Don't Bet On It:
Don’t Bet On It: Evaluating Bookmaker Biases & Player Contribution in Spain’s Liga BBVA
Gillian Rose Kemmerer Candidate Number: 81767 LSE Master’s of Science Dissertation (2013) MSc International Management 2012-2013 The London School of Economics & Political Science Supervisor: Dr. Yona Rubinstein Course Code: MN499 Word Count: 7,118 (excluding references)
ABSTRACT: How much does a star athlete contribute to team outcomes in professional football, and how does the market evaluate their worth? This paper examines four players from Spain’s La Liga in the 2012-13 season to determine how absences—due to injuries and other factors—change fixed betting odds, conditional on observed outcomes. As a player’s participation affects and is affected by team performance, injuries are used as an instrument for absence to overcome the issue of endogeneity. Players are broken into two categories—stars and non-stars—based on relative media attention and public sentiment. The regressions show that conditional on observed match results, the absence of star players is exaggerated in the odds, resulting in higher payouts for bettors when a team wins without them. Non-stars, on the other hand, do not have a significant effect on the odds when they are absent. When general absence and injuries are regressed together, player injury is revealed to be the source of this bias for the star player group. Finally, when injury is instrumented for participation, the results confirm that a star player’s injury results in systemically inflated payouts, whereas injuries of non-stars have a net effect close to zero. The paper additionally confirms the presence of a home-away bias as discussed in previous literature. Ultimately, this paper rejects the notion that betting odds appropriately value player contribution to teams, and presents a new source of bias—namely, the injury of a star—to the literature on betting market efficiency.
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Table of Contents I. Introduction
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II. Relevant Literature A. Individual Contribution to Firm Output & Market Evaluation of Skill B. Athlete Contribution to Team Performance C. The Efficiency of Sport Betting Odds
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III. Motivation & Player Choices
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IV. Data A. League Data B. Player Data
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V. Empirical Strategy
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VI. Regression Results A. The Effect of Absence on Betting Odds B. The Effect of Injury on Betting Odds C. Injury and Participation Regressed Together: Determining the Source of the Bias D. D. Two-Stage Least-Squares Employing Injury as an Instrument for Participation
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VII. Conclusions & Further Research
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VIII. References
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Data & Figures Table 1: Player Characteristics & Injuries
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Table 2: Sample of Bet365 Decimal Fixed Odds for La Liga 2012-13 Matches
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Table 3: Constantinou & Fenton (2013) Bookmaker Profit Margins
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Table 4: Bet365 Odds Reaction to Star Player Injury or Absence Conditional on Observed Outcomes
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Table 5: Bet365 Odds Reaction to Non-Star Player Injury or Absence Conditional on Observed Outcomes
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Table 6: Two-Stage Least-Squares Regression Employing Injury as an Instrument for Participation, Conditional on Observed Outcomes
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“There was but one question he left unasked, and it vibrated between his lines: if gross miscalculations of a person's value could occur on a baseball field, before a live audience of thirty thousand, and a television audience of millions more, what did that say about the measurement of performance in other lines of work? If professional baseball players could be over- or under valued, who couldn't?” -Michael Lewis, “Moneyball: The Art of Winning an Unfair Game” I. Introduction How much does Lionel Messi increase Barcelona’s chances of winning simply by stepping onto the field? Do star players really make a difference in whether or not a team performs well, and more specifically, does the market appropriately value them? The question of an individual's effect on team performance is a key topic in personnel economics, as well as the economics of sport. Whether in the boardroom or on a football pitch, the acquisition of talent is paramount for major organizations—but the question remains, is the market susceptible to a “star bias,” and does it lead to an exaggeration of individual contribution? We can often observe tangible contributions players make to team outcomes. The number of goals scored, minutes played, and assists made are recorded and mass distributed in modern sport media. However, the effect of a team member's participation—the simple act of being present within an organizational structure—has on overall productivity is difficult to measure and not clearly observed in data. One attempt to observe a CEO's effect on firm productivity in this manner was presented in Bennesden, Morten, et. al.'s work, "Do Ceos Matter?" (2006), a study that used untimely deaths of CEOs as the exogenous variation in participation necessary to evaluate his or her effect on firm output. Football provides an interesting context in which agents’ decisions and team outcomes are publicly observed. In spite of the prevalence of data and popularity of the industry, talent has long been evaluated without much consideration to its raw contribution to results. The recent popularity of Michael Lewis’ groundbreaking work “Moneyball: The Art of Winning an Unfair Game” (2004) suggests a new era in the world of sport in which the gut instincts of talent scouts have been replaced with regression analysis. Whereas recruitment at this level has traditionally been dominated by an arms race for the biggest names bearing the highest price tags, Lewis presented a model in which talent was chosen based on careful prediction of contribution to team
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outcomes. This resulted in the drafting of athletes with niche skills deemed vital to a winning strategy, rather than traditional “stars” with all-around talent. While the contribution of a top performer is an interesting question on its own, this paper seeks to understand how the market values footballers—and whether or not that evaluation stands up ex-post when it concerns a star player. Though teams may only play one or two times per week, the sports media cycle is twenty-four hours; the performance of certain key players is predicted, observed, and evaluated on a constant basis. Public sentiments on a team’s outlook can be captured in the betting market; football has ascended to the most popular sport in gambling in recent years (Finnigan & Nordsted 2010). The high level of market saturation pressures betting agencies to craft accurate predictions based on publicly available information. Whether or not these agencies exaggerate the effect of player absence is the subject of this study. Although any footballer who participates in a top European league can be deemed a “star” in one respect or another, there are certain players who receive more media attention and emphasis than others. Given that betting odds are determined on publicly available information and are not immune to market sentiment, we hypothesize that players with higher degrees of star power will generate stronger exaggeration on betting odds when removed from the roster. The study breaks players into two groups—stars and non-stars—to assess this question. Whether in football or within the confines of a corporation, the level of endogeneity introduced when attempting to tease out the value of one team member’s participation on outcome is difficult to overcome. To a large extent, whether or not a team member participates is dependent on the team’s performance. In “CEO Ability, Pay, and Firm Performance” (2010), Chang, Dasgupta, and Hilary attempt to evaluate the contribution of CEOs to firms by analyzing stock market reactions to CEO departures. While their findings suggest that CEOs inform company performance, the inability to randomize departures leaves room for endogeneity. Possibilities arise such as the likelihood that a CEO will depart a firm when he or she possesses knowledge of poor future returns. The nature of production in football introduces natural variations in participation, namely injuries; this opens an opportunity to overcome the endogeneity of participation to team performance. Unearthing the causal relationship between participation and outcome is 5
problematic because participation influences and is influenced by match results. A manager's decision to bench a player from a game and the collection of penalties may have strategic implications. Injuries, on the other hand, are natural and non-strategic variations in participation that provide a useful instrument to address this research question. Using data collected from the 2012-13 season of Spain’s La Liga BBVA, four players were selected and designated into two groups—star and non-star—to determine the effect of their absences on betting odds. The first test will examine the effect of player absence for any reason, conditional on observed match results. The second test will use injury instead of absence, and the third will include both to determine the source of the bias. Lastly, a two-stage least-squares model that employs injuries as an instrument for participation will be employed to overcome questions of endogeneity. This paper makes several contributions to the literature. First, it demonstrates that the absence of star players does, in fact, have a positive net effect on betting odds. Namely, bettors are overpaid when a team wins and a star is omitted from play. Secondly, the absence of non-star players demonstrates little to no effect on betting odds, limiting the bias to players with the highest levels of media attention. Lastly, when injury and absence are regressed together, the source of the bias is determined to come from injury-related absences. Previous works have studied other biases to betting odds, including whether a team plays home or away. The regression models employed in this paper confirm, albeit through a different mode of analysis than prior studies, that the home bias persists, and bettors are systemically underpaid when a team wins at home. The research is organized in the following manner: Part II reviews relevant literature in the arenas of personnel economics, sport, and betting. Part III discusses the motivation behind player and leagues choices made in the study. Part IV outlines the nature of the data and determination of betting odds used in this paper. Part V reviews the empirical methodology. Part VI describes the results of regression analysis, and Part VII states conclusions and lines of further research. II. Relevant Literature in Personnel Economics, Sport, and Weak Form Efficiency in Betting Markets
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This study is related to literature published both in a purely managerial context, and the evaluation of sport. The first question—to what extent does a player’s participation impact team outcomes—has been addressed in the context of CEOs most prominently, and is a major concern of the Moneyball hypothesis in American professional baseball. The second question regarding market evaluation of contribution has also been applied to the question of CEO ability. A discussion of research on the accuracy of betting odds will follow. A. Individual Contribution to Firm Output & Market Evaluation of Skill Much of the literature centered on the evaluation of personnel and their contributions focuses on CEO ability and stock market reactions to leadership change. Chang, Dasgupta, and Hilary (2010) analyzed stock market reactions around a given CEO’s departure to determine whether or not performance is a reflection of CEO ability. They found a negative correlation between stock market reaction, previous performance of the firm, and the CEO’s pre-departure salary. The paper does not address the possible endogeneity of departure to firm performance, and introduces the possibility of reverse causality. Additionally, voluntary leaves and firings are not distinguished in the results. Our study employs the use of injury as an instrument for participation in an attempt to overcome this bias. Bennedsen, Perez, and Wolfenzen (2006) address the issue of endogeneity by using the deaths of CEOs, board members, and CEO family members as exogenous variations in participation. They find that CEO death and the death of CEO family members is negatively correlated with firm performance, however the death of board members does not change future course—suggesting that the results vary across positions and status. One issue that arises as demonstrated in Slovin and Sushka (1993) is that CEOs who are founders versus later generations of leaders may trigger different stock market reactions. This paper mimics the results of Bennedsen, et. al.’s study in that injuries are used as natural variation in footballer participation, and separates players with different levels of “star power” to address variation across groups. B. Athlete Contribution to Team Performance The hiring strategy outlined in Michael Lewis’ best-selling book Moneyball (2003) centered on acquiring baseball players with skills most predictive of offensive success. Economists hired by 7
Oakland Athletics’ manager Billy Beane argued that certain player attributes were systemically overvalued (and hence expensive to acquire), whereas the true determinants of game outcomes were often overlooked. Regression analysis demonstrated that on-base percentage was a powerful predictor of success, however it was a skill consistently undervalued in the talent market. According to an economic evaluation of the Moneyball hypothesis conducted by Hakes & Sauer (2006), “The A’s were able to purchase a successful team less expensively by focusing on players with a higher on-base percentage” (182). Athletes were hired on their ability to increase probability of winning, whether or not that coincided with highly valued skills in the market such as batting average. One critical issue with the Moneyball hypothesis was the inability to randomize line-ups in regression analysis, which limits causal interpretation of onbase percentage to offensive success. Our paper employs injuries as a method of randomization, and turns to bookmakers as the source of market evaluation rather than the labor market for footballers. The quantification of player contribution to performance has arisen in the context of many sports. Following the Moneyball approach, Cohea and Payton (2011) set out to determine which National Football League (NFL) statistics best predicted an individual’s contribution to team outcome. Chan, Cho, and Novati (2013) analyzed to what extent playing position determined contribution in the National Hockey League (NHL). Goalkeepers generally commanded among the highest salaries in hockey and were found to be the most important, demonstrating a degree of efficiency in the labor market. This paper does not seek to evaluate the factors that contribute to an athlete’s effectiveness, but rather forces a second look at how the market evaluates their participation. Brady, Bolchover, and Sturgess (2008) posed the question of whether or not team talent matters, and the role of the individual within team structures. They argued that most of the prior research—such as Kahn (1993), which analyzes change in individual performance during baseball managerial shifts—is concerned with establishing metrics, rather than addressing the causality question. Brady, Bolchover, and Sturgess focus, much like the literature of personnel economics, on the role of the manager, whereas this paper seeks to evaluate market perception of individual player contribution. Additionally, both papers turn to salary as reflection of market appraisal, whereas this paper establishes bookmakers’ odds as the market of interest.
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C. The Efficiency of Sport Betting Odds There has been a great deal of literature devoted to the efficiency of bookmakers in professional sport, and whether or not arbitrage opportunities exist. Many works have lauded the predictive abilities of betting agencies in a garden variety of empirical settings; Slamka et. al. (2008) argued betting odds and play-money prediction markets outperformed the FIFA World Rankings in predictive power. Spann and Skiera (2008) compared the efficiency of prediction markets and betting odds to tipsters in Bundesliga football, and determined that the former two consistently outperformed the latter. Graham & Stott (2008) generated two models based on match results and betting history, and found that current betting odds were not significantly different from what the combined model produced. On the other side, Pope and Peel (1989) found inefficiencies in the betting market ex-post, but determined there were no better strategies that could have been undertaken at the time that the odds were set. Much of the research on betting has been devoted to uncovering systemic biases in fixed odds over the past decade. Forrest & Simmons (2008) argued that fans generate biases in Spanish football betting, as it appears that more “likeable” teams faced better odds. The relevance of timing within a season is underscored in Goddard & Asimakopoulos (2004), a paper that found the beginning and end of the English Premier League season to be problematic for fixed odds betting. Deschamps and Gergaud (2007) provided evidence for the favorite-longshot bias, a subject of intense prior study including Dixon and Pope (2004), Ottaviani and Sorensen (2005), and later confirmed by Constantinou & Fenton (2013). A bias this paper confirms to be true, the home-away bias, was demonstrated in 14 major football leagues in Constantinou & Fenton (2013), as well as the American National Football League (NFL) in Dare and Dennis (2011). This paper contributes to the existing literature in that it employs regression to test the home bias, while Constantinou & Fenton assess forecasting with Rank Probability Score (RPS) analysis. Additionally, their study found that bookmaker accuracy had not improved between the 2006 and 2011 seasons. This paper extends the existence of the bias into the 2012-2013 season of La Liga. While it is clear from prior study that betting agencies have enduring inconsistencies, the question of whether or not a player’s absence generates a bias has yet to be addressed. This paper 9
adds to the literature in the suggestion of a “star” bias, or systemic exaggeration of a popular player’s contribution to team performance. III. Motivation & Player Choices Talent in La Liga is primarily concentrated in Football Club Barcelona (“FC Barcelona”) and Real Madrid, two teams that dominate the top spot in Spanish football. According to Senior Analyst Manuel Traquete of The Bleacher Report, “Ever since the inception of La Liga, the competition has been dominated by the two giants, who won 51 of the 80 editions” (Traquete 2011). Since the publication of that article two seasons ago, Barcelona and Madrid have continued to trade the title. The four players chosen for this study were selected evenly from both squads, as they represent the highest concentration of talent and greatest levels of media interest in La Liga. The players included in this paper share several common characteristics; they are widely believed to be major contributors to team success, and sustained injuries within the 2012-2013 season that allow for instrumental variable analysis discussed later. Table 1 lists key characteristics of the players, including details of the injuries they sustained. Lionel Messi and Cristiano Ronaldo are classified as stars in this study, and stand among the most celebrated players in the history of the sport. Both players compete in comparable offensive positions, and it is of note that the top five highest paid footballers in 2012 are forwards (Forbes). Messi and Ronaldo top that list behind English midfielder David Beckham, and are highly visible in social media and advertising endorsements. Famecount, a tool used to evaluate the popularity of celebrities and athletes based on social media visibility, ranked Ronaldo and Messi within the top three most widely-discussed footballers in the world. This ranking was established across several media platforms and takes into account fan engagement, YouTube views, and size of following (Rawlings 2011). Given their astronomical level of coverage and popular interest, Messi and Ronaldo are classified as “stars” within the data and were analyzed together. This paper hypothesizes that the market will have stronger reactions to the injuries of players that occupy the highest levels of media attention, and potentially exaggerate the effect of these players on probability of winning.
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The other players included in this study are Carles Puyol, veteran defender of Barcelona, and Iker Casillas, goalkeeper of Madrid. Though both are highly prominent figures in Spanish football, their salaries, relative media attention, and global visibility pale in comparison to their aforementioned teammates (Forbes). This study separates the players in two tiers based on level of media concentration. Table 1: Player Characteristics & Injuries Injuries Sustained
Player
Team
Position
Status
Lionel Messi
Barcelona
Forward
Thigh, Calf, Hamstring
STAR = 1
Cristiano Ronaldo
Madrid
Forward
Thigh, Back
STAR = 1
Iker Casillas
Madrid
Goalkeeper
Hand
STAR = 0
Carles Puyol
Barcelona
Defender
Knee, Cheek
STAR = 0
Notes. Star status is determined by relative media and public attention when compared to other players in the study. Star=1 when a player is deemed to have the highest level of market concentration. There are 40 observations for each player; injuries were determined to have occurred via data provider Soccerway. The nature and projected severity was confirmed through match day reports taken from the Associated Press (AP). IV. Data The dataset used in this paper was drawn from two sources. The first is extensive coverage of match statistics externally compiled from international sports media outlets ESPN and Sporting Life. The second dataset was constructed using match-by-match participation data for selected players. A. League Data This paper focuses upon the first division in Spanish football (referred to from this point forward as “La Liga”) across the 2012-2013 season. The data was obtained from www.footballdata.co.uk and contains match-specific statistics for the 380 games played, excluding non-league play such as the UEFA Champions League. These statistics include designations of the “home”
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and “away” teams, full-time and half-time results, goals scored, fouls committed, and match-day odds as posted by nineteen of the world’s major betting agencies. Football-Data acquired full and half time results from TBWSport and Livescore data services. More detailed match statistics were assembled from Sportinglife and ESPN Soccer, two global sport media outlets. Betting agency Bet365 Group Ltd. was chosen as the focus of this study due to its prominence and profit margins; the company boasts over two million customers based in nearly 150 countries worldwide (Euroslam). Bet365 is headquartered in the United Kingdom and reflects a global rather than local perception of La Liga play. As defined by Spann & Skiera (2008), “Bookmakers determine fixed betting odds according to their expectations of game outcome probabilities, and once they are published, fixed odds rarely change” (5). Match day odds in the dataset were collected on Friday afternoons for weekend matches and Tuesday afternoons for midweek matches. Bet365 odds are expressed as decimal odds, therefore they demonstrate what the payout would be if the bettor placed a £1 bet. A sample of Bet365’s odds for La Liga matches is included in Table 2. Table 2: Sample of Bet365 Decimal Fixed Odds for La Liga 2012-13 Matches Match
Bet365 Home Win
Bet365 Away Win
Bet365 Draw
Celta v. Malaga
2.25
3.2
3.25
Mallorca v. Espanyol
2
3.8
3.3
Sevilla v. Getafe
1.62
5.5
3.75
Barcelona v Sociedad
1.1
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Notes. This table shows sample Bet365 odds for four matches in week one of La Liga 2012-13 play. Decimal odds are the preferred type in the European market and demonstrate the payout for a bet of one unit of currency. As defined by Constantinou & Fenton (2013), “The bookmakers’ profit margin, also known as ‘over-round,’ refers to the margin by which the sum of the probability odds of the total outcomes exceeds 1 (thus, making the odds unfair for the bettor)” (2). According to their study, Bet365 demonstrated the lowest profit margin of top bookmakers in the English Premier League in 2011-12 (4), casting them as the “fairest” among competitors such as Ladbrokes, Bwin, and
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William Hill. Table 3 is taken from Constantinou & Fenton, demonstrating the variation in profit margins across betting agencies. Additionally, Constantinou & Fenton make use of the Rank Probability Score (RPS) to appraise the accuracy of bookmakers’ odds across the 2005-2012 seasons. Although the profit margins vary significantly across agencies, RPS scores do not. Bet365 is among the top three most accurate (hence lowest RPS) in the 2011-12 season (7), but it should be noted that the results are fairly consistent across the bookmakers listed in Table 3. Table 3: Constantinou & Fenton (2013) Bookmaker Profit Margins 2005
2006
2007
2008
2009
2010
2011
William Hill
12.49%
12.49%
12.37%
7.01%
7.35%
6.50%
6.70%
Bet365
7.91%
7.95%
5.98%
5.31%
5.43%
5.44%
5.46%
Bwin
10.13%
10.07%
10.06%
10.07%
8.30%
8.01%
6.42%
Gamebookers 8.11%
8.04%
7.45%
7.29%
7.75%
7.68%
7.67%
Interwetten
12.33%
11.35%
11.39%
10.21%
8.36%
10.13%
10.07%
Ladbrokes
12.27%
12.32%
12.19%
9.26%
7.48%
6.49%
6.65%
Sportingbet
8.14%
10%
10.13%
10.14%
10.12%
10.12%
7.66%
Notes. This table was taken from Constantinou & Fenton (2013). It displays the average profit margin per season in the English Premier League. Bet365 is the main focus of this study and demonstrates the lowest profit margin in the 2011-12 season. According to the authors, lower profit margin is an indication of fairness toward the bettor. Data on Bet365’s odds was provided to Football-Data by Betbrain and Betbase, independentlyoperated odds comparison services. As the data could be filtered based on when a team played home or away, odds are included and excluded in the regressions from the vantage point of the player being analyzed. For example, the Bet365 odds for home win are included when analyzing Messi or Puyol, conditional on Barcelona winning at home stadium Camp Nou. B. Player Data
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Data on each player’s participation was collected on a match-by-match basis gleaned from football data service Soccerway. For each match, the lineup was assessed to determine whether or not the player in question participated. Players were determined to be “absent” when they were sidelined or omitted from the roster. There were several instances in which the player was listed among substitutes but never entered play. These were not counted as absences, given that the market did not know ex-ante whether the player would be subbed-in. Using Soccerway’s information and press releases gathered around match day via the Associated Press, the motivation behind a player’s lack of participation was recorded and classified into two categories: injury, and non-injury. Additionally, data was collected on whether or not a player was substituted during the match, and the time at which the substitution took place. There are forty observations for each player as that is the number of matches played per team within the 2012-13 season of La Liga. Additionally, the players are coded based on “star” status—judged by media attention, performance, and global fan interest—and separated into two tiers as explained in Table 1. The number of observed injuries and absences naturally varies across players, however the four were chosen with knowledge of an extended absence from play during the 2012-13 season. V. Empirical Strategy The empirical strategy of this study takes advantage of the fact that betting odds and match outcomes are observed ex-post; this enables an evaluation of whether or not the market (in this case, Bet365) appropriately valued a player’s contribution to team performance. Additionally, we are able to observe how another major factor—playing at home versus away—contributes to the fluctuation of betting odds. This paper first tests whether a player’s lack of participation (denoted in the variable ‘absence’)—due to any number of factors, including coaching decision, injury, or penalty—is valued appropriately when setting betting odds. Conditional on observed match outcome, we would expect to see an additional, positive net effect on betting odds if the market exaggerates a certain star’s contribution to team performance when he is injured. Simply stated, if a certain player is overvalued, bettors are overpaid when the team wins without him.
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As the players are broken into two tiers—“stars” and “non-stars” for the purposes of this study— the results are permitted to vary across groups. For the latter pairing of Casillas and Puyol, we may expect to find less exaggerated consequences on the betting odds when they do not participate. The use of “participation” on its own may have empirical consequences—namely, participation affects and is affected by team performance. Top players may be benched for games in which the team expects to win easily, for example. The acquisition of penalties is an additional motivation behind absence that may also be endogenous to outcome. In order to overcome the issue of endogeneity, this paper employs injuries as natural, non-strategic variations in participation. It is possible that injuries do not generate perfect assignment. Top players are unmistakably “marked” by the opposition and often clock more minutes on the field. However, this paper will assume that the timing and gravity of the injuries are assigned randomly. The same action can generate injuries of varying severity and omit the victim from play for different periods of time, therefore providing a useful instrument to address this question. There are two criteria that must be met in order for an instrumental variable to be generated: •
The instrument is correlated with the causal variable of interest (in this case, participation);
•
It is not correlated with other determinants of dependent variable Yi (known as the “exclusion restriction”).
Injury is clearly correlated with whether or not a player participates, and given its random assignment in both timing and severity, is assumed to have no correlation with team outcomes in this study. Lastly, this paper tests whether or not playing at home is evaluated properly by the betting agency. The home bias has been discussed frequently in the literature, and we expect the coefficient to be negative if the home-field advantage is overvalued. This translates into bettors receiving smaller payouts than they should have when a team wins at home.
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VI. Regression Results Four regressions were ran on both the star and non-star groups in the study. They differ on the metric used to evaluate participation. In regression I, a binary variable “absent” demarcates whenever a player is omitted from the roster for any reason. In regression II, a binary variable “injured” is used and takes on value only when the player is omitted due to injury. Regression III employs both variables, and Regression IV is a two-stage least-squares regression instrumenting injury for absence. The “result” variable allows all regressions to be conditioned on observed outcomes, enabling effects over and above those generated by a team’s performance to be discussed as potential biases. Tables 4, 5, and 6 report the results of the following regressions for each group: (I) BETWIN365 = β0 + β1HOME + β2RESULT + β3ABSENT + β4BARCELONA + β5MADRID + ε
if STAR = {0,1}
(II) BETWIN365 = β0 + β1HOME + β2RESULT + β3INJURED + β4BARCELONA + β5MADRID + ε
if STAR = {0,1}
(III) BETWIN365 = β0 + β1HOME + β2RESULT + β3ABSENT + β4INJURED + β5BARCELONA + β6MADRID + ε
if STAR = {0,1}
(IV) BETWIN365IV = β0 + β1HOME + β2RESULT + β3(ABSENT = INJURED) + β4BARCELONA + β5MADRID + ε
if STAR = {0,1}
A. The Effect of Absence on Betting Odds We first test for the effect of a player’s absence on Bet365 odds, conditional on observed outcomes. The variable “absence” does not distinguish between injuries and other participationrelated decisions such as benching or penalization. Table 4 Column (I) displays regression results for the star player category when only the variable absent is included. The coefficient on absent is positive and statistically significant at the 1% level. Consistent with our hypothesis, Bet365 overpays bettors conditional on observed match outcome when a star is absent from the roster.
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We also find that, on average, whether a team plays home or away presents an exaggerated effect on fixed odds. The impact of playing at home on Bet365 odds is -0.317, which is statistically significant at the 1% level. As the agency has overestimated the home-field advantage, bettors are paid less than they should have been when the team wins at home. Interestingly, the results for non-star players as classified in this study tell a different story, as demonstrated in Table 5 Column (I). While the coefficient on absent is positive, it is much smaller in absolute value—0.068 versus 0.323—and statistically insignificant. Whether or not a non-star player participates in this sample is not reflected in a bias. The coefficient on home is again negative and significant at the 1% level. It is similar in magnitude for both the star and non-star regressions that include the absent variable. B. The Effect of Injury on Betting Odds In order to break down the effect of injury versus absence on Bet365 odds, we next specified a model in which injuries alone were used to estimate whether or not a bias exists. Column II of Table 4 presents the results for this regression in the star player group, again conditional on observed match results. The coefficient on injury is positive and statistically significant at the 1% level; it is similar in magnitude to the coefficient on absent in the first specification. Again, we find that the bias is in favor of the bettor, and generally payouts are higher when a star is absent due to injury. Column II of Table 5 reports the results for the same regression conducted on the non-star group. The coefficient on injury is close to zero in magnitude—smaller than the coefficient on participation in the previous specification—and statistically insignificant. Again, there is no evidence of a bias in the odds when a non-star is benched due to injury. C. Injury and Participation Regressed Together: Determining the Source of the Bias In order to better determine the source of the participation bias—whether it lies primarily in noninjury related absences, or vice versa—the next specification regresses Bet365’s odds on both participation and injury. This yields interesting results that demonstrate injuries are the primary motivation behind exaggeration in the agency’s payouts.
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For the star player group, Column III of Table 4 demonstrates the evidence for this bias. The coefficient on participation is of smaller magnitude, negative, and statistically insignificant. The coefficient on injury, however, is larger—0.565 in (III) versus 0.375 in (II)—and significant at the 1% level. This suggests that the overstatement of contribution to team performance arises specifically when the star is injured, rather than absent for other reasons. The results for non-stars are consistent with previous specifications that show neither participation nor injury present robust biases on betting odds. Column III of Table 5 shows the coefficients on absent and injury to be 0.114 and -0.077 respectively. The signs have reversed from the star model, but the results are again smaller in magnitude and statistically insignificant. D. Two-Stage Least-Squares Employing Injury as an Instrument for Participation Earlier in the paper, the issue of endogeneity was discussed in regards to whether or not a player participates in a given match. In order to overcome the bias, injuries were observed and recorded for each player across the 2012-13 season. The simplest specification of the model regresses Bet365’s odds on injuries rather than all absences. The last model specification runs Two-Stage Least-Squares (2SLS) instrumenting injury for participation. The second column in Table 6 again demonstrates systemic exaggeration of star contribution. When injury is instrumented for participation, the coefficient is 0.379 and significant at the 1% level. For bets placed on a given match when either Messi or Ronaldo is injured, bettors earn more conditional on observed results. The 2SLS results for non-stars, illustrated in the third column of Table 6, generates a coefficient on injury that is nearly zero (0.002) and statistically insignificant. Again, we find little effect on match day fixed odds when a non-star in the sample is injured. It should be noted that the home bias is confirmed throughout the models, including the 2SLS specification for both star and non-star groups. The coefficient is -0.315 and -0.332 for stars and non-stars respectively, significant at the 1% level for both. As discussed in related literature, the home bias persists in betting odds and results in payouts that are too low when a team wins at home.
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Table 4: Bet365 Odds Reaction to Star Player Injury or Absence Conditional on Observed Outcomes I
II
III
Intercept
0.005 (0.04)
0.010 (0.07)
0.213 (0.16)
Home
-0.317*** (-5.23)
-0.321*** (-5.46)
-0.324*** (-5.49)
Result Dummy 2
0.087 (1.01)
0.118 (1.41)
0.134* (1.55)
Result Dummy 3
-0.137 (-1.27)
-0.135 (-1.28)
-0.137 (-1.30)
Absent (includes injuries)
0.323*** (4.05)
Injured
-0.192 (-0.78) 0.375*** (4.65)
0.565** (2.19)
FC Barcelona
1.348*** (10.29)
1.333*** (10.50)
1.322*** (10.32)
Real Madrid
1.486 (10.94)***
1.483*** (11.26)
1.476*** (11.15)
Observations
80
80
80
R2
0.727
0.742
0.745
Notes. The above table reports three sets of regression results—including estimated coefficients, respective t-statistics denoted in parentheses below, and R2 values. The dependent variable is BetWin365’s decimal fixed odds reported for each match of the 2012-13 La Liga season. These can be interpreted as the amount (in pounds sterling) a bettor wins after placing a £1 bet. Home is a binary variable equal to 1 when a team plays at home. The Result variables take on values of 1,2, and 3 when match results are win, loss, and draw respectively. Absent is a binary variable equal to 1 when the player does not participate in a given match. Injured is a binary variable equal to 1 when the player misses a match due to injury. FC Barcelona and Real Madrid are binary variables equal to 1 when a player competes for the respective team. *Significant at 10% level; **Significant at 5% level; ***Significant at 1% level.
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Table 5: Bet365 Odds Reaction to Non-Star Player Injury or Absence Conditional on Observed Outcomes I
II
III
Intercept
0.089 (0.59)
0.112 (0.74)
0.152 (0.56)
Home
-0.331*** (-4.96)
-0.332*** (-4.92)
-0.326*** (-4.86)
Result Dummy 2
0.108 (1.14)
0.103 (1.08)
0.113 (1.18)
Result Dummy 3
-0.171* (-1.44)
-0.182* (-1.52)
-0.174* (-1.46)
Absent (includes injuries)
0.068 (1.09)
Injured
0.114 (1.40) 0.002 (0.02)
-0.077 (-0.89)
FC Barcelona
1.292*** (8.89)
1.311*** (8.94)
1.300*** (8.91)
Real Madrid
1.412*** (9.44)
1.427*** (9.49)
1.407 (9.38)***
Observations
80
80
80
R2
0.667
0.661
0.671
Notes. The above table reports three sets of regression results—including estimated coefficients, respective t-statistics denoted in parentheses below, and R2 values. The dependent variable is BetWin365’s decimal fixed odds reported for each match of the 2012-13 La Liga season. These can be interpreted as the amount (in pounds sterling) a bettor wins after placing a £1 bet. Home is a binary variable equal to 1 when a team plays at home. The Result variables take on values of 1,2, and 3 when match results are win, loss, and draw respectively. Absent is a binary variable equal to 1 when the player does not participate in a given match. Injured is a binary variable equal to 1 when the player misses a match due to injury. FC Barcelona and Real Madrid are binary variables equal to 1 when a player competes for the respective team. *Significant at 10% level; **Significant at 5% level; ***Significant at 1% level.
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Table 6: Two-Stage Least-Squares Regression Employing Injury as an Instrument for Participation, Conditional on Observed Outcomes STAR=1
STAR=0
Intercept
-0.130 (-0.09)
0.111 (0.72)
Home
-0.315*** (-5.17)
-0.332*** (-4.93)
Result Dummy 2
0.084 (0.97)
0.103 (1.08)
Result Dummy 3
-0.130 (-1.19)
-0.182 (-1.51)
Injured
0.379*** (4.50)
0.002 (0.02)
FC Barcelona
1.354*** (10.30)
1.311*** (8.85)
Real Madrid
1.497*** (10.97)
1.426*** (9.41)
Observations
80
80
R2
0.725
0.662
Notes. The above table reports 2SLS regression results—including estimated coefficients, respective tstatistics denoted in parentheses below, and R2 values. The dependent variable is BetWin365’s decimal fixed odds reported for each match of the 2012-13 La Liga season. These can be interpreted as the amount (in pounds sterling) a bettor wins after placing a £1 bet. Home is a binary variable equal to 1 when a team plays at home. The Result variables take on values of 1,2, and 3 when match results are win, loss, and draw respectively. Injured is instrumented for absence in this regression, and is a binary variable equal to 1 when the player misses a match due to injury. FC Barcelona and Real Madrid are binary variables equal to 1 when a player competes for the respective team. *Significant at 10% level; **Significant at 5% level; ***Significant at 1% level.
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VII. Conclusions & Further Research The contribution of a star player to team outcomes, particularly in the eyes of the market, is a prominent question in the literature of economics and sport. There is evidence to suggest that while betting odds are generally efficient predictors of team outcomes, they exaggerate the consequences of a star footballer’s absence from play. In order to assess this issue, we merged two datasets that allowed us to match team outcomes from the 2012-13 La Liga season with player participation data on a match-by-match basis. First, we acquired a broad league-specific dataset that included extensive information for all 380 games played, including match day odds from the world’s major betting agencies. Next, four players were selected for the study and a dataset was assembled on an individual basis. For each subject, data was recorded on whether or not the player participated in a given match, and the motivation behind that absence was gleaned from Soccerway data and confirmed through match day reports of the Associated Press. The players were broken into two groups—stars versus nonstars—on the basis of market visibility, press attention, and perceived value to team outcome. The betting agency Bet365 was chosen as the focus for the study, and its fixed match day odds served as the dependent variable in the regressions. Bet365 is a global agency with the lowest profit margins among major competitors, suggesting it is one of the fairest and most accurate bookmakers. The tests ran were conditional on observed match outcomes, which allowed for analysis of potential exaggerations in payouts. First, we used absence—whether for injury or other, potentially strategic reasons—to evaluate this hypothesis. Consistent with predictions, absence in the star group demonstrated a positive and statistically significant effect on betting odds conditional on observed outcomes; this suggests that bettors were systemically overpaid when Messi and Ronaldo did not play during the 2012-13 season. The nonstar group showed a much smaller, statistically insignificant coefficient on absence. Regressions that employed player injury rather than absence elicited similar results. One of the most interesting results of the study was presented in regressions where both absence and injury were included to determine the source of the bias. In the star group, injury proved to
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generate the exaggeration of payouts as its coefficient was large, positive, and statistically significant at the 1% level. Conversely, the coefficient on absence was small, negative and lost its significance. The non-star group again demonstrated no evidence of a bias. Absence is a potentially contaminated variable; whether or not a player participates in a given game may affect and be affected by team performance. In order to overcome the issue of endogeneity, injury was selected as an instrumental variable based on its fulfillment of the IV identifying assumptions: it is correlated with participation, and the exclusion restriction holds. The last set of regressions—a two-stage least-squares model instrumenting injury for participation—demonstrated results consistent with the hypothesis proposed earlier in the paper. The star group showed a positive and statistically significant coefficient on injury, while the nonstar group’s coefficient was close to zero in magnitude and insignificant. This is consistent with the prediction that star footballers exaggerate payouts when omitted from the roster, whereas non-stars have little to no effect on betting odds when injured. Lastly, we confirmed that the home-away bias as discussed in Constantinou & Fenton (2013) persists in Bet365 odds. The coefficient on home was negative and statistically significant at the 1% level across all models in both groups. Further research could determine whether or not the star bias is specific to certain player positions and leagues. The empirical strategy and mode of analysis could be easily applied across other sports in which gambling data is available and prominent.
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References Bennedsen, Morten, Francisco Perez-Gonzalez, and Daniel Wolfenzon. "Do Ceos Matter?" Copenhagen Business School, 18 Oct. 2006. Web. Brady, Chris, David Bolchover, and Brian Sturgess. "Managing the Talent Economy: The Football Model for Business." California Management Review 50.4 (2008): n. pag. Print. Brown, William O., and Raymond D. Sauer. "Fundamentals or Noise? Evidence from the Professional Basketball Betting Market." Journal of Finance 48.4 (1993): 1193-209. Print. Chan, Timothy C.Y., Justin A. Cho, and David C. Novati. "Quantifying the Contribution of NHL Player Types to Team Performance." Interfaces 43.4 (2013): 131-45. Print. Chang, Y. Y., S. Dasgupta, and G. Hilary. "CEO Ability, Pay, and Firm Performance." Management Science 56.10 (2010): 1633-652. Print. Cohea, Christopher, and Mark E. Payton. "Relationships Between Player Actions and Game Outcomes in American Football." Sport Science 15 (2011): 19-24. Print. Constantinou, Anthony C., and Norman E. Fenton. "Profiting from Arbitrage and Odds Biases of the European Football Gambling Mark." University of London (2013): n. pag. Web. Dare, William H., and Steven A. Dennis. "A Test for Bias of Inherent Characteristics in Betting Markets." Journal of Sports Economics 12.6 (2011): 660-65. Print. Deschamps, Bruno, and Olivier Gergaud. "Efficiency in Betting Markets: Evidence from English Football." The Journal of Prediction Markets 1 (2007): 61-73. Print. Dixon, Mark J., and Peter F. Pope. "The Value of Statistical Forecasts in the UK Association Football Betting Market." International Journal of Forecasting 20.4 (2004): 697-711. Print. Euroslam. "Bet365 Sportsbook Review & Bet365 Bonus." Bet365 Sportsbook Review. Euroslam.com, 2013. Web. 11 July 2013. Forrest, David, and Robert Simmons. "Sentiment in the Betting Market on Spanish Football." Applied Economics 40.1 (2008): 119-26. Print. 24
Goddard, John, and Ioannis Asimakopoulos. "Modeling Football Match Results and the Efficiency of Fixed-Odds Betting." University of Wales Swansea, 2003. Web. 4 July 2013. Hakes, Jahn K., and Raymond D. Sauer. "An Economic Evaluation of the Moneyball Hypothesis." Journal of Economic Perspectives 20.3 (2006): 173-85. Print. Kahn, Lawrence M. "Managerial Quality, Team Success, and Individual Player Performance in Major League Baseball." Industrial and Labor Relations Review 46.3 (1993): 531-47. JSTOR. 1 Apr. 1993. Web. 12 Sept. 2013. Kain, Kyle J., and Trevor D. Logan. "Are Sports Betting Markets Prediction Markets? Evidence from a New Test." NBER (2011): n. pag. Jan. 2011. Web. 3 June 2013. Lewis, Michael. Moneyball: The Art of Winning an Unfair Game. New York: W.W. Norton, 2003. Print. Nordsted, Pete, and Matt Finnigan. The Premier Football Betting Handbook 2010/11. Hampshire: Harriman House, 2010. Print. Ottaviani, Marco, and Peter Norman Sørensen. "Noise, Information, and the Favorite-Longshot Bias in Parimutuel Predictions." American Economic Journal: Microeconomics 2.1 (2010): 5885. Print. Peel, David A., and Peter F. Pope. "Information, Prices and Efficiency in a Fixed-Odds Betting Market." Economica 56 (1989): 323-41. Print. Rawlings, Owen. "Cristiano Ronaldo Ranked 'World's Most Popular Footballer'" The Independent. Independent Digital News and Media, 12 Aug. 2011. Web. 12 July 2013. Settimi, Christina. "The World's Highest-Paid Soccer Players." Forbes. Forbes Magazine, 18 Apr. 2012. Web. 18 Aug. 2013. Slamka, Christine, Stefan Luckner, Thomas Seeman, and Jan Schroder. "An Empirical Investigation of the Forecast Accuracy of Play-Money Prediction Markets and Professional Betting Markets." ECIS 2008 Proceedings (2008): n. pag. AIS Electronic Library. Web. 15 June
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2013. Slovin, Myron B., and Marie E. Sushka. "Ownership Concentration, Corporate Control Activity, and Firm Value: Evidence from the Death of Inside Blockholders." Journal of Finance 48.4 (1993): 1293-321. Print. Spann, Martin, and Bernd Skiera. "Sports Forecasting: A Comparison of the Forecast Accuracy of Prediction Markets, Betting Odds and Tipsters." Journal of Forecasting 28.1 (2009): 55-72. Print. Traquete, Manuel. "La Liga: Are FC Barcelona and Real Madrid CF Slowly Killing the Spanish League?" Bleacher Report, 19 July 2011. Web. 19 July 2013.
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Gillian Rose Kemmerer Candidate Number: 81767 LSE Master’s of Science Dissertation (2013) MSc International Management 2012-2013 The London School of Economics & Political Science Supervisor: Dr. Yona Rubinstein Course Code: MN499 Word Count: 7,118 (excluding references)
ABSTRACT: How much does a star athlete contribute to team outcomes in professional football, and how does the market evaluate their worth? This paper examines four players from Spain’s La Liga in the 2012-13 season to determine how absences—due to injuries and other factors—change fixed betting odds, conditional on observed outcomes. As a player’s participation affects and is affected by team performance, injuries are used as an instrument for absence to overcome the issue of endogeneity. Players are broken into two categories—stars and non-stars—based on relative media attention and public sentiment. The regressions show that conditional on observed match results, the absence of star players is exaggerated in the odds, resulting in higher payouts for bettors when a team wins without them. Non-stars, on the other hand, do not have a significant effect on the odds when they are absent. When general absence and injuries are regressed together, player injury is revealed to be the source of this bias for the star player group. Finally, when injury is instrumented for participation, the results confirm that a star player’s injury results in systemically inflated payouts, whereas injuries of non-stars have a net effect close to zero. The paper additionally confirms the presence of a home-away bias as discussed in previous literature. Ultimately, this paper rejects the notion that betting odds appropriately value player contribution to teams, and presents a new source of bias—namely, the injury of a star—to the literature on betting market efficiency.
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Table of Contents I. Introduction
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II. Relevant Literature A. Individual Contribution to Firm Output & Market Evaluation of Skill B. Athlete Contribution to Team Performance C. The Efficiency of Sport Betting Odds
6
III. Motivation & Player Choices
10
IV. Data A. League Data B. Player Data
11
V. Empirical Strategy
14
VI. Regression Results A. The Effect of Absence on Betting Odds B. The Effect of Injury on Betting Odds C. Injury and Participation Regressed Together: Determining the Source of the Bias D. D. Two-Stage Least-Squares Employing Injury as an Instrument for Participation
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VII. Conclusions & Further Research
22
VIII. References
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Data & Figures Table 1: Player Characteristics & Injuries
11
Table 2: Sample of Bet365 Decimal Fixed Odds for La Liga 2012-13 Matches
12
Table 3: Constantinou & Fenton (2013) Bookmaker Profit Margins
13
Table 4: Bet365 Odds Reaction to Star Player Injury or Absence Conditional on Observed Outcomes
19
Table 5: Bet365 Odds Reaction to Non-Star Player Injury or Absence Conditional on Observed Outcomes
20
Table 6: Two-Stage Least-Squares Regression Employing Injury as an Instrument for Participation, Conditional on Observed Outcomes
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3
“There was but one question he left unasked, and it vibrated between his lines: if gross miscalculations of a person's value could occur on a baseball field, before a live audience of thirty thousand, and a television audience of millions more, what did that say about the measurement of performance in other lines of work? If professional baseball players could be over- or under valued, who couldn't?” -Michael Lewis, “Moneyball: The Art of Winning an Unfair Game” I. Introduction How much does Lionel Messi increase Barcelona’s chances of winning simply by stepping onto the field? Do star players really make a difference in whether or not a team performs well, and more specifically, does the market appropriately value them? The question of an individual's effect on team performance is a key topic in personnel economics, as well as the economics of sport. Whether in the boardroom or on a football pitch, the acquisition of talent is paramount for major organizations—but the question remains, is the market susceptible to a “star bias,” and does it lead to an exaggeration of individual contribution? We can often observe tangible contributions players make to team outcomes. The number of goals scored, minutes played, and assists made are recorded and mass distributed in modern sport media. However, the effect of a team member's participation—the simple act of being present within an organizational structure—has on overall productivity is difficult to measure and not clearly observed in data. One attempt to observe a CEO's effect on firm productivity in this manner was presented in Bennesden, Morten, et. al.'s work, "Do Ceos Matter?" (2006), a study that used untimely deaths of CEOs as the exogenous variation in participation necessary to evaluate his or her effect on firm output. Football provides an interesting context in which agents’ decisions and team outcomes are publicly observed. In spite of the prevalence of data and popularity of the industry, talent has long been evaluated without much consideration to its raw contribution to results. The recent popularity of Michael Lewis’ groundbreaking work “Moneyball: The Art of Winning an Unfair Game” (2004) suggests a new era in the world of sport in which the gut instincts of talent scouts have been replaced with regression analysis. Whereas recruitment at this level has traditionally been dominated by an arms race for the biggest names bearing the highest price tags, Lewis presented a model in which talent was chosen based on careful prediction of contribution to team
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outcomes. This resulted in the drafting of athletes with niche skills deemed vital to a winning strategy, rather than traditional “stars” with all-around talent. While the contribution of a top performer is an interesting question on its own, this paper seeks to understand how the market values footballers—and whether or not that evaluation stands up ex-post when it concerns a star player. Though teams may only play one or two times per week, the sports media cycle is twenty-four hours; the performance of certain key players is predicted, observed, and evaluated on a constant basis. Public sentiments on a team’s outlook can be captured in the betting market; football has ascended to the most popular sport in gambling in recent years (Finnigan & Nordsted 2010). The high level of market saturation pressures betting agencies to craft accurate predictions based on publicly available information. Whether or not these agencies exaggerate the effect of player absence is the subject of this study. Although any footballer who participates in a top European league can be deemed a “star” in one respect or another, there are certain players who receive more media attention and emphasis than others. Given that betting odds are determined on publicly available information and are not immune to market sentiment, we hypothesize that players with higher degrees of star power will generate stronger exaggeration on betting odds when removed from the roster. The study breaks players into two groups—stars and non-stars—to assess this question. Whether in football or within the confines of a corporation, the level of endogeneity introduced when attempting to tease out the value of one team member’s participation on outcome is difficult to overcome. To a large extent, whether or not a team member participates is dependent on the team’s performance. In “CEO Ability, Pay, and Firm Performance” (2010), Chang, Dasgupta, and Hilary attempt to evaluate the contribution of CEOs to firms by analyzing stock market reactions to CEO departures. While their findings suggest that CEOs inform company performance, the inability to randomize departures leaves room for endogeneity. Possibilities arise such as the likelihood that a CEO will depart a firm when he or she possesses knowledge of poor future returns. The nature of production in football introduces natural variations in participation, namely injuries; this opens an opportunity to overcome the endogeneity of participation to team performance. Unearthing the causal relationship between participation and outcome is 5
problematic because participation influences and is influenced by match results. A manager's decision to bench a player from a game and the collection of penalties may have strategic implications. Injuries, on the other hand, are natural and non-strategic variations in participation that provide a useful instrument to address this research question. Using data collected from the 2012-13 season of Spain’s La Liga BBVA, four players were selected and designated into two groups—star and non-star—to determine the effect of their absences on betting odds. The first test will examine the effect of player absence for any reason, conditional on observed match results. The second test will use injury instead of absence, and the third will include both to determine the source of the bias. Lastly, a two-stage least-squares model that employs injuries as an instrument for participation will be employed to overcome questions of endogeneity. This paper makes several contributions to the literature. First, it demonstrates that the absence of star players does, in fact, have a positive net effect on betting odds. Namely, bettors are overpaid when a team wins and a star is omitted from play. Secondly, the absence of non-star players demonstrates little to no effect on betting odds, limiting the bias to players with the highest levels of media attention. Lastly, when injury and absence are regressed together, the source of the bias is determined to come from injury-related absences. Previous works have studied other biases to betting odds, including whether a team plays home or away. The regression models employed in this paper confirm, albeit through a different mode of analysis than prior studies, that the home bias persists, and bettors are systemically underpaid when a team wins at home. The research is organized in the following manner: Part II reviews relevant literature in the arenas of personnel economics, sport, and betting. Part III discusses the motivation behind player and leagues choices made in the study. Part IV outlines the nature of the data and determination of betting odds used in this paper. Part V reviews the empirical methodology. Part VI describes the results of regression analysis, and Part VII states conclusions and lines of further research. II. Relevant Literature in Personnel Economics, Sport, and Weak Form Efficiency in Betting Markets
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This study is related to literature published both in a purely managerial context, and the evaluation of sport. The first question—to what extent does a player’s participation impact team outcomes—has been addressed in the context of CEOs most prominently, and is a major concern of the Moneyball hypothesis in American professional baseball. The second question regarding market evaluation of contribution has also been applied to the question of CEO ability. A discussion of research on the accuracy of betting odds will follow. A. Individual Contribution to Firm Output & Market Evaluation of Skill Much of the literature centered on the evaluation of personnel and their contributions focuses on CEO ability and stock market reactions to leadership change. Chang, Dasgupta, and Hilary (2010) analyzed stock market reactions around a given CEO’s departure to determine whether or not performance is a reflection of CEO ability. They found a negative correlation between stock market reaction, previous performance of the firm, and the CEO’s pre-departure salary. The paper does not address the possible endogeneity of departure to firm performance, and introduces the possibility of reverse causality. Additionally, voluntary leaves and firings are not distinguished in the results. Our study employs the use of injury as an instrument for participation in an attempt to overcome this bias. Bennedsen, Perez, and Wolfenzen (2006) address the issue of endogeneity by using the deaths of CEOs, board members, and CEO family members as exogenous variations in participation. They find that CEO death and the death of CEO family members is negatively correlated with firm performance, however the death of board members does not change future course—suggesting that the results vary across positions and status. One issue that arises as demonstrated in Slovin and Sushka (1993) is that CEOs who are founders versus later generations of leaders may trigger different stock market reactions. This paper mimics the results of Bennedsen, et. al.’s study in that injuries are used as natural variation in footballer participation, and separates players with different levels of “star power” to address variation across groups. B. Athlete Contribution to Team Performance The hiring strategy outlined in Michael Lewis’ best-selling book Moneyball (2003) centered on acquiring baseball players with skills most predictive of offensive success. Economists hired by 7
Oakland Athletics’ manager Billy Beane argued that certain player attributes were systemically overvalued (and hence expensive to acquire), whereas the true determinants of game outcomes were often overlooked. Regression analysis demonstrated that on-base percentage was a powerful predictor of success, however it was a skill consistently undervalued in the talent market. According to an economic evaluation of the Moneyball hypothesis conducted by Hakes & Sauer (2006), “The A’s were able to purchase a successful team less expensively by focusing on players with a higher on-base percentage” (182). Athletes were hired on their ability to increase probability of winning, whether or not that coincided with highly valued skills in the market such as batting average. One critical issue with the Moneyball hypothesis was the inability to randomize line-ups in regression analysis, which limits causal interpretation of onbase percentage to offensive success. Our paper employs injuries as a method of randomization, and turns to bookmakers as the source of market evaluation rather than the labor market for footballers. The quantification of player contribution to performance has arisen in the context of many sports. Following the Moneyball approach, Cohea and Payton (2011) set out to determine which National Football League (NFL) statistics best predicted an individual’s contribution to team outcome. Chan, Cho, and Novati (2013) analyzed to what extent playing position determined contribution in the National Hockey League (NHL). Goalkeepers generally commanded among the highest salaries in hockey and were found to be the most important, demonstrating a degree of efficiency in the labor market. This paper does not seek to evaluate the factors that contribute to an athlete’s effectiveness, but rather forces a second look at how the market evaluates their participation. Brady, Bolchover, and Sturgess (2008) posed the question of whether or not team talent matters, and the role of the individual within team structures. They argued that most of the prior research—such as Kahn (1993), which analyzes change in individual performance during baseball managerial shifts—is concerned with establishing metrics, rather than addressing the causality question. Brady, Bolchover, and Sturgess focus, much like the literature of personnel economics, on the role of the manager, whereas this paper seeks to evaluate market perception of individual player contribution. Additionally, both papers turn to salary as reflection of market appraisal, whereas this paper establishes bookmakers’ odds as the market of interest.
8
C. The Efficiency of Sport Betting Odds There has been a great deal of literature devoted to the efficiency of bookmakers in professional sport, and whether or not arbitrage opportunities exist. Many works have lauded the predictive abilities of betting agencies in a garden variety of empirical settings; Slamka et. al. (2008) argued betting odds and play-money prediction markets outperformed the FIFA World Rankings in predictive power. Spann and Skiera (2008) compared the efficiency of prediction markets and betting odds to tipsters in Bundesliga football, and determined that the former two consistently outperformed the latter. Graham & Stott (2008) generated two models based on match results and betting history, and found that current betting odds were not significantly different from what the combined model produced. On the other side, Pope and Peel (1989) found inefficiencies in the betting market ex-post, but determined there were no better strategies that could have been undertaken at the time that the odds were set. Much of the research on betting has been devoted to uncovering systemic biases in fixed odds over the past decade. Forrest & Simmons (2008) argued that fans generate biases in Spanish football betting, as it appears that more “likeable” teams faced better odds. The relevance of timing within a season is underscored in Goddard & Asimakopoulos (2004), a paper that found the beginning and end of the English Premier League season to be problematic for fixed odds betting. Deschamps and Gergaud (2007) provided evidence for the favorite-longshot bias, a subject of intense prior study including Dixon and Pope (2004), Ottaviani and Sorensen (2005), and later confirmed by Constantinou & Fenton (2013). A bias this paper confirms to be true, the home-away bias, was demonstrated in 14 major football leagues in Constantinou & Fenton (2013), as well as the American National Football League (NFL) in Dare and Dennis (2011). This paper contributes to the existing literature in that it employs regression to test the home bias, while Constantinou & Fenton assess forecasting with Rank Probability Score (RPS) analysis. Additionally, their study found that bookmaker accuracy had not improved between the 2006 and 2011 seasons. This paper extends the existence of the bias into the 2012-2013 season of La Liga. While it is clear from prior study that betting agencies have enduring inconsistencies, the question of whether or not a player’s absence generates a bias has yet to be addressed. This paper 9
adds to the literature in the suggestion of a “star” bias, or systemic exaggeration of a popular player’s contribution to team performance. III. Motivation & Player Choices Talent in La Liga is primarily concentrated in Football Club Barcelona (“FC Barcelona”) and Real Madrid, two teams that dominate the top spot in Spanish football. According to Senior Analyst Manuel Traquete of The Bleacher Report, “Ever since the inception of La Liga, the competition has been dominated by the two giants, who won 51 of the 80 editions” (Traquete 2011). Since the publication of that article two seasons ago, Barcelona and Madrid have continued to trade the title. The four players chosen for this study were selected evenly from both squads, as they represent the highest concentration of talent and greatest levels of media interest in La Liga. The players included in this paper share several common characteristics; they are widely believed to be major contributors to team success, and sustained injuries within the 2012-2013 season that allow for instrumental variable analysis discussed later. Table 1 lists key characteristics of the players, including details of the injuries they sustained. Lionel Messi and Cristiano Ronaldo are classified as stars in this study, and stand among the most celebrated players in the history of the sport. Both players compete in comparable offensive positions, and it is of note that the top five highest paid footballers in 2012 are forwards (Forbes). Messi and Ronaldo top that list behind English midfielder David Beckham, and are highly visible in social media and advertising endorsements. Famecount, a tool used to evaluate the popularity of celebrities and athletes based on social media visibility, ranked Ronaldo and Messi within the top three most widely-discussed footballers in the world. This ranking was established across several media platforms and takes into account fan engagement, YouTube views, and size of following (Rawlings 2011). Given their astronomical level of coverage and popular interest, Messi and Ronaldo are classified as “stars” within the data and were analyzed together. This paper hypothesizes that the market will have stronger reactions to the injuries of players that occupy the highest levels of media attention, and potentially exaggerate the effect of these players on probability of winning.
10
The other players included in this study are Carles Puyol, veteran defender of Barcelona, and Iker Casillas, goalkeeper of Madrid. Though both are highly prominent figures in Spanish football, their salaries, relative media attention, and global visibility pale in comparison to their aforementioned teammates (Forbes). This study separates the players in two tiers based on level of media concentration. Table 1: Player Characteristics & Injuries Injuries Sustained
Player
Team
Position
Status
Lionel Messi
Barcelona
Forward
Thigh, Calf, Hamstring
STAR = 1
Cristiano Ronaldo
Madrid
Forward
Thigh, Back
STAR = 1
Iker Casillas
Madrid
Goalkeeper
Hand
STAR = 0
Carles Puyol
Barcelona
Defender
Knee, Cheek
STAR = 0
Notes. Star status is determined by relative media and public attention when compared to other players in the study. Star=1 when a player is deemed to have the highest level of market concentration. There are 40 observations for each player; injuries were determined to have occurred via data provider Soccerway. The nature and projected severity was confirmed through match day reports taken from the Associated Press (AP). IV. Data The dataset used in this paper was drawn from two sources. The first is extensive coverage of match statistics externally compiled from international sports media outlets ESPN and Sporting Life. The second dataset was constructed using match-by-match participation data for selected players. A. League Data This paper focuses upon the first division in Spanish football (referred to from this point forward as “La Liga”) across the 2012-2013 season. The data was obtained from www.footballdata.co.uk and contains match-specific statistics for the 380 games played, excluding non-league play such as the UEFA Champions League. These statistics include designations of the “home”
11
and “away” teams, full-time and half-time results, goals scored, fouls committed, and match-day odds as posted by nineteen of the world’s major betting agencies. Football-Data acquired full and half time results from TBWSport and Livescore data services. More detailed match statistics were assembled from Sportinglife and ESPN Soccer, two global sport media outlets. Betting agency Bet365 Group Ltd. was chosen as the focus of this study due to its prominence and profit margins; the company boasts over two million customers based in nearly 150 countries worldwide (Euroslam). Bet365 is headquartered in the United Kingdom and reflects a global rather than local perception of La Liga play. As defined by Spann & Skiera (2008), “Bookmakers determine fixed betting odds according to their expectations of game outcome probabilities, and once they are published, fixed odds rarely change” (5). Match day odds in the dataset were collected on Friday afternoons for weekend matches and Tuesday afternoons for midweek matches. Bet365 odds are expressed as decimal odds, therefore they demonstrate what the payout would be if the bettor placed a £1 bet. A sample of Bet365’s odds for La Liga matches is included in Table 2. Table 2: Sample of Bet365 Decimal Fixed Odds for La Liga 2012-13 Matches Match
Bet365 Home Win
Bet365 Away Win
Bet365 Draw
Celta v. Malaga
2.25
3.2
3.25
Mallorca v. Espanyol
2
3.8
3.3
Sevilla v. Getafe
1.62
5.5
3.75
Barcelona v Sociedad
1.1
9
26
Notes. This table shows sample Bet365 odds for four matches in week one of La Liga 2012-13 play. Decimal odds are the preferred type in the European market and demonstrate the payout for a bet of one unit of currency. As defined by Constantinou & Fenton (2013), “The bookmakers’ profit margin, also known as ‘over-round,’ refers to the margin by which the sum of the probability odds of the total outcomes exceeds 1 (thus, making the odds unfair for the bettor)” (2). According to their study, Bet365 demonstrated the lowest profit margin of top bookmakers in the English Premier League in 2011-12 (4), casting them as the “fairest” among competitors such as Ladbrokes, Bwin, and
12
William Hill. Table 3 is taken from Constantinou & Fenton, demonstrating the variation in profit margins across betting agencies. Additionally, Constantinou & Fenton make use of the Rank Probability Score (RPS) to appraise the accuracy of bookmakers’ odds across the 2005-2012 seasons. Although the profit margins vary significantly across agencies, RPS scores do not. Bet365 is among the top three most accurate (hence lowest RPS) in the 2011-12 season (7), but it should be noted that the results are fairly consistent across the bookmakers listed in Table 3. Table 3: Constantinou & Fenton (2013) Bookmaker Profit Margins 2005
2006
2007
2008
2009
2010
2011
William Hill
12.49%
12.49%
12.37%
7.01%
7.35%
6.50%
6.70%
Bet365
7.91%
7.95%
5.98%
5.31%
5.43%
5.44%
5.46%
Bwin
10.13%
10.07%
10.06%
10.07%
8.30%
8.01%
6.42%
Gamebookers 8.11%
8.04%
7.45%
7.29%
7.75%
7.68%
7.67%
Interwetten
12.33%
11.35%
11.39%
10.21%
8.36%
10.13%
10.07%
Ladbrokes
12.27%
12.32%
12.19%
9.26%
7.48%
6.49%
6.65%
Sportingbet
8.14%
10%
10.13%
10.14%
10.12%
10.12%
7.66%
Notes. This table was taken from Constantinou & Fenton (2013). It displays the average profit margin per season in the English Premier League. Bet365 is the main focus of this study and demonstrates the lowest profit margin in the 2011-12 season. According to the authors, lower profit margin is an indication of fairness toward the bettor. Data on Bet365’s odds was provided to Football-Data by Betbrain and Betbase, independentlyoperated odds comparison services. As the data could be filtered based on when a team played home or away, odds are included and excluded in the regressions from the vantage point of the player being analyzed. For example, the Bet365 odds for home win are included when analyzing Messi or Puyol, conditional on Barcelona winning at home stadium Camp Nou. B. Player Data
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Data on each player’s participation was collected on a match-by-match basis gleaned from football data service Soccerway. For each match, the lineup was assessed to determine whether or not the player in question participated. Players were determined to be “absent” when they were sidelined or omitted from the roster. There were several instances in which the player was listed among substitutes but never entered play. These were not counted as absences, given that the market did not know ex-ante whether the player would be subbed-in. Using Soccerway’s information and press releases gathered around match day via the Associated Press, the motivation behind a player’s lack of participation was recorded and classified into two categories: injury, and non-injury. Additionally, data was collected on whether or not a player was substituted during the match, and the time at which the substitution took place. There are forty observations for each player as that is the number of matches played per team within the 2012-13 season of La Liga. Additionally, the players are coded based on “star” status—judged by media attention, performance, and global fan interest—and separated into two tiers as explained in Table 1. The number of observed injuries and absences naturally varies across players, however the four were chosen with knowledge of an extended absence from play during the 2012-13 season. V. Empirical Strategy The empirical strategy of this study takes advantage of the fact that betting odds and match outcomes are observed ex-post; this enables an evaluation of whether or not the market (in this case, Bet365) appropriately valued a player’s contribution to team performance. Additionally, we are able to observe how another major factor—playing at home versus away—contributes to the fluctuation of betting odds. This paper first tests whether a player’s lack of participation (denoted in the variable ‘absence’)—due to any number of factors, including coaching decision, injury, or penalty—is valued appropriately when setting betting odds. Conditional on observed match outcome, we would expect to see an additional, positive net effect on betting odds if the market exaggerates a certain star’s contribution to team performance when he is injured. Simply stated, if a certain player is overvalued, bettors are overpaid when the team wins without him.
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As the players are broken into two tiers—“stars” and “non-stars” for the purposes of this study— the results are permitted to vary across groups. For the latter pairing of Casillas and Puyol, we may expect to find less exaggerated consequences on the betting odds when they do not participate. The use of “participation” on its own may have empirical consequences—namely, participation affects and is affected by team performance. Top players may be benched for games in which the team expects to win easily, for example. The acquisition of penalties is an additional motivation behind absence that may also be endogenous to outcome. In order to overcome the issue of endogeneity, this paper employs injuries as natural, non-strategic variations in participation. It is possible that injuries do not generate perfect assignment. Top players are unmistakably “marked” by the opposition and often clock more minutes on the field. However, this paper will assume that the timing and gravity of the injuries are assigned randomly. The same action can generate injuries of varying severity and omit the victim from play for different periods of time, therefore providing a useful instrument to address this question. There are two criteria that must be met in order for an instrumental variable to be generated: •
The instrument is correlated with the causal variable of interest (in this case, participation);
•
It is not correlated with other determinants of dependent variable Yi (known as the “exclusion restriction”).
Injury is clearly correlated with whether or not a player participates, and given its random assignment in both timing and severity, is assumed to have no correlation with team outcomes in this study. Lastly, this paper tests whether or not playing at home is evaluated properly by the betting agency. The home bias has been discussed frequently in the literature, and we expect the coefficient to be negative if the home-field advantage is overvalued. This translates into bettors receiving smaller payouts than they should have when a team wins at home.
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VI. Regression Results Four regressions were ran on both the star and non-star groups in the study. They differ on the metric used to evaluate participation. In regression I, a binary variable “absent” demarcates whenever a player is omitted from the roster for any reason. In regression II, a binary variable “injured” is used and takes on value only when the player is omitted due to injury. Regression III employs both variables, and Regression IV is a two-stage least-squares regression instrumenting injury for absence. The “result” variable allows all regressions to be conditioned on observed outcomes, enabling effects over and above those generated by a team’s performance to be discussed as potential biases. Tables 4, 5, and 6 report the results of the following regressions for each group: (I) BETWIN365 = β0 + β1HOME + β2RESULT + β3ABSENT + β4BARCELONA + β5MADRID + ε
if STAR = {0,1}
(II) BETWIN365 = β0 + β1HOME + β2RESULT + β3INJURED + β4BARCELONA + β5MADRID + ε
if STAR = {0,1}
(III) BETWIN365 = β0 + β1HOME + β2RESULT + β3ABSENT + β4INJURED + β5BARCELONA + β6MADRID + ε
if STAR = {0,1}
(IV) BETWIN365IV = β0 + β1HOME + β2RESULT + β3(ABSENT = INJURED) + β4BARCELONA + β5MADRID + ε
if STAR = {0,1}
A. The Effect of Absence on Betting Odds We first test for the effect of a player’s absence on Bet365 odds, conditional on observed outcomes. The variable “absence” does not distinguish between injuries and other participationrelated decisions such as benching or penalization. Table 4 Column (I) displays regression results for the star player category when only the variable absent is included. The coefficient on absent is positive and statistically significant at the 1% level. Consistent with our hypothesis, Bet365 overpays bettors conditional on observed match outcome when a star is absent from the roster.
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We also find that, on average, whether a team plays home or away presents an exaggerated effect on fixed odds. The impact of playing at home on Bet365 odds is -0.317, which is statistically significant at the 1% level. As the agency has overestimated the home-field advantage, bettors are paid less than they should have been when the team wins at home. Interestingly, the results for non-star players as classified in this study tell a different story, as demonstrated in Table 5 Column (I). While the coefficient on absent is positive, it is much smaller in absolute value—0.068 versus 0.323—and statistically insignificant. Whether or not a non-star player participates in this sample is not reflected in a bias. The coefficient on home is again negative and significant at the 1% level. It is similar in magnitude for both the star and non-star regressions that include the absent variable. B. The Effect of Injury on Betting Odds In order to break down the effect of injury versus absence on Bet365 odds, we next specified a model in which injuries alone were used to estimate whether or not a bias exists. Column II of Table 4 presents the results for this regression in the star player group, again conditional on observed match results. The coefficient on injury is positive and statistically significant at the 1% level; it is similar in magnitude to the coefficient on absent in the first specification. Again, we find that the bias is in favor of the bettor, and generally payouts are higher when a star is absent due to injury. Column II of Table 5 reports the results for the same regression conducted on the non-star group. The coefficient on injury is close to zero in magnitude—smaller than the coefficient on participation in the previous specification—and statistically insignificant. Again, there is no evidence of a bias in the odds when a non-star is benched due to injury. C. Injury and Participation Regressed Together: Determining the Source of the Bias In order to better determine the source of the participation bias—whether it lies primarily in noninjury related absences, or vice versa—the next specification regresses Bet365’s odds on both participation and injury. This yields interesting results that demonstrate injuries are the primary motivation behind exaggeration in the agency’s payouts.
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For the star player group, Column III of Table 4 demonstrates the evidence for this bias. The coefficient on participation is of smaller magnitude, negative, and statistically insignificant. The coefficient on injury, however, is larger—0.565 in (III) versus 0.375 in (II)—and significant at the 1% level. This suggests that the overstatement of contribution to team performance arises specifically when the star is injured, rather than absent for other reasons. The results for non-stars are consistent with previous specifications that show neither participation nor injury present robust biases on betting odds. Column III of Table 5 shows the coefficients on absent and injury to be 0.114 and -0.077 respectively. The signs have reversed from the star model, but the results are again smaller in magnitude and statistically insignificant. D. Two-Stage Least-Squares Employing Injury as an Instrument for Participation Earlier in the paper, the issue of endogeneity was discussed in regards to whether or not a player participates in a given match. In order to overcome the bias, injuries were observed and recorded for each player across the 2012-13 season. The simplest specification of the model regresses Bet365’s odds on injuries rather than all absences. The last model specification runs Two-Stage Least-Squares (2SLS) instrumenting injury for participation. The second column in Table 6 again demonstrates systemic exaggeration of star contribution. When injury is instrumented for participation, the coefficient is 0.379 and significant at the 1% level. For bets placed on a given match when either Messi or Ronaldo is injured, bettors earn more conditional on observed results. The 2SLS results for non-stars, illustrated in the third column of Table 6, generates a coefficient on injury that is nearly zero (0.002) and statistically insignificant. Again, we find little effect on match day fixed odds when a non-star in the sample is injured. It should be noted that the home bias is confirmed throughout the models, including the 2SLS specification for both star and non-star groups. The coefficient is -0.315 and -0.332 for stars and non-stars respectively, significant at the 1% level for both. As discussed in related literature, the home bias persists in betting odds and results in payouts that are too low when a team wins at home.
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Table 4: Bet365 Odds Reaction to Star Player Injury or Absence Conditional on Observed Outcomes I
II
III
Intercept
0.005 (0.04)
0.010 (0.07)
0.213 (0.16)
Home
-0.317*** (-5.23)
-0.321*** (-5.46)
-0.324*** (-5.49)
Result Dummy 2
0.087 (1.01)
0.118 (1.41)
0.134* (1.55)
Result Dummy 3
-0.137 (-1.27)
-0.135 (-1.28)
-0.137 (-1.30)
Absent (includes injuries)
0.323*** (4.05)
Injured
-0.192 (-0.78) 0.375*** (4.65)
0.565** (2.19)
FC Barcelona
1.348*** (10.29)
1.333*** (10.50)
1.322*** (10.32)
Real Madrid
1.486 (10.94)***
1.483*** (11.26)
1.476*** (11.15)
Observations
80
80
80
R2
0.727
0.742
0.745
Notes. The above table reports three sets of regression results—including estimated coefficients, respective t-statistics denoted in parentheses below, and R2 values. The dependent variable is BetWin365’s decimal fixed odds reported for each match of the 2012-13 La Liga season. These can be interpreted as the amount (in pounds sterling) a bettor wins after placing a £1 bet. Home is a binary variable equal to 1 when a team plays at home. The Result variables take on values of 1,2, and 3 when match results are win, loss, and draw respectively. Absent is a binary variable equal to 1 when the player does not participate in a given match. Injured is a binary variable equal to 1 when the player misses a match due to injury. FC Barcelona and Real Madrid are binary variables equal to 1 when a player competes for the respective team. *Significant at 10% level; **Significant at 5% level; ***Significant at 1% level.
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Table 5: Bet365 Odds Reaction to Non-Star Player Injury or Absence Conditional on Observed Outcomes I
II
III
Intercept
0.089 (0.59)
0.112 (0.74)
0.152 (0.56)
Home
-0.331*** (-4.96)
-0.332*** (-4.92)
-0.326*** (-4.86)
Result Dummy 2
0.108 (1.14)
0.103 (1.08)
0.113 (1.18)
Result Dummy 3
-0.171* (-1.44)
-0.182* (-1.52)
-0.174* (-1.46)
Absent (includes injuries)
0.068 (1.09)
Injured
0.114 (1.40) 0.002 (0.02)
-0.077 (-0.89)
FC Barcelona
1.292*** (8.89)
1.311*** (8.94)
1.300*** (8.91)
Real Madrid
1.412*** (9.44)
1.427*** (9.49)
1.407 (9.38)***
Observations
80
80
80
R2
0.667
0.661
0.671
Notes. The above table reports three sets of regression results—including estimated coefficients, respective t-statistics denoted in parentheses below, and R2 values. The dependent variable is BetWin365’s decimal fixed odds reported for each match of the 2012-13 La Liga season. These can be interpreted as the amount (in pounds sterling) a bettor wins after placing a £1 bet. Home is a binary variable equal to 1 when a team plays at home. The Result variables take on values of 1,2, and 3 when match results are win, loss, and draw respectively. Absent is a binary variable equal to 1 when the player does not participate in a given match. Injured is a binary variable equal to 1 when the player misses a match due to injury. FC Barcelona and Real Madrid are binary variables equal to 1 when a player competes for the respective team. *Significant at 10% level; **Significant at 5% level; ***Significant at 1% level.
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Table 6: Two-Stage Least-Squares Regression Employing Injury as an Instrument for Participation, Conditional on Observed Outcomes STAR=1
STAR=0
Intercept
-0.130 (-0.09)
0.111 (0.72)
Home
-0.315*** (-5.17)
-0.332*** (-4.93)
Result Dummy 2
0.084 (0.97)
0.103 (1.08)
Result Dummy 3
-0.130 (-1.19)
-0.182 (-1.51)
Injured
0.379*** (4.50)
0.002 (0.02)
FC Barcelona
1.354*** (10.30)
1.311*** (8.85)
Real Madrid
1.497*** (10.97)
1.426*** (9.41)
Observations
80
80
R2
0.725
0.662
Notes. The above table reports 2SLS regression results—including estimated coefficients, respective tstatistics denoted in parentheses below, and R2 values. The dependent variable is BetWin365’s decimal fixed odds reported for each match of the 2012-13 La Liga season. These can be interpreted as the amount (in pounds sterling) a bettor wins after placing a £1 bet. Home is a binary variable equal to 1 when a team plays at home. The Result variables take on values of 1,2, and 3 when match results are win, loss, and draw respectively. Injured is instrumented for absence in this regression, and is a binary variable equal to 1 when the player misses a match due to injury. FC Barcelona and Real Madrid are binary variables equal to 1 when a player competes for the respective team. *Significant at 10% level; **Significant at 5% level; ***Significant at 1% level.
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VII. Conclusions & Further Research The contribution of a star player to team outcomes, particularly in the eyes of the market, is a prominent question in the literature of economics and sport. There is evidence to suggest that while betting odds are generally efficient predictors of team outcomes, they exaggerate the consequences of a star footballer’s absence from play. In order to assess this issue, we merged two datasets that allowed us to match team outcomes from the 2012-13 La Liga season with player participation data on a match-by-match basis. First, we acquired a broad league-specific dataset that included extensive information for all 380 games played, including match day odds from the world’s major betting agencies. Next, four players were selected for the study and a dataset was assembled on an individual basis. For each subject, data was recorded on whether or not the player participated in a given match, and the motivation behind that absence was gleaned from Soccerway data and confirmed through match day reports of the Associated Press. The players were broken into two groups—stars versus nonstars—on the basis of market visibility, press attention, and perceived value to team outcome. The betting agency Bet365 was chosen as the focus for the study, and its fixed match day odds served as the dependent variable in the regressions. Bet365 is a global agency with the lowest profit margins among major competitors, suggesting it is one of the fairest and most accurate bookmakers. The tests ran were conditional on observed match outcomes, which allowed for analysis of potential exaggerations in payouts. First, we used absence—whether for injury or other, potentially strategic reasons—to evaluate this hypothesis. Consistent with predictions, absence in the star group demonstrated a positive and statistically significant effect on betting odds conditional on observed outcomes; this suggests that bettors were systemically overpaid when Messi and Ronaldo did not play during the 2012-13 season. The nonstar group showed a much smaller, statistically insignificant coefficient on absence. Regressions that employed player injury rather than absence elicited similar results. One of the most interesting results of the study was presented in regressions where both absence and injury were included to determine the source of the bias. In the star group, injury proved to
22
generate the exaggeration of payouts as its coefficient was large, positive, and statistically significant at the 1% level. Conversely, the coefficient on absence was small, negative and lost its significance. The non-star group again demonstrated no evidence of a bias. Absence is a potentially contaminated variable; whether or not a player participates in a given game may affect and be affected by team performance. In order to overcome the issue of endogeneity, injury was selected as an instrumental variable based on its fulfillment of the IV identifying assumptions: it is correlated with participation, and the exclusion restriction holds. The last set of regressions—a two-stage least-squares model instrumenting injury for participation—demonstrated results consistent with the hypothesis proposed earlier in the paper. The star group showed a positive and statistically significant coefficient on injury, while the nonstar group’s coefficient was close to zero in magnitude and insignificant. This is consistent with the prediction that star footballers exaggerate payouts when omitted from the roster, whereas non-stars have little to no effect on betting odds when injured. Lastly, we confirmed that the home-away bias as discussed in Constantinou & Fenton (2013) persists in Bet365 odds. The coefficient on home was negative and statistically significant at the 1% level across all models in both groups. Further research could determine whether or not the star bias is specific to certain player positions and leagues. The empirical strategy and mode of analysis could be easily applied across other sports in which gambling data is available and prominent.
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