ࡱ> dfck5 {bjbj ;ϿdϿdyK %%%%%9998qD9&(J]y%%%%%%%$-(*%i%%%%4=& %%% % :$:%?܎%%S&0& %++4:%+%:%` %% &+ : AN EXAMPLE PAPER SUBMITTED FOR THE 14TH AUSTRALASIAN MATHEMATICS AND COMPUTERS IN SPORT CONFERENCE First Author a,d , Second Author a,b , Third Author c a University of Sports b Affiliation not specified c Corporate affiliation d Corresponding author: first.author@email.com Abstract Please keep your abstract to no longer than 300 words. The following is an example abstract. In many sports, the measure of a teams success is often attributed to the coach. Notably, when a team performs poorly, it is the coach that is sacrificed as a ritual scapegoat. Extensive research has evaluated the validity of this mentality, yielding conflicting results. However no research, to our knowledge, has attempted to measure exactly what a coach can influence during a game and how different sports compare. In this research, we consider a number of professional sports on the level of influence coachs have on their players/teams outcome during a match. By considering level of communication, strategic ability, substitutions available and officiating influence which are all determined by the rules of a sport, we develop a coaching influence rating model. This model yields a single measure which is used to rank the degree of influence a coach has during a match and enables comparison of coaching influence across the rated sports. Then, assuming that coaching turnover is related to coach accountability, we validate the coaching influence model using coaching turnover data for the ranked sports for the previous ten seasons. We find our ratings model and coach turnover are strongly correlated, indicating that the more influence a coach has in the run, the higher the turnover of coachs in that sport. The results of the analysis not only make for interesting analytical discussion but also provide a framework for assessing and researching the exact impact that a coach has on the day of a sporting event. Keywords: Coaching, turnover, firings, coach influence 1. INTRODUCTION With the advances in technology, billion dollar budgets, wealth of support staff, technical teams, and advanced training methods, the pressure on coaches to get their players and support team to perform is critical. Wood (2008) states the [role of the] coach will be many and varied, from instructor, assessor, friend, mentor, facilitator, chauffeur, demonstrator, adviser, supporter, fact finder, motivator, counselor, organizer, planner and the Fountain of all Knowledge no less, all this on top of the technical and analytical roles. So the question is how much of a teams performance is actually attributable to the coach? Previous research conducted on coach influence has typically looked at the effect that coaching change has on a teams performance. These studies ask the question of whether firing a coach is effective in improving a teams performance. Early research suggested that firing baseball managers increased team performance in the short-term but this improvement soon regressed to the mean (Fabianic, 1994). Further studies have been inconsistent. Audas, Dobson and Goddard (1997) found that short-term performance did increase after firing a coach in soccer whereas Balduck and Buelens (2007) concluded that firings had no short-term impact on a teams performance. Other studies on the four most popular North American sports, basketball, baseball, ice hockey, and American football have established that coaching change does seem to increase short-term performance although in the following season performance did not change (McTeer, White, & Persad, 1995). Koning (2003) argued that apparent team performance increases after a coaching change dis-appears after controlling for opposition quality and Bruinshoofd and ter Weel (2003) contended that this apparent improvement was due to regression to the mean and not due to the coaching change itself. More surprisingly, Audas, Dobson and Goddard (2002) have even found that managerial change in football (soccer) can have an adverse effect on performance. According to this research it would appear that sacking a coach is a highly controversial strategy to improve a teams performance. However, many teams in many different sports still fire coaches or put coaches in positions where they are forced to resign in a ritualistic scapegoat manner (Gamson & Scotch, 1964). Our research aims to assess the possibility that the amount of influence a coach can have on a game in-the-run is related to the rate of coaching turnovers and firings. We develop a new model used to determine the level of influence in major worldwide team sports, and assess the correlation between the influence level and coach turnover. 2. METHODS COACHING INFLUENCES To effectively evaluate the influence of a coach in-the-run we developed a Coachs Influence Rating Model (CIRM). This level of influence is directly related to what the rules of a sport enable a coach to do. Given the high variability between sporting rules, this model was developed keeping in mind that any sport should be able to be rated using the CIRM. This rating is best interpreted only as a way of comparing coaching influence among different sports and should not be generalised beyond that purpose. To construct the CIRM we had to determine what a coach can do to influence the results of a game keeping in mind sports of all types. Three sources of information gathering where used including the literature, sport rule books, and a group Delphi. Literature on coaching competency identified motivation and game strategy (Myers, Feltz, Maier, Wolfe, & Reckase, 2006) as two important but broad on-the-day coaching influences. Analysis of sport rule books enabled a further break-down of the different areas of influence. Because motivation would be troublesome to quantify or rank, the group Delphi decided that motivation should be related to the ability to communicate with players. Thus communication became the first factor of CIRM. We later added a second component called field size to this factor as the Delphi agreed that the larger the field the harder it is to communicate with players. The second factor, game strategy, was defined by on-field strategic changes and strategic substitution. Both of these factors were further determined by how often and how many changes could be made. The last factor identified was influence over game officiating. For example, NFL (American football) allows coaches to make two challenges to a game officials decision using video replay. Therefore, we proposed that coaching influence on-the-day was a function of their ability to communicate with players, make strategic changes both on the field and through substitution, and influence officiating. The next step in the development of CIRM was to determine how to score each sport on each of the three coaching influence factors. While many methods were proposed in the Delphi, difficulty with resulting large variation in coaching influence indicators informed us that a simple approach was the best. Therefore, an ordinal system of scoring each factor was developed. This scoring system along with the CIRM is shown in Table 2. The first factor, communication, was determined by the sub-factors contact and field size. Contact enables a sport to be ranked on the coachs ability to communicate with players. This ranges from two extremes; no contact (e.g. Tennis), to full contact (e.g. Basketball). We also added the concept of in-directness if the coach had to communicate through another person (e.g. runners in AFL). Field size was included to take into account the coachs ability to communicate effectively especially in stadiums full of spectators. There was debate over how to break this factor into level but the agreed upon conventions were fields (e.g. Football, Rugby and Cricket) and courts or rinks (e.g. Basketball and Ice Hockey). The second factor, game strategy, was divided into on-field changes and substitution. On-field changes refer to the changes that coaches can make between different positions on the field and substitution refers to the changes that the coach can make off a bench if one exists. Both of these sub-factors were measured by two determinants: the timing of changes and the quantity of changes. Timing of changes rates a sport in terms of when changes can be made. Sports can range from no changes at all (e.g. tennis) to changes anytime during the play of a match (e.g. ice hockey). Quantity of changes scores a sport in terms of how many possible combinations or changes a coach can make during a match. Some sports can only make very subtle changes (e.g. switching forwards in netball) whereas others can make substantial changes (e.g. substitution of players virtually at will in basketball). OFFICIATING The final factor that was included was influence over officiating. This aimed to score sports on a coachs ability to influence official decisions during a game. With most sports there are clear rules that prevent coaches and player from questioning official rulings, however, some sports allow either the captain, or even the coach, to voice their concerns. We proposed that sports which allow a coach to have an impact on game officiating give coaches the potential ability to have a greater effect on the outcome of the game compared to sports that do not, even if it may be detrimental to a teams chances of winning. A measure for indirect influence was also included in sports where coaches had to question officiating decisions through team captains (e.g. Ice Hockey). The broad equation for CIRM is given by CIRM = Communication + Game Strategy + Officiating Influence (1) where values of variables are taken from Table 2. Data on coaching turnover was sourced from a number of different websites for each sport. While many websites had information about coaches and the years of their coaching tenure, many sites did not specify the nature of the turnover. This required extensive research using a number of different internet resources, and where information was not available, email and telephone calls were made to respective team officials. We coded coaching turnover as simply a change in coaches for any reason such as resignations, contract conclusions, and terminations. We then coded a coaching turnover as a coach firing if the turnover was involuntary on the coachs behalf, e.g. termination or non-renewal of coaching contract, or forced resignation due to the hiring of another coach. Contract conclusions could go either way. For example, a coach could choose not to continue with a team at the end of a contract even though they were offered a contract extension or whether the contract ended and no extension was offered. The later was coded as a firing. We also had to determine if any of the listed coaches were designated as interim coach. Changes of interim coaches were coded as turnovers but never as a firing. In the end we had two measures of coaching changes; an all in measure of coaching turnover and a more specific measure of involuntary firings. Both were deemed to provide related but unique indications of the nature of coaching turnover in a sport. It is also important to note here that our information about turnovers and firings are only as good as the validity of the sites that reported the coaching change. Sporting websites were consulted for data pertaining to coaching turnovers over a period of ten seasons for each sport. Table 2 lists the sports included in the analysis and the websites used to gather the required data. These sports were chosen because of the ease of access to information about coaches and coaching turnover, and were restricted to team sports. 3. RESULTS CLASSIFYING TEAM SPORTS Rule books and the Delphi procedure were used to classify each team sport on each of the factors. Where there was uncertainty or disagreements, respective sporting experts were contacted and queried to make a final decision. The results of the CIRM analysis for the sports analysed ranked and listed in descending order are shown in Table 2. The sport with the most in-the-run coaching influence is basketball whereas cricket is scored quite low. The coaching turnover data that was gathered for each sport was converted into a turnover measure used to compare all sports. This required a measure that would control for the number of teams in a sporting league and the differing length of seasons. The length of a season was an important variable to control for as it varies substantially between sports (e.g. NHL 28 weeks vs. NFL 17 weeks). SportCIRM Factors1.11.22.12.22.32.43TotalBasketball313424219Ice Hockey313334118American Football302424217Baseball202323214Australian Football203431013Football (Soccer)303321113Rugby League213421013Rugby Union10312209Cricket10230006Table 1: Coaching Influence Ratings as Scored by CIRM CONTROLLONG FOR SEASON LENGHTH We believed that we had to control for season length as sports that had longer season would have more opportunities to turnover coaches as opposed to a sport with a shorter season. The season length was measured in weeks from the week of the first game to the last game of the regular season. If this period varied from season to season we recorded the season length as the median number of weeks per season over the ten seasons gathered. We did not use games played as a measure of season length be-cause it created massive variability (e.g. MLB 162 games per season compared to NFL 16 games per season). This ended up considerably skewing the turnover measures for different sports when compared to others. Weeks of season was found to offer the best compromise of controlling for season length but at the same time not creating excessive variability. Thus, coaching turnover for each season of the sport in question was measured by  EMBED Equation.3  where xi = coach turnovers for a season, y = the number of teams in the competition, and zi = the number of weeks of the respective sports regular season. Once this was calculated for each sport for each of the ten seasons, the average coaching turnover was obtained by  EMBED Equation.3  where n = the number of seasons that (2) is calculated for. This gives a measure of coaching turnover defined as the average coaching turnover per team per season. We also calculated coaching firings by substituting coach firings in xi of (2) and (3). This gave a measure of the average firings per team per season. The correlation between these two measures was high at r = .79 (p = .012 [Spearmans  = .98, p < .001]). Coaching Turnover and Firings for each sport are shown in Table 4.  Figure 1: The relationship between coaching turnover and the CIRM (Super 14 included) 4. DISCUSSION Eight out of the nine sports seem to conform relatively well to the CIRM except for the Super 14 competition. The relationship between coaching turnover and CIRM score with the Super 14 outlier included was not significant (r = -.017, p = .97 [Spearman s  = .51, p = .16], Figure 1). However, with Super 14 removed there was a significant positive trend between coaching turnover and CIRM scores (r = .9, p = .003 [Spearman s  = .98, p < .001], Figure 2). For coaching firings the Super 14 also acted as an apparent outlier. With the Super 14 included in the data, the relationship between coaching firings and CIRM score was positive but not significant r = .58 (p = .11 [Spearman s  = .49, p = .18], Figure 3). Again, with the influence of the Super 14 removed, the correlation returned a strong positive linear trend between coaching firings and CIRM score (r = .96, p < .001 [Spearman s  = .95, p < .001, Figure 3). Overall, it appears that coaching turnover and firings seem to co-vary with on-the-day coaching influence as measured by the CIRM. However, the Super 14 outlier complicates this conclusion. SportTurnoversFiringsTeams*Season WeeksCoaching Turnover (2)Coaching Firings (2)CIRM ScoreNBA1096730240.01550.009519NHL1077330280.01470.010018NFL734832170.01370.009017MLB875830260.01140.007614EPL824520390.01070.005913AFL361816220.01020.005113NRL331816260.00860.004613S14**411614120.02770.01109IC42910520.00830.00186* = Team numbers vary for each season because of defunct teams or relegation. ** = Outlier Table 2: An example table  Figure 2: An example graph 5. CONCLUSIONS Coaches are under increasing pressure to get the most out of players, and to obtain success for their club with some consistency. By determining the influence coaches have in-the-run we find that a strong positive correlation exists between coaching influence and coaching firings, with the exception of Super 14s. The rugby union super 14s level of firing is dramatically higher than the fit line, suggesting firings are too frequent given the level of influence coaches have in the code. The Super 14s result is somewhat suspect given that the code is only a few years old in its current format. Removing the rugby union code from consideration, we find that the Australian rugby league competition fires somewhat lower number of coaches than the fit line, and MLB/NHL somewhat higher than the fit line. Overall we determine that coach turnover and firings is linearly related to the level of influence coaches have on a game. Further investigation is needed into other potential factors, including the influence of performance, out-of-run communication and training, and financial positions of each club. Acknowledgements We wish to thank Superman; Batman; Wonder Woman; and The League of Superheroes for their assistance in data retrieval. References Audas, R., Dobson, S., & Goddard, J. (1997). Team performance and managerial change in the English Football League. 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(2002). The impact of managerial change on team performance in professional sports. Journal of Economics and Business, 54, 633-650. Balduck, A.-L., & Buelens, M. (2007). Does sacking the coach help or hinder the team in the short term? Evidence from Belgian soccer. Ghent University. Bruinshoofd, A., & ter Weel, B. (2003). Managers to go? Performance dips reconsidered with evidence from Dutch football. European Journal of Operational Research, 148, 233-246. Fabianic, D. (1994). Managerial change and organizational effectiveness in Major League Baseball: Findings for eighties. Journal of Sport Behavior, 70, 69-72. Gamson, W. A., & Scotch, N. A. (1964). Scapegoating in baseball. The American Journal of Sociology, 70, 69-72. Koning, R. H. (2003). An econometric evaluation of the effect of firing a coach on team performance. Applied Economics, 35, 555-564. McTeer, W., White, P. G., & Persad, S. (1995). Manager/coach mid-season replacement and team performance in professsional team sport. Journal of Sport Behavior, 18, 58-68. Myers, N., Feltz, D. L., Maier, K. S., Wolfe, E. W., & Reckase, M. D. (2006). Athletes' evaluations of their head coach's coaching competency. Research Quarterly for Exercise and Sport, 77, 111-121. Wood, R. (2008). The Role of the Coach in Sport. Rob's Home of Fitness Testing, www.topendsports.com.      PAGE 1 ykҞez ()F_`bcefhikmntuvwxyz{Ưxh:h )6CJOJQJaJ(hBp0J6CJOJQJaJmHnHu#h:h )0J6CJOJQJaJ,jh:h )0J6CJOJQJUaJh )hGPjhGPUh )CJOJQJaJh{'h )CJOJQJaJhC h )CJOJQJaJ&_abdeghjklmxyz{$r^`ra$gd ) $ (#a$gd )9 0&P 1h:p 7 . 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