzger 2006, International Ski Federation, 2006).  Despite the common and, at times, mandatory use of the system, the USSA point system has been criticized by racers and coaches over the years for failure to accurately capture a skier’s ability (Anonymous, 2006; Smith, 2002; Trecker 2005).

Methods:

Given the importance and criticism of USSA points, this study develops a systematic comparison of prior USSA points results of skiers to their USSA points earned in a common competition.  One would hypothesize that a skier’s points prior to a competition would predict a skier’s points earned within the competition.   Points earned by Junior skiers (ages 14 to 19) in the 2005-2006 season are compared to USSA points in the 2006 Junior Olympics.  The use of linear regression allows one to determine if a linear relationship exists between prior performance and performance in the Junior Olympics and whether other, easily obtained variables can improve the ability to predict performance at the Junior Olympics.  (Hill, Griffiths, & Judge, 1997; Johnston, 1984)

Before the Junior Olympics, skiers earned USSA points in different races throughout the northern part of the United States.  Skiers within any of the ten USSA districts competed against each other, but there was limited competition among skiers from different districts.  The top 400 skiers then competed in the Junior Olympics in March, 2006 in Houghton, Michigan.  The end of season Junior Olympics allows skiers to be directly compared on the same course and with the same snow conditions, so USSA points assigned in these races can be used in this study free of the bias of course and snow conditions.

A general linear model (equation 1) with USSA points earned in the Junior Olympics as the dependent variable and USSA points prior to the Junior Olympics, junior class (J2, J1, or OJ) division (team) were used as independent variables.  The parameters c and ak (where k = 1, 2, and 3) were estimated.  Estimated parameters in bold are matrices of parameters associated with a matrix of dummy variables.  Equation 1 is the most comprehensive linear model used.

yi = c + a1*Pi + a2* JCLASSi + a3*DIVi + ei          equation 1

Where

yi = USSA points in the 2006 Junior Olympics for the ith skier,

c = an estimated constant,

Pi = USSA points prior to the Junior Olympics for the ith skier,

a1 = the estimated parameter associated with Pi,

JCLASSi = a matrix of junior classes with dummy variables for OJ, J1, and J2 where the value is 1 in the ith skier’s junior class and zero for other classes,

a2 = a matrix of estimated parameters associated with JCLASSi,

DIVi  = a matrix of regional divisions with dummy variables for Alaska, Great Lakes, Midwest, Intermountain, Rocky Mountain, Mid-Atlantic, New England, Far West, High Plains, and Pacific Northwest where the value is 1 in the ith skier’s division and zero for other divisions,

a3 = a matrix of estimated parameters associated with DIVi, and

ei = the residual value for the ith skier.

The model was run using USSA points from all three individual races at the Junior Olympics (yi): freestyle, classic, and sprint.  USSA points prior to the Junior Olympics included (Pi) for distance, sprints, and overall points were used in separate regressions.  Thus, there are several versions of equation 1 that use different techniques (classic and freestyle) and USSA disciplines (sprint, distance, and overall).

While equation 1 represents the most extensive model tested, other models using a subset of the independent variables were also tested to determine the stability of the model.  When sets of independent dummy variables would have resulted in a full rank matrix, one of the variables was not included in the regression.   Technical definitions associated with cross-country skiing terms can be found in the USSA’s Nordic Competition Guide (Bodensteiner & Metzger, 2006). Analyses were run using the GLM procedure in SAS 9.1 for Windows.

Data:

Pre-Junior Olympics distance, sprint, and overall USSA points; names; USSA numbers (to confirm this data with results from the Junior Olympics); junior class (J2, J1, or OJ); and year of birth information were obtained from the national list of USSA points, which had been updated just prior to the Junior Olympics.  Data were downloaded on March 27, 2006.  Junior Olympic classic, freestyle, and sprint USSA points; skier’s division (team); name; and USSA number were obtained from itiming.com via the web in the week following the 2006 Junior Olympics.  In all cases, as complete a data set as possible was used in the regression.  However, some skiers entered the Junior Olympics without prior USSA points or with only a partial set of information.  The most common missing data were USSA sprint points prior to the Junior Olympics.  Whenever a valid number was available for a skier, that skier was entered in the data set for a particular regression analysis.  In a few cases, skiers did not start or finish a race or were disqualified during the race.  The largest data set included information for 271 skiers.

Results:

USSA Points prior to the Junior Olympics – the simplest models.

The first part of the statistical analysis was to determine if USSA points alone could predict USSA points in the Junior Olympics.  The model used to test this question was:

yi = c + a1*Pi + ei          equation 2

Since skiers have sprint, distance, and overall points prior to the Junior Olympics and compete in sprint, freestyle distance, and classic distance events, there are six logical combinations of dependent and independent variables.  Table 1 shows the results of each regression.

Table 1:  Results from the regression of USSA points earned at the Junior Olympics (yi) on USSA points earned prior to the Junior Olympics (Pi).  Equation 2

yi JO Points (Source) Pi Prior (Source)  

estimated c

 

estimated a

 

r2

Freestyle Overall 87.1 0.57 0.59
Freestyle Distance 82.8 0.59 0.59
Classic Overall 116.9 0.79 0.36
Classic Distance 106.7 0.85 0.37
Sprint Overall 74.4 0.80 0.54
Sprint Sprint 84.8 0.60 0.49

Note:  All estimated parameters were significant at the 0.0001 level.

At best, the USSA points earned prior to the Junior Olympics predict only 59% of the variability in the final USSA points earned at the Junior Olympics.  Equation 2 is least effective when used to predict the classic results, explaining only 36% of the variability when the independent variable is Overall USSA points prior to the Junior Olympics.  Figure 1 shows the relationship between the Overall USSA points prior to the Junior Olympics and USSA points earned in the Junior Olympics classic race.  The top five skiers based upon prior USSA points also ended up with results close to what one would expect.  However, after this elite group of skiers, the prior USSA points exhibit poor predictive ability for the remaining skiers.  Some skiers with relatively high USSA points skied well and moved up dramatically at the Junior Olympics.  The reverse was also true; some skiers skied less competitively than one would have predicted from their prior USSA points.  While this is to be expected to some extent (athletes have good and bad days), the large number of skiers who deviated from the expected indicates something other than a few atypical performances by a small number of skiers has occurred.  While the correlation between prior USSA points and the freestyle and sprint race results were better than the classic, the same general pattern is evident the results of these two races are plotted.  The top skiers were identified by prior USSA points while predictive power diminishes for average and relatively weaker skiers at the Junior Olympics.  In fact, even finish order is poorly predicted by prior USSA points.

Figure 1
Figure 1.  Relationship between Overall USSA points prior to the Junior Olympics and USSA points earned in the classic race at the 2006 Junior Olympics.

Figure 1 also shows that this data set is heteroscedastic.  The heteroscedasticity of the data is discussed in the Appendix.

USSA Points prior to the Junior Olympics – adding independent variables

Given that USSA points earned prior to the Junior Olympics are relatively poor predictors for results at the Junior Olympics, whether or not it is it possible to use other readily available information to improve the estimate of where a skier would finish is of importance. Equation 1, a more robust model, was estimated for the same six data sets used for equation 2.  Equation 1 includes the JO class of the ski and the division (team) of the skier. The r2 associated with each equation is shown in Table 2.

Table 2.  Comparison of Equation 2, only prior JO points, with Equation 1, prior JO points, Junior class, and division (team).

yi JO Points (Source) Pi Prior
(Source)
equation 2
r2
equation 1
r2
Freestyle Overall 0.59 0.69
Freestyle Distance 0.59 0.68
Classic Overall 0.36 0.51
Classic Distance 0.37 0.52
Sprint Overall 0.54 0.65
Sprint Sprint 0.49 0.64

Using Junior class and division and team of the skier improved the r2 for all six combinations of Junior Olympics USSA points and points earned prior to the Junior Olympics.  Unfortunately, the best r2 is 0.69, indicating that there is still a substantial amount of unexplained variability in the data set.  Equation 1 is an improvement, but still does not leave one with the ability to use the model with confidence if the purpose is to use past performance to predict expected performance.

Because there is little difference between the use of overall points and other prior USSA points as independent variables in equation 1, only results for equation 1 with overall points are reported.  Table 3 shows the variables, estimated parameters, and P values for each independent variable for the classic, freestyle, and sprint races at the 2006 Junior Olympics.

Table 3.  Estimated parameters and probability level for the parameters, in parentheses, for equation 1.  Estimations are for all three individual events at the Junior Olympics using skiers’ overall USSA points, division (team), and junior class as independent variables.

Independent           Estimated Parameter and P Value (Pr > |t|)
Variable                Classic               Freestyle                 Sprint        
Constant               135.90                 83.47                   44.38
(<0.001)            (<0.001)                 (0.003)
OVERALL                  0.89                  0.55                     0.77
(<0.001)            (<0.001)              (<0.001)
NE                       -46.43               -17.78                  -22.73
(0.005)              (0.015)                 (0.063)
MA                        -7.61                  4.50                     5.13
(0.731)              (0.647)                 (0.743)
GL                       -28.74               -21.40                   53.06
(0.102)              (0.044)                 (0.012)
MW                         1.15                 -6.50                     0.87
(0.961)              (0.405)                 (0.946)
HP                         50.07                 56.54                   69.19
(0.047)            (<0.001)              (<0.001)
IM                         -5.15                 20.21                   58.61
(0.754)              (0.006)              (<0.001)
RM                        -4.40                 -3.12                   33.66
(0.794)              (0.677)                 (0.004)
FW                       -32.77               -17.09                   51.88
(0.090)              (0.047)              (<0.001)
PN                         -2.75                  0.63                   23.66
(0.887)              (0.942)                 (0.079)
J1                        -16.16                  9.91                   26.69
(0.163)              (0.053)                 (0.002)
J2                        -93.08                  8.23                   13.23
                          (<0.001)              (0.211)                 (0.231)                
Notes:  Alaska and OJ are omitted to avoid estimation of a full-rank matrix.
NE = New England, MA = Mid-Atlantic, GL = Great Lakes, MW = Midwest,
HP = High Plains, IM = Intermountain, RM = Rocky Mountain, FW = Far West,
PN = Pacific Northwest.

Each of the equations is estimated with Alaska omitted as a team and the OJ class omitted.  This prevents full rank estimation of the equation.  The Classic estimation shows that New England and Far West skiers ski relatively faster than Alaskan skiers given their predicted times.  High Plains skiers are slower than predicted relative to the Alaskan skiers.  The estimated parameters for other divisions are not significantly different from zero.  In the freestyle race, the estimated parameter for the dummy variable representing skiers from the New England, Great Lakes, and Far West indicated that, given their prior USSA points, members of these teams were relatively faster than the Alaskan skiers as indicated by USSA points earned in the Junior Olympics race.  The phrase “relatively faster” is important.  In general, Alaskan skiers finished ahead of Great Lakes skiers, although the estimated parameter associated with the Great Lakes is negative.  The dummy variables for teams improve the estimation by adjusting for a skier’s team given the other variables used in the estimation, especially the overall USSA points prior to the Junior Olympics.  Using Alaska and the Great Lakes as an example, the average Alaskan skier entered the Junior Olympics with a better USSA points ranking and than the average Great Lakes skier.  The Alaskan skiers also outperformed the Great Lakes skiers on average at the Junior Olympics.  However, in the freestyle competition at the Junior Olympics, the Great Lakes skiers’ improvements from predicted to actual performance was substantially better than that of the Alaskan skiers.  Dummy variables capture this distinction.

In the freestyle race, the estimated parameters for the High Plains and Intermountain teams were positive.  In the sprint race, the teams from New England again had a significant, negative estimated parameter while the Great Lakes, High Plains, Intermountain, Rocky Mountain, Far West, and Pacific Northwest all had significant, positive estimated parameters.  Both the Far West and Great Lakes had significant, negative estimated parameters in the freestyle race but significant, positive estimated parameters in the sprint race.  (New England skiers can take heart that they outperformed their expected results and won the Alaskan Cup despite whatever disadvantage may accrue to weaker seeding.)

The estimated parameter for junior class was also significant for one of the classes in each of the equations, indicating that including class in the estimate improves the equation.  Junior class can help predict USSA points earned.

Stability of the Models

It would be tempting to state that the use of additional variables improves the equation and would help somebody trying to use prior USSA points in estimating performance or performance gains.  However, several factors argue against this.

1.  This data set represents only the top junior skiers, ages 14 to 19, over one season.

2.  The three versions of equation (1) estimated with classic, freestyle, and sprint results from the Junior Olympics are not similar.  Both the constant and parameter associated with the overall points vary considerably with the different estimations, indicating that the model is not stable.

3.  The parameters associated with dummy variables representing divisions (teams) and junior classes are not consistent and, in some cases, change dramatically from estimation to estimation.  For example, Great Lakes skiers have a positive and significant parameter associated with the dummy variable in the freestyle equation, but they have a negative and significant parameter associated with the dummy variable in the sprint equation.

4.  The r2 values associated with all equations estimated are not strong enough to justify the use of the model to predict the future results of skiers.

Given these concerns, it is likely that estimating these equations using data from other years or older skiers would generate substantially different equations.  It is unlikely that the model would be stable (that is, the estimated parameters would be similar), if different versions of the model were estimated or different data sets were used.

Conclusions:

This paper provides a clear test of the ability of USSA points to compare the relative ability of skiers.  The initial points of skiers earned in their best races prior to the Junior Olympics were used to estimate a linear regression model with points earned in three separate races at the Junior Olympics less than a month after the prior points list was released by the United States Ski and Snowboard Association.  The prior points were a poor predictor and the general model showed poor stability from estimation to estimation.  While these results were derived from a data set composed of junior skiers, they support the broader anecdotal concerns about USSA points.  This study provides a reliable quantitative basis for those concerns with a substantial and consistent data set.  Most observers of cross-country ski racing would not be surprised by these results.  However, the instability in the data set is striking and is less easily observed through casual observation of ski results.  Not only are the predictions relatively poor, those poor predictions vary with the subset of the data and the specific model used to make the prediction.  USSA points should be used with caution and with other information for critical decisions in cross-country ski racing.  Their value in monitoring skier performance in physiological trials is questionable.

References:

Anonymous.  (2006).  U.S. Olympic Cross Country Team Announced.  Retrieved October 6, 2006 from http://www.fasterskier.com/news2962.html  .

Bodensteiner, L., & Metzger, S.  (2006).  2006 USSA Nordic Competition Guide.  Park City, UT.

Hill, C., Griffiths, W., & Judge, G.  (1997).  Undergraduate Econometrics.   J. Wiley & Sons, New York.

International Ski Federation.  (2006).  Cross Country Rules and Guidelines of the FIS Points 2006/07.  Retrieved October 11, 2006 from http://www.fis-ski.com/data/document/pktrgl0607-neu.pdf

Johnston, J.  (1984).  Econometric Methods (3rd ed.)  McGraw-Hill, New York.

Smith, C.  (2002).  U.S. Olympic Team Selection.  Retreived July 17, 2006 from http://www.xcskiracer.com/rants.shtml

Staib, J.L., Im, J.,Caldwell, Z., & Rundell, K.W.  (2000).  Cross-country ski racing performance predicted by aerobic and anaerobic double poling power.  Journal of Strength and Conditioning 14(3), 282-288.

Trecker, M.  (2005).  Following the Olympic Trials, Who’s Hot, Who’s Not, and the Strange Anomalies of USSA Scoring.  Retrieved July 17, 2006 from http://www.fasterskier.com/opinion2749.html

Appendix – Heteroscedasticity in the Data Set:

This portion of the study on heteroscedasticity is placed in the appendix because most people interested in skiing will not be interested in statistical methods and assumptions.  They want to know if current USSA points predict future skiing results.  However, from an analytical viewpoint, improper use of statistics can lead to incorrect results and correct procedures lead to improved analysis.  One assumption of linear regression is that the variance of the random error term is 2 for all x.  If this is not the case, then the estimate remains linear and unbiased but it is no longer the best linear unbiased estimator and standard errors are often incorrect (Johnston, 1984).  Confidence intervals and results of statistical tests can be misleading.  This appendix covers four topics:  heteroscedasticity in equation 2, correcting for heteroscedasticity using data transformations, heteroscedasticity in the complete data set, and a brief conclusion.

Heteroscedasticity in equation 2

Equation 2 is the intuitive equation to test whether prior performance as measured by USSA points can predict future performance.

yi = c + a1*Pi + ei          equation 2.

Figure 1 shows a much wider variance in the dependent variables as USSA points increase.  White’s test for heteroscedasticity indicates a probability of greater than 99.99% that heteroscedasticity does exist (test statistic= 15.37 with two degrees of freedom).

Correcting for heteroscedasticity using data transformations

Data may be adjusted using transformations to eliminate heteroscedasticity (Hill et al, 1997, Johnston 1984).  In the data set used in this study, the variance in the residuals is larger for the larger values of the independent variable.  Two logical transformations are to take the logarithm of the independent variable and the square root of the independent variable.  Separate regressions were estimated using equation (2) where

(a)  Pi = the square root of the competitors USSA points earned prior to the Junior Olympics and

(b)  Pi = the natural logarithm of the competitors USSA points earned prior to the Junior Olympics.

In both cases, the r2 value improved less than 0.02, and the White’s test indicated that heteroscedasticity remained a problem.

Heteroscedasticity in the complete data set

The complete data set, including division and junior class of the competitor, not only improves the estimation, it is less likely heteroscedasticity exists.  White’s test for heteroscedasticity indicates a probability of approximately 80% that heteroscedasticity does exist (test statistic= 49.46 with 42 degrees of freedom).  Most researchers would not reject the null hypothesis at this level.  This indicates that the additional independent variables have the greatest impact on improving prediction for skiers with the higher (less competitive) prior USSA points.

Conclusion:

The original goal of this study was not only to determine what statistical model would work best for the data, but to determine if USSA points were a good predictor of future performance of athletes.  From a practical standpoint, a complex model used in the prediction would indicate that USSA points alone are a poor predictor and a complex model would be difficult to justify and administer.  The heteroscedasticity and the development of more complicated, but still unstable, models reinforce the results of the main paper.  Prior USSA points are poor predictors of Junior races.

Competitive Balance in Men’s and Women’s Basketball: The Cast of the Missouri Valley Conference

Abstract:

Competitive balance typically fosters fan interest. Since revenue associated with men’s sports is typically greater than with women’s, one might expect to find greater levels of competitive balance in men’s sport than women’s sport. The purpose of this research was to test this hypothesis by comparing the competitive balance in a high revenue intercollegiate sport, basketball, for both men and women over a 10-year period in the Missouri Valley Conference.  Three measures of competitive balance were employed. In each case, competitive balance was found to be greater among the men’s teams than the women’s. The findings support the hypothesis that where there is greater revenue potential, there should be greater competitive balance.

Introduction:

One of the important differences between sports organizations and other industrial organizations is the issue of competitive balance.  Whereas most industrial enterprises attempt to keep competition to a minimum, a lack of competition in the case of sport teams makes for boring games and ultimately fans lose interest (Depken & Wilson, 2006; El Hodiri & Quirk, 1971; Kesenne, 2006; Quirk & Fort, 1992; Sanderson & Siegfried, 2003).  This lack of interest would lead to a loss of revenue, as fewer fans would attend games or listen to or watch media presentations. While fans certainly prefer to see their teams win, they want them to at least have a chance of losing.  Economists refer to this as the uncertainty of outcome hypothesis (Leeds & Von Allmen, 2005).

In professional sports some teams, frequently those in large markets, normally receive more revenue than their competitors. Those teams are in a position to sign better players and win more frequently, leading to the problem of competitive imbalance.  Efforts to alleviate this problem have included salary caps, luxury taxes, revenue sharing, and reverse order of finish drafts.  In intercollegiate athletics, attempts to alleviate competitive imbalance are undertaken by the NCAA through its various rules and regulations (National Collegiate Athletics Association, 2006). Likewise, various intercollegiate athletic conferences do this through budgeting and scheduling requirements and the selection of institutional membership (Rhoads, 2004).

In order to maintain fan interest, competitive balance is important in all sports. From the viewpoint of program administrators, it would appear to be particularly important in sports such as basketball and football, in which there are potentially large sources of revenue involved.  Similarly, because revenue is typically so much greater for men’s than for women’s sports, one might expect to find greater efforts being made to bring about competitive balance in men’s sports than in sports for women.   This might be singularly true where there was a post-season tournament, thus a need to keep fan interest intense throughout the season to help insure interest for post-season play.

The purpose of this study is to test the hypothesis that one would expect to find more competitive balance in men’s than in women’s basketball.  More specifically, the researchers compared the degree of competitive balance in both men’s and women’s basketball in the Missouri Valley Conference (MVC) for the 10-year period 1996-97 through 2005-06. The MVC was selected because it annually holds a post-season tournament, and the authors had access to financial data indicating that there was significantly larger revenue associated with men’s basketball than women’s basketball (Missouri Valley Conference, 2006a). The particular time frame was selected as a period of stable membership within the conference.

The Missouri Valley Conference

Established in 1907 as the Missouri Valley Intercollegiate Athletic Association, the MVC is the oldest collegiate athletic conference west of the Mississippi River and the fourth oldest league in the nation (Markus, 1982).  The league has been comprised of 32 member institutions at varying times through its history, and it has seen members win national titles on 25 occasions (Missouri Valley Conference, 2006b).

The MVC now features 10 league members:  Bradley University, Creighton University, Drake University, the University of Evansville, Illinois State University (ILSU), Indiana State University (INSU), Missouri State University (MSU), the University of Northern Iowa (UNI), Southern Illinois University (SIU), and Wichita State University (WSU).

While the conference’s membership has changed on several occasions since its founding, the most recent changes occurred in the early and mid 1990s.  The MVC and the Gateway Collegiate Athletic Conference merged in 1992 (Benson, 2006; Markus, 1982; Missouri Valley Conference, 2006b; Richardson, 2006).  The merger resulted in the addition of UNI to bring total league membership to 10 institutions (Carter, 1991; Richardson, 2006).  It also resulted in the establishment of MVC championship programs in women’s sports for the first time in conference history.

In 1994, Evansville joined the conference, giving the conference an all-time high 11 league members (Richardson, 2006).  Conference membership dropped back to 10 institutions in 1996, when the University of Tulsa left the MVC to join the Western Athletic Conference (Bailey, 2005; Richardson, 2006)

Measuring Competitive Balance

There are several ways of measuring competitive balance, and there is some debate as to which approach is best.  Each method attempts to measure something different.  Which is best often depends on what the parties to the debate find most useful for their purposes (Humphreys, 2002).  Among the more popular measures are the standard deviations of winning percentages of the various teams in the conference or league, the Hirfindahl-Hirschman Index, and the range of winning percentages.

Winning Percentage Imbalance

One popular measure of competitive balance calculates each team’s winning percentage in the conference in a given season.  Since there will, outside of a tie, always be one winner and one loser for each game, the average winning percentage for the conference will be .500.

In order to get some idea of competitive balance, the researchers needed to measure the dispersion of winning percentages around this average.  To do this, they measured the standard deviation.  This statistic measures the average distance the observations lie from the mean of the observations in the data set.
_________________
σ = √ Σ (WPCT – .500)2
N

The larger the standard deviation, the greater the dispersion of winning percentages around the mean, and thus the less the competitive balance.  (If all teams had a winning percentage of .500, there would be a standard deviation of zero, and there would be perfect competitive balance.)

Championship Imbalance

Whereas the standard deviation as a measure of competitive balance provides a good picture of the variation among the winners, it does not indicate whether it is the same teams winning every season or if there is considerable turnover among the winners from one season to the next.

Therefore, another method economists use to measure competitive imbalance is the Hirfindahl-Hirschman Index (HHI), which was originally used to measure concentration among firms within an industry (Leeds & Von Allmen, 2005).  Since the standard deviation is used to measure percentage winning imbalance, the HHI is used to measure championship imbalance – how the championship or first place finish is spread amongst the various teams.  Using this method, the greater the number of teams that achieve championship status over a specific time period, the greater the competitive balance.

The HHI can be calculated by measuring the number of times that each team wins the championship, squaring that number, adding the numbers together, and dividing by the number of years under consideration.  Using this measure, it can be concluded that the lower the HHI, the more competitive balance among the teams.

Range of Winning Percentage Imbalance

As suggested above, the standard deviation of winning percentages explains variation around the mean, but it does not specifically reveal if it is the same teams winning or losing from season to season.  Likewise, the HHI provides perspective on the number of teams which win the championship over a period of time, but it does not indicate what is happening to the other teams in the conference.  It is possible that a few teams could always finish first, but that the other teams could be moving up or down in the standings from one year to another.

One way of gaining some insight into the movement in the standings of all teams over time is to get the mean percentage wins for each team over a specific period.  The closer each team is to .500, the greater the competitive balance over this period.  If several teams had a very high winning percentage and others had a very low winning percentage, it would suggest that there was not strong competitive balance over time, but that the same teams were winning and the same teams losing year after year.

Results:
In order to arrive at conclusions concerning competitive balance in the MVC, the researchers employed each of the above measures and compared the results for men’s and women’s basketball over the selected period.

Standard Deviation of Winning Percentages

Tables 1 and 2 display the winning percentages for the women’s and men’s basketball teams. Table 3 displays the standard deviations for both the women’s and men’s winning percentages each season.  As indicated in Table 3, the men had a mean standard deviation of .2184 compared to a .2404 for the women.  This is approximately a 10% difference favoring competitive balance among the men.  It can also be noted that the men had a lower standard deviation than the women in seven of the 10 years studied.  Likewise, it can be seen that the highest standard deviation for women .2644 (2004-95) exceeded the highest for men, which was .2551 (2002-03).  Similarly, the lowest standard deviation for women .2010 (2002-03) was considerably higher than a comparable figure for the men, which was a very low .1527 (1998-99).

Table 1. Winning Percentages- Missouri Valley Conference Women’s Basketball

  Bradley Creighton Drake Evansville ILSU INSU MSU SIU UNI WSU
1996-97 0.5 0.389 0.778 0.111 0.722 0.5 0.722 0.5 0.278 0.5
1997-98 0.222 0.611 0.944 0.056 0.5 0.556 0.778 0.389 0.444 0.5
1998-99 0 0.5 0.778 0.611 0.222 0.556 0.833 0.278 0.667 0.556
1999-00 0.167 0.389 0.833 0.778 0.167 0.278 0.778 0.278 0.556 0.778
2000-01 0.278 0.611 0.889 0.444 0.167 0.389 0.889 0.222 0.667 0.444
2001-02 0.389 0.889 0.833 0.5 0.278 0.389 0.667 0.111 0.5 0.444
2002-03 0.5 0.722 0.611 0.278 0.278 0.722 0.611 0.167 0.667 0.444
2003-04 0.389 0.833 0.611 0.333 0.5 0.556 0.889 0.111 0.389 0.389
2004-05 0.444 0.722 0.444 0.556 0.389 0.722 0.833 0.056 0.722 0.111
2005-06 0.278 0.278 0.722 0.611 0.389 0.889 0.389 0.333 0.667 0.444
Mean 0.317 0.594 0.744 0.428 0.361 0.556 0.739 0.245 0.556 0.461

Source: Missouri Valley Conference 2005-06 Women’s Basketball Media Guide

Table 2. Winning Percentages- Missouri Valley Conference Men’s Basketball

  Bradley Creighton Drake Evansville ILSU INSU MSU SIU UNI WSU
1996-97 0.667 0.556 0 0.611 0.788 0.333 0.667 0.333 0.611 0.444
1997-98 0.5 0.667 0 0.5 0.888 0.556 0.611 0.444 0.222 0.611
1998-99 0.611 0.611 0.278 0.722 0.389 0.556 0.611 0.556 0.333 0.333
1999-00 0.556 0.611 0.222 0.5 0.278 0.788 0.722 0.667 0.389 0.278
2000-01 0.667 0.788 0.444 0.5 0.667 0.556 0.444 0.556 0.167 0.222
2001-02 0.278 0.788 0.5 0.222 0.667 0.222 0.611 0.788 0.444 0.5
2002-03 0.444 0.833 0.278 0.444 0.278 0.111 0.667 0.888 0.389 0.667
2003-04 0.389 0.667 0.389 0.278 0.222 0.278 0.5 0.944 0.667 0.667
2004-05 0.333 0.611 0.389 0.278 0.444 0.278 0.556 0.833 0.611 0.667
2005-06 0.611 0.667 0.278 0.278 0.222 0.222 0.667 0.667 0.611 0.778
Mean 0.506 0.68 0.278 0.433 0.484 0.39 0.606 0.668 0.444 0.517

Source: Missouri Valley Conference 2005-06 Men’s Basketball Media Guide

Championship Imbalance

Using the HHI to measure competitive balance for men’s and women’s basketball, the researchers found more competitive balance among the various institutions playing men’s basketball than among their counterparts playing women’s basketball.

Using the HHI for men’s basketball, the researchers found that six teams achieved an outright first place finish (SIU 3, ILSU 2, Evansville 1, Creighton 1, INSU 1, and WSU 1) over the 10-year period studied.  In one year, there was a tie for first place (SIU and Creighton in 2001-02).  If one point for each outright first place finish and .5 point for each two way tie is given:

HHI= 3.52+22+1.52+12+12+12 = 21.50/10 = 2.150

For women, over the 10-year period only four teams achieved an outright first place finish (Drake 3, MSU 3, Creighton 1, and INSU 1).  In 2 years, there was a tie for first place 2000-01 MSU and Drake, and 2002-03 Creighton and INSU).  Using the same point distribution as above:

HHI= 3.52+3.52+1.52+1.52 = 29/10= 2.9

In this case, the HHI showed considerably more competitive balance among the men’s basketball teams, than among the women’s.  Indeed, the HHI is about 33% higher for the women than for the men.  As indicated above this competitive balance advantage for the men can also be seen by the fact that over the 10-year period six different men’s teams achieved a first-place finish, while in the case of the women only four teams finished first.

Range of Winning Percentage Imbalance

If one arbitrarily sets .100 plus or minus the perfect balance, i.e., .500 as a range, which would suggest a high degree of competitive balance over the ten-year period, one once again finds more competitive balance among the men’s teams than among the women’s.

Table 2 suggests that, using this approach, five teams (50%) fit this range.  Those teams were Bradley, Evansville, ILSU, UNI, and WSU. Among the others, Creighton, MSU, and SIU seemed to be more consistent winners, while Drake and INSU were at the bottom.  But even among the latter, INSU had a winning percentage in 4 of the 10 years.  Indeed only one team—Creighton had a winning season each of the ten years. When viewing the range from top to bottom, a variation of .680 (Creighton) to .278 (Drake) a range of .402 is found.

Table 1 indicates that among the women’s teams over this 10-year period a similar five teams fit this range.  Those teams were Creighton, Evansville, INSU, NIU, and WSU.  Drake and Missouri State were consistent winners, each having only one losing season over the period studied. Meanwhile Bradley, ILSU, and SIU were on the lower end, none of which had an actual winning season over the last 9 years.

While both the men and women had five teams fitting our defined range for a high degree of competitive balance, it should be noted that the range from top to bottom was .499 for the women as compared to .402 for the men.  This range is almost 25% greater for women, which again suggests less competitive balance among the women’s teams

Table 3. Standard Deviations of Winning Percentages in Women’s and Men’s Basketball

Year Women Men
1996-97 0.2078 0.2298
1997-98 0.2538 0.2442
1998-99 0.2606 0.1527
1999-00 0.2746 0.201
2000-01 0.258 0.1942
2001-02 0.24 0.2142
2002-03 0.201 0.2551
2003-04 0.2342 0.2313
2004-05 0.2644 0.1851
2005-06 0.2095 0.2208
Mean 0.2404 0.2184

Source: Authors’ calculations based on data in Tables 1 and 2.

Conclusions:

The uncertainty of outcome hypothesis suggests that a lack of competitive balance among teams in a league or conference can lead to a lack of interest in the games outcome and thus a loss of revenue to teams sponsoring the games.  If this were indeed the case, it should follow that the greater the potential revenue possible, the more likely there would be an attempt to bring about competitive balance.

The purpose of this research was to test this hypothesis by comparing the competitive balance in a high revenue intercollegiate sport, basketball, for both men and women over a period of time.  Expectations were that, because of the greater revenue associated with men’s basketball, there would be greater competitive balance.

Using the standard deviation of winning percentages, the Hirfindahl-Hirschman Index, and the range of winning percentage imbalance to measure competitive balance, the researchers found in each case that there was greater competitive balance among the men’s basketball teams than for the women’s teams.  These findings would support the hypothesis that where there is greater revenue potential, there should be greater competitive balance.

In conclusion, the usual caveats are in order.  It is possible that if the researchers analyzed a different time frame within the MVC, or if a different intercollegiate conference was chosen for analysis, a different conclusion may have been reached.  It may also be that as women’s basketball continues to grow and generate greater amounts of revenue from ticket sales, media rights fees, and corporate sponsorship, levels of competitive balance may also change.  These possibilities provide further research opportunities to test the hypothesis.

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Missouri Valley Conference. (2006b). This is the Missouri Valley Conference. Retrieved April 27, 2007 from http://www.mvc-sports.com/ViewArticle.dbml?DB_OEM_ID=7600&KEY=&ATCLID=271380.

National Collegiate Athletics Association (2006). 2006-07 NCAA Division I manual. Indianapolis, IN: Author.

Quirk, J. & Fort, R.D.  (1992). Pay Dirt: The Business of Professional Team Sports. Princeton, NJ: Princeton University Press.

Rhoads, T.A. (2004). Competitive Balance and Conference Realignment in the NCAA. Paper presented at the 74th Annual Meeting of Southern Economic Association, New Orleans, LA.

Richardson, S. (2006). A Century of Sports: Missouri Valley Conference. St. Louis: Missouri Valley Publications.

Sanderson, A.R., & Siegfried, J.J. (2003). Thinking about Competitive Balance. Unpublished manuscript. Vanderbilt University.

Relations between Role Ambiguity and Athletes’ Satisfaction among Team Handball Players

Abstract

This study examined the relationship between role ambiguity and athlete satisfaction among team handball players. The sample consisted of 169 Greek team handball players, 53 (33%) men and 116 (67%) women, with a mean age of 16.5 years (SD=1.3). The Role Ambiguity Scale and the Scale of Athlete Satisfaction were used. The results indicated a negative relationship between Role Ambiguity and Athlete Satisfaction. Additionally, role ambiguity, as represented by the subscale of Scope of Responsibilities, accounted for most of the variance in both regression analyses. Finally, the multidimensional role of Role Ambiguity was shown. The results are discussed and future research is suggested.

Review of Literature

The literature has defined role ambiguity as the lack of clear, consistent information that is associated with a person’s position (Kahn, Wolfe, Quinn, Snoek, & Rosenthal, 1964). It has also provided a theoretical model in which role ambiguity had two dimensions: (a) task ambiguity, related to performance aspects of one’s responsibilities, and (b) socio-emotional ambiguity, regarding the psychological consequences and discomfort an individual might experience while failing to fulfil role responsibilities.

Behrman and Perreault (1984) supported the idea that role conflict and role ambiguity were related negatively to job satisfaction. Schuller, Aldag, and Brief, (1977), evaluating the affect of role conflict and role ambiguity, concluded that they were associated with low satisfaction, absenteeism, low involvement, and tension at the work place. Beehr, Walsh, and Taber, (1976) found that role stress was related to dissatisfaction with work. Finally, Boles and Babin (1996) suggested that increased role conflict and role ambiguity diminished job satisfaction among customer service employees.

Role ambiguity is important in productivity and performance in business and industry. A meta-analysis by Jackson and Schuler (1985) found that greater role ambiguity was associated with greater job dissatisfaction, as well as increased anxiety, lower commitment, and a diathesis to leave the organization. Recent research shows that ambiguity follows many negative and corruptive consequences: decreased satisfaction with one’s job, higher level of tension and anxiety, and the greater possibility of leaving the organization (Beard, 1999). Additionally, research showed that ambiguity is related with increased somatic and cognitive anxiety (Beauchamp, Bray, Eys, & Carron, 2003) and decreased role-related efficacy (Beauchamp & Bray, 2001; Eys & Carron, 2001; Beauchamp, Bray, Eys, & Carron, 2002; Bray & Brawley, 2002).

Beachamp and his colleagues (2002) presented a conceptual model of role ambiguity specific to sport. This model originated with Kahn and his colleagues (1964) as well as early work by Eys and Carron (2001) and by Beachamp and Bray (2001). More specifically, it was proposed by the researchers that role ambiguity contains four dimensions (multidimensional construct): scope of responsibilities, which refers to a lack of clear information about one’s responsibilities; role behaviours, which refer to a lack of clear information about behaviors associated with one’s role; role evaluation, which refers to a lack of clear information about how one’s responsibilities are evaluated; and role consequences, which refer to a lack of clear information about the consequences of failure to fulfill one’s role responsibilities. Based on research among school rugby players, Beauchamp et al. (2002) provided evidence of the factorial validity of the model with the use of confirmatory factor analysis. Also, Eys, Carron, Beauchamp, and Bray (2003) provided evidence about the construct validity of the operational definition of role ambiguity by examining the changes of role ambiguity over time and the influence of player status on perceptions for role ambiguity.

Studies show that a negative relationship between role ambiguity and performance exists among athletes whose roles were identified by a high degree of interdependence, compared to those whose roles were identified as independent of others’ (Tubre & Collins, 2000). Additional research indicates a positive correlation between ambiguity and burnout (Capel, 1986), and that among players of variety interdependent sports, starters reported lower levels of role ambiguity than non-starters (Beauchamp & Bray, 2001).

Chelladurai and Riemer (1997) have defined athlete satisfaction as “… a positive affective state resulting from a complex evaluation of the structures, processes, and outcomes associated with the athletic experience” (p. 135). As Chelladurai and Riemer (1997) have pointed out, athletes are the “prime beneficiaries” of athletic programs. In other words, sport organizations exist primarily for the benefit of athletes (Reimer & Chelladurai, 2001). The concept of athlete satisfaction has received little attention from researchers. In contrast, a great deal of research in sport-related literature has focused on the satisfaction of coaches, administrators, spectators, and participants across a range of sports settings (Danylchuk, 1993; Li, 1993; Pastore, 1993; Madrigal, 1995; Alexandris & Palialia, 1999; Koustelios, Kellis, & Bagiatis, 1999).

In most of the above research, athletes’ satisfaction has been considered a dependent or independent variable in various theoretical frameworks (Reimer & Chelladurai, 2001), usually as the outcome of various leader or coach behaviors (Chelladurai, 1984; Horne & Carron, 1985; Weiss & Friedrichs, 1986; Schliesman, 1987; Chelladurai, Inamura, Yamaguchi, Oinuma, & Miyauchi, 1988; Riemer & Chelladurai, 2001; Bebetsos & Theodorakis, 2003; Theodorakis & Bebetsos, 2003). For example, in a study of 251 college basketball players in the U.S., Weiss and Friedrichs (1986) found that coaches who engaged in frequently rewarding behavior, social support behavior, and a democratic style of leadership increased athletes’ satisfaction. In some studies, although fewer in number, researchers used athlete satisfaction as an independent variable in their models (Carron, 1982; Reimer, & Chelladurai, 2001). For example, Riemer and Chelladurai (2001), in a study of 649 student athletes from 14 Canadian universities, reported that only a limited number of facets of athlete satisfaction significantly predicted the commitment of athletes to the team, or conversely, a desire to leave the team.

Although there is very limited research on the possible relationship between role ambiguity and satisfaction in sports, research has been done in industrial and organizational psychology. Several studies have identified the negative relationship between role ambiguity and satisfaction (Abramis, 1994; Fisher & Gitelson, 1983; Horne & Carron, 1985). A meta-analysis by Jackson and Schuler (1985) indicated that role ambiguity was negatively associated with multiple aspects of employee job satisfaction. The limited investigation in sport settings on these two domains indicated that lower levels of role ambiguity were related to higher athlete satisfaction (Eys, Carron, Beauchamp, & Bray, 2003). Additionally, Bray, Beauchamp, Eys, and Carron (2005) found that the need for role clarity moderated the relationship between role ambiguity and athlete satisfaction.

Therefore, the purpose of the present study was to examine the relationship between athletes’ perceptions of role ambiguity and their satisfaction as regards Greek team handball players. The hypothesis was twofold: first, that role ambiguity dimensions (subscales) are negatively related to athlete satisfaction dimensions and second, that Scope of Responsibilities would be the most prominent manifestation of role ambiguity related to the dimensions (subscales) of athlete satisfaction.

Method

Participants and Procedures

Data were collected from 169 Greek team handball players: 53 (31.4%) men and 116 (68.6%) women. Their mean age was 16.4 years (SD=1.3), and ages ranged from 13 to 19 years. On average, their association with their respective teams was 4.9 years (SD=2.3), and their playing experience in organized team handball was 5.4 years (SD=1.9). Participants practiced an average of 4.4 times per week (SD=1.7).

Measures

The Role Ambiguity Scale (RAS; Beauchamp et al., 2002). This scale contains four subscales: (a) Scope of Responsibilities (e.g., “I understand the extent of my responsibilities.”), (b) Role Behaviors (e.g., “I understand what adjustments to my behavior need to be made to carry out my role.”), (c) Role Evaluation (e.g.,“I understand the criteria by which my role responsibilities are evaluated.”), and (d) Role Consequences (e.g., “It is clear to me what happens if I fail to carry out my role responsibilities.”). Each subscale has five items (questions). The scale has two batteries of statements, since it is designed to assess role ambiguity in an offensive and defensive context. In the present study, only the 20-items (5 items per subscale) that corresponded to offensive responsibilities were used, following suggestions made by Eys and Carron (2001) and Beauchamp et al. (2003) that role ambiguity might be more relevant in an offensive context. Respondents rated agreement with each item on a 9-point scale anchored by 1: strongly disagree and 9: strongly agree. Higher scores reflected greater role clarity and hence less role ambiguity. The scale was translated into Greek using a back translation procedure. For the purpose of the study, the Greek version was administered to 10 team handball athletes to examine whether the items of this version were comprehensive and well understood. No further modifications were made after the above process.

The Scale of Athlete Satisfaction (Chelladurai, et al., 1988). This scale measured satisfaction in leadership (seven items, e.g., “The leadership provided by my coach”), and Personal Outcome (three items, e.g., “The way I am performing”). Respondents rated satisfaction by item on a 7-point scale anchored by 1: strongly dissatisfied and 7: strongly satisfied. The scale was translated into Greek and used in earlier studies (Bebetsos & Theodorakis, 2003; Theodorakis & Bebetsos, 2003).

Procedure

The method chosen to conduct the research was that of self-completed questionnaires. Researchers informed all subjects that participation was completely voluntary and that individual responses would be held in strict confidence.

Results

Descriptive statistics including means, standard deviations, Cronbach coefficients α for all subscales, and Pearson intercorrelations between role ambiguity and athlete satisfaction dimensions are presented in Table 1. Relatively high mean scores were observed for the four role ambiguity dimensions ranging from 7 (Role Evaluation) to 7.3 (Role Consequences and Scope of Responsibilities) of a possible 9. It should be noted that higher Role Ambiguity scores mean less uncertainty. Participants reported moderate satisfaction from their personal performance (M=5.1, SD=1.2) and with their leaders’ behaviors (M=5.8, SD=1.1).

Table 1

Descriptive statistics for athlete satisfaction and role ambiguity dimensions

M SD Cronbach’s
a
r
1 Leadership 5.8 1.1 .87
2 Personal outcome 5.1 1.2 .71 .42**
3 Scope of Responsibilties 7.3 1.3 .83 .39** .32**
4 Role Behaviors 7.1 1.2 .80 .18* .37** .76**
5 Role Evaluation 7.0 1.4 .80 .35** .30** .68** .64**
6 Role Consequences 7.3 1.5 .82 .35** .15* .72** .49** .65**

*p<.05, **p<.001

Using the Cronbach coefficient α for internal consistency, acceptable estimates were observed for the Athlete Satisfaction subscales (Table 1). In contrast, rather low internal consistensy coefficients were observed for the four Role Ambiguity subscales. More specifically, alpha coefficients were .71 for Scope of Responsibilities, .61 for Role Behavior, .66 for Role Evaluation, and .69 for Role Concequences. Item analysis indicated that the internal consistency of each dimension could substantially be improved if certain items were removed from each subscale. It should be noted that these items (total of 4, 1 for each subscale) were reversed (negative wording). After removing these items, alpha coefficients raised to .83 for Scope of Responsibilities, .80 for Role Behavior, .80 for Role Evaluation, and .82 for Role Concequences.

As hypothesized, Role Clarity (lower Role Ambiguity) was positively related to Athlete Satisfaction (Table 1). The bivariate correlation sample size (N=169) was adequate to assure power of .80 and effect size of at p = .05 (46). A power analysis was performed using the Gpower statistical program (Erdfelder, Faul, & Buchner, 1996). To further explore relationships between Role Ambiguity and Athlete Satisfaction subscales, two hierarchical regression analyses were performed. For each analysis, an Athlete Satisfaction subscale was the dependent variable, and the four subscales of Role Ambiguity were the independent variables. Following suggestions by Eys, Carron, Bray, and Beauchamp (2003) the Scope of Responsibilities subscale was entered as the predictor variable on the first step for each analysis. The remaining three subscales of Role Ambiguity (Role Behavior, Role Evaluation, and Role Consequences) were entered as a block in the second step. In the first model, Scope of Responsibilities predicted a significant proportion of the variance, 8% in Leadership (F1,134=11.7, p< .001). When the other three Role Ambiguity subscales entered in the model, variance prediction increased to 12% (F4,131=4.7, p< .001). The subscales of Role Behavior and Role Evaluation offered significant contributions (t=-2.0, p< .05, and t=-2.1, p< .05). In the second model, Scope of Responsibilities predicted 11% of Personal Outcome (F1,134=16.7, p< .001). In the next step, the other three subscales increased the prediction of Personal Outcome to 21% (F4,134=8.9, p< .001). The subscales of Role Behavior and Role Consequences offered significant contribution to the prediction (t=-2.0, p< .05, and t=-2.8, p< .05, respectively).

 

Table 2

Hierarchical regression analysis for role ambiguity dimensions predicting athletes’ satisfaction

Δ R2 ΔF p Β β t P
Leadership Scope of Responsibilites .08 11.78 < .001 .32 .36 2.33 < .05
Role Behaviors .12 4.72 < .001 -.23 -.27 -2.03 < .05
Role Evaluation 1.95 .25 2.14 < .05
Role Consequences -.34 -.39 -.39 ns
Personal Outcome Scope of Responsibilites .11 16.76 < .001 .25 .25 1.74 .05
Role Behaviors .21 8.96 < .001 .25 .27 2.08 .05
Role Evaluation .12 .14 1.28 ns
Role Consequences -.26 -.32 -2.82 .05

Discussion

The aim of the study was to examine the relationship between athletes’ satisfaction and role ambiguity among team handball players. It was predicted that role ambiguity would have a negative relationship to the satisfaction dimensions and that Scope of Responsibilities was the most prominent manifestation of role ambiguity related to the dimensions (subscales) of athlete satisfaction.

First, the reliability estimates showed that after the exemption of four items, which were removed from the analysis on the ambiguity instrument, all factors from both questionnaires had good internal consistency. The exclusion of the items significantly improved the internal reliability of the factors. It should be noted that only these items had negative wording, whereas the other items of the questionnaire had positive wording. There is evidence suggesting that item wording may influence the results of a study (Spector, Van Katwyk, & Brannick, 1997; Brown, 2003; Tsiggilis, Masmnidis, & Koustelios, 2004; Proios, Tsiggilis, & Doganis, 2005). Schriesheim, Eisenbach, and Hill (1991) demonstrated that regular items (e.g., “I am happy”) are the most reliable and produced the most accurate responses in comparison to negated regular (e.g., “I am not happy”), polar opposite (e.g., “I am sad”), and negated polar opposite (e.g., “I am not sad”) items.

Second, the means of role ambiguity are above average (Table 1), which translates to high role clarity and lower role ambiguity. This might have occurred because, as it was mentioned previously, the players were members in their teams for a quite long time (4.9 years), their sport experience (5.4 years) was extensive and the research was conducted near the end of the season. In a previous study, Eys and his colleagues (2003) indicated that athletes with greater sport experience, being members of the same team for a quite long time, had lower indicators of role ambiguity in comparison to younger and less experienced athletes. Additionally, indicators of athlete satisfaction were also above average. Similar results of previous research (Bebetsos & Theodorakis, 2003; Theodorakis & Bebetsos, 2003) indicate that in the end of the season athletes were satisfied with their leaders’ behaviors as well as with their personal performance.

Third, role ambiguity was found to have a negative relationship to athletes’ satisfaction. These results are consistent with previous research findings that indicate role ambiguity was inversely correlated with job satisfaction (Abramis, 1994; Jackson & Schuler, 1985). More specifically, Jackson and Schuler (1985) mentioned in their meta-analysis of the industrial literature that the overall correlation between satisfaction and ambiguity was in a moderate to high range, showing the important contribution to satisfaction. In addition, Eys et al. (2003) concluded that lower perceptions of role ambiguity were related to higher athlete satisfaction. Riemer and Chelladurai (1998) indicated that satisfaction has been proposed and shown to be a consequence of several group dynamics constructs, including leadership and team cohesion.

Forth, the results of this study supported the importance of Scope of Responsibilities over the other four dimensions of role ambiguity. It accounted for most of the variance in both regression analyses. Previous research found that Scope of Responsibilities had the strongest relationship with cohesion (Eys, & Carron, 2001) and cognitive state anxiety (Beauchamp, Bray, Eys, & Carron, 2003) and was the strongest predictor of role efficacy and role performance (Beauchamp, Bray, Eys, & Carron, 2002). In the present study, Scope of Responsibilities accounted for the most variance in both hierarchical regression analyses, consistent with previous research results (Eys, Carron, Bray, & Beauchamp, 2003).

The findings of this study showed the significant contribution of other dimensions in the regression analyses. More specifically, for the first model, Role Behavior and Role Evaluation offered significant contributions, and for the second, Role Behavior and Role Consequences offered significant contribution to the prediction. These results reinforce the possible modification of the instrument from its hierarchical to its multidimensional role. More specifically, the results supported the multidimensional nature of ambiguity. A reason might be the possibility that Scope of Responsibilities may not reflect an overall representation of role ambiguity and does not develop in a hierarchical fashion. In contrast with what Eys and his colleagues (2003) stated, the other dimensions proposed by Beauchamp and his colleagues (2002) may not form sub-categories beneath Scope of Responsibilities in a hierarchical model.

The results showed that the players tend to understand the direct relationship that exists between Leadership (i.e. coach) and the criteria by which their team responsibilities are evaluated, what the leadership wants and expects from them. Likewise, for Personal Outcome, the results indicated the players understand their roles in the team, what responsibilities these roles have, and that these roles have a direct relationship with athletic growth and development. Finally, they understand that consequences might follow if they do not carry these roles out.

In conclusion, the present results have indicated that role ambiguity (Beauchamp, et al., 2003) is associated with athletes’ satisfaction among Greek team handball players. Additionally, the results indicated the importance of Scope of Responsibilities and that four specific dimensions of role ambiguity dimensions could predict two facets of athletes’ satisfaction. Future research should continue to investigate relationships with variables such as intention, motivation, aggressiveness, as well as explore the importance and mechanisms of role ambiguity within team sports. A possible limitation of the study might be the lack of information regarding on-field defensive roles. Athletes’ responses regarding their defensive roles were not included in this study. Also, the sample consisted of experienced athletes and the study was conducted only on the sport of team handball.

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