Sentiment bias and asset prices: evidence from sports betting markets and social media.

Feddersen, Arne ; Humphreys, Brad R. ; Soebbing, Brian P. 等

I. INTRODUCTION

A growing literature examines the effects of investor sentiment on prices in financial markets. Investor sentiment refers to behavior on the part of investors that differs systematically from the predictions of standard rational choice models. Early research on investor sentiment focused on explaining the apparent over-reaction and under-reaction of stock prices to good and bad news in financial markets (Lee, Shleifer, and Thaler 1991). Later research expanded investor sentiment to include any "nonmaximizing trading pattern among noise traders that can be attributed to a particular exogenous motivation" (Avery and Chevalier 1999, 493).

Identifying settings where investor sentiment occurs is important; several recent papers look for evidence in sports betting markets. These simple financial markets have clear payoffs at a specific point in time, and the teams involved have identifiable characteristics plausibly linked to the presence of investor sentiment. In this setting, investor sentiment can stem from the popularity and emotional attachment to certain teams that would lead bettors to wager on certain teams due to loyalty (Braun and Kvasnicka 2013; Franck, Verbeek, and Ntiesch 2011). The presence of sentiment bias can affect bookmakers' odds or point spreads. Bookmakers may adjust their odds or point spreads due to the presence of investor sentiment but cannot adjust too much because informed and unbiased bettors could take the other side when odds or point spreads reflect sentiment, reducing the bookmaker's profit.

This article develops evidence consistent with the presence of sentiment bias in prices in sports betting markets in professional leagues in Europe and North America. Our sample contains all regular season games from the "big 5" European football leagues (England, France, Germany, Italy, and Spain), the National Basketball Association (NBA), and the National Football League (NFL), over several seasons. The paper builds on the research by Braun and Kvasnicka (2013), Forrest and Simmons (2008), and Franck, Verbeek, and Ntiesch (2011) who analyzed bet outcomes and found evidence of sentiment bias in European football betting. In contrast to the sentiment bias proxy variable used in previous research, differences in attendance at home games or matches, we use a team popularity measure based on information revealed by fans on the social media platform Facebook to identify the presence of investors with sentiment bias. We employ the number of Facebook "Likes" received by each team as a proxy for the presence of fans exhibiting sentiment bias in betting markets.

As of March 2013, Facebook had over one billion active users worldwide (Associated Press 2013). Nearly all sports teams in major professional leagues have official pages on Facebook where all members of this social networking platform can click the "Like" button to signal approval of or affinity with the team. Facebook "Likes" represent a better proxy for the size of a team's fan base and the number of bettors who exhibit sentiment bias toward this team than the existing attendance-based proxies used in the literature, which are limited to fans who can travel to games or matches and constrained by stadium capacity.

This analysis of prices set in sports betting markets--betting odds in five top European professional football leagues and two major North-American professional sports leagues--reveals evidence of price-insensitive investors with sentiment bias. The larger the share of Facebook "Likes" attributable to the home team, the lower the odds or the larger the point spreads set by bookmakers for home wins on those matches, even when controlling for the relative strengths of the two teams involved and other unobservable factors. These price changes indicate investor sentiment in these markets, supporting results in the existing literature using attendance-based indicators for investor sentiment. However, previous results were consistent with the presence of price-sensitive bettors; the social media-based sentiment proxy may reflect different aspects of investor sentiment, or the composition of the pool of biased sports bettors may have changed over time.

An analysis of bet outcomes suggests that these changes in prices are not large enough to generate excess profits for bettors; the probability of a bet placed on the home team winning does not appear to be related to relative differences in Facebook "Likes." Our results suggest that the presence of investor sentiment is broader than indicated by previous research, as prices in betting markets for five top European domestic leagues and two major North American professional leagues reflect the presence of investor sentiment.

II. LITERATURE REVIEW

Sports betting markets have been identified as "simple financial markets" (Sauer 1998, 2021) containing well-defined outcomes (i.e., wins and losses) and clear ending times (playing of the game or match). Bookmakers set prices, either in the form of a point spread, common in sports where scoring is frequent, or betting odds, common in lower scoring sports. In markets with odds betting, bettors wager on match outcomes; in markets with point spread betting, bettors wager on the expected margin of victory.

Investor sentiment can be broadly defined as "any nonmaximizing trading pattern among noise traders that can be attributed to a particular exogenous motivation" (Avery and Chevalier 1999, 493). Avery and Chevalier (1999) identified unanticipated and anticipated sentiment. Unanticipated sentiment, resulting in the price of the asset shifting away from the true market value, is generally attributed to an unanticipated demand shock shifting the demand curve. Anticipated sentiment is known to all parties prior to the completion of trading. Specific conditions that can affect the demand curve for a bet on a sporting event include dynamic uncertainty, myopic pricing, irrationality of the market maker (defined in sports betting markets as book makers underestimating the power and degree that the particular sentiment has in the market), price discrimination, and composition of the market in terms of informed and uniformed bettors. Brown and Sauer (1993) outlined some fundamental factors, like investor biases, that could influence point spreads and betting odds. These fundamental factors are all potential sources of investor sentiment bias.

Sentiment due to the popularity of sports teams affects both bettors decisions and prices offered by bookmakers. Forrest and Simmons (2008, 120) defined this type of sentiment as "different returns to betting according to whether one wagers on more or less glamorous teams." Forsythe, Rietz, and Ross (1999) developed evidence that bettors in political prediction markets purchased "shares" of the candidates of the political party in which they were affiliated. Avery and Chevalier (1999) found bettors wagered more on NFL teams that received more media coverage. Humphreys, Paul, and Weinbach (2013) found that bettors in the NFL betting market have clear and predictable tendencies for betting on the best team and, thus, identified significant bettor biases that are both persistent and predictable.

Evidence that bookmakers account for bettor sentiment based on the popularity of certain club or national teams has been found in betting markets for European football (soccer). Forrest and Simmons (2008) identified bettor sentiment in their analysis of betting on Spanish and Scottish football. Using the difference in average attendance from each team's previous season as measure of sentiment, they concluded that betting odds were more favorable for the more popular team.

Based on an analysis of betting on English football matches, Franck, Verbeek, and Nuesch (2011) developed evidence supporting the findings of Forrest and Simmons (2008) in a different setting. In addition, Franck, Verbeek, and Nuesch (2011) examined the impact of weekday versus weekend matches on investor sentiment and showed that more favorable odds were offered on weekend matches, attributable to an increased number of casual bettors wagering on weekend games compared to weekday games. Braun and Kvasnicka (2013) found evidence of bias in the prices bookmakers offered for their country's national football team matches. These results support two types of bias: perception bias, due to confidence of the bettors that their home country will win, and loyalty bias, due to the loyalty of bettors to their home country.

Bookmakers must recognize various biases in order to set point spreads or betting odds exploiting them. Recent research suggests that bookmakers exploit these various biases, which can be interpreted as a form of investor sentiment. Baker and Wurgler (2006) noted that the relevant question for future research on sentiment bias is not whether sentiment has an effect on prices, but rather how to measure investor sentiment more accurately and ascertain its effects on the market. This article extends the research on sentiment bias by developing a novel measure of the presence of biased bettors based on social media data. This approach reflects the presence of investor sentiment more accurately in sports betting markets.

A. Social Media

The use of the internet and, by extension, social media web sites and services provides opportunities for researchers to study phenomena that they were not able to study in the past (Edelman 2012b). The use of the internet to gather information allowed researchers to analyze phenomena like pricing by online merchants (Brown and Goolsbee 2002; Chevalier and Goolsbee 2003), market volatility (Edelman 2012a), and search costs (Brynjolfsson, Hu, and Simester 2011). (1)

Social media also provides researchers with access to information that would be otherwise difficult to obtain. Edelman (2012b. 196) observed: The Internet's newest sen'ices also facilitate research on users' views of companies and organizations. Every company and organization page on Facebook includes a 'like' button, and Facebook. Google, and others now let sites present 'like', '+ 1', and similar buttons to garner user endorsements. The number and/or identity of users clicking these buttons is often available to researchers and the interested public-facilitating research about trends and trendsetters, reaction to news, and more.

Previous research proxied the popularity of teams with attendance (Feddersen, Humphreys, and Soebbing 2016; Forrest and Simmons 2008; Franck, Verbeek, and Nuesch 2011). This measure may not fully reflect popularity. For example, a U.S. resident may be a fan of the Arsenal Football Club but never attend a match and, thus, would not be reflected in an attendance-based measure of team popularity. The use of social media, such as Facebook and Twitter, to proxy for popularity mitigates the effect of proximity to match locations inherent in attendance-based measures.

We use Facebook "Likes" to measure bettor sentiment. As reported in March 2013, Facebook had 1.11 billion users around the world (Associated Press 2013). On the Facebook website, a user can "Like" a particular event or business. According to the Facebook help page, "When you click 'Like' on a Facebook Page, in an advertisement, or on content off of Facebook, you are making a connection." (2) This connection extends to businesses. According to Wallace, Wilson, and Miloch (2011), Facebook launched a Page feature, allowing businesses and other organizations to communicate with Facebook users. In addition to launching the Page feature, the company also allowed Facebook users to connect with businesses through the "Like" feature. This "Like" feature on Facebook is what we use to examine sentiment bias in the betting market of sports leagues in both North America and Europe. Since this feature is free for Facebook users to not only participate by "liking" a particular organization or business but also remove their "liking" of a particular organization or business at any time. Facebook "Likes" seems to be an appropriate proxy for the size of a team's fan base and the number of bettors who might exhibit sentiment bias toward the team.

III. EMPIRICAL ANALYSIS

A. Empirical Strategy

One key element in the analysis of sentiment bias in betting markets is to identify observable factors likely to be associated with the presence of investor sentiment. Identifying an appropriate observable proxy variable for the presence of investors with sentiment bias can be difficult. In previous research, various proxy variables have been used. Avery and Chevalier (1999), for example, used expert opinions, performance in the previous year, and conference affiliation as proxy variables for the presence of bettors with sentiment bias in NFL betting markets. Forrest and Simmons (2008) used the difference in mean home attendance in the previous season between the two teams participating in a given football match in the Spanish and Scottish top divisions. Braun and Kvasnicka (2013) analyzed data from domestic book makers' odds on games played by the national team. Feddersen. Humphreys, and Soebbing (2016) used the difference in the percent of seating capacity tilled in the two teams' home arenas in the previous season in the NBA and the share of All Star Game votes received by each team.

These proxies can be criticized in two ways. First, attendance-based measures of the presence of sentiment bias might only be a local measure of the popularity. If these proxies only capture local popularity, they might strongly depend on the market potential of the surrounding region, while biased bettors might exist nation--or worldwide. Furthermore, attendance and capacity utilization can be influenced by the team through, for example, reducing ticket prices or intensifying promotional activities. Based on this critique, Feddersen, Humphreys, and Soebbing (2016) identified two criteria for a measure of popularity as a proxy for the presence of bettors with sentiment bias, which might be better suited than attendance-based measures. The proxy variables should be (a) not only a local measure and (b) not under direct control of the teams. Data from social media (e.g., Facebook "Likes" or Twitter followers) represent an obvious measure of team popularity.

This article looks for evidence of sentiment bias in both the prices set by bookmakers, and in betting market outcomes. Previous research focused either on analyzing bet outcomes (Forrest and Simmons 2008; Franck, Verbeek, and Ntiesch 2011) or analyzing changes in points spreads or betting odds (Avery and Chevalier 1999; Braun and Kvasnicka 2013) in the presence of bettors with sentiment bias; these wagers depend on game or match outcomes. (3) We estimate reduced form models of the determination of bookmaker home and away win probabilities implied by betting odds and point spreads in seven sports leagues in Europe and North America. Furthermore, reduced form models of the outcomes of bets, based on a dichotomous-dependent variable that is equal to one if a bet on that team won, are estimated using a probit model. Both empirical models include variables that proxy for the presence of bettors with sentiment bias in the market. The sign of the estimated parameters on these variables will be statistically significant if bettors with sentiment bias bet on these games, or if bookmakers believe such bettors are present.

In order to determine how the popularity of teams affects prices set by bookmakers, we estimate the following reduced form model of the determination of betting lines or odds using the ordinary least squares (OLS) estimator:

(1)

[P.sub.hvik] = [[beta].sub.0] + [[beta].sub.1] [Winpct.sub.hik] + [[beta].sub.2] [Winpct.sub.vik] + [[beta].sub.3] [Popular.sub.hvk] + [[theta].sub.j] + [[alpha].sub.j,k] + [[gamma].sub.k] + [[epsilon].sub.hvik].

In Equation (1), li indexes home teams, v indexes visiting teams, i indexes games, and k indexes seasons. [[theta].sub.j] are team-specific effects, [[gamma].sub.k]k is a season fixed effect, [[alpha].sub.j,k] is a team x season fixed effect for home teams and visiting teams, and [[epsilon].sub.hvik] is the equation error term. The regression model controls for unobservable heterogeneity in teams over the sample, seasons in the sample, and unobservable team-season heterogeneity. We assume that [[epsilon].sub.hvit] is a mean zero, constant variance, identically and independently distributed random variable: the variance of this variable is assumed to be heteroscedastic.

P, the dependent variable in Equation (1), is the price of a bet on game i played by home team h and visiting team v in season k. For the two North American leagues, the price is the published closing point spread. For the five European football leagues, P is the bookmaker home win probability implied by the published final fixed decimal odds. Forrest and Simmons (2008) showed that the implied bookmaker probability can be derived from decimal odds as follows. Let [d.sub.H], [d.sub.D], and [d.sub.L] be the decimal odds for a home win, a draw, or a home loss, respectively. The bookmaker probability for a home win is:

(2) bookprob = (1/[d.sub.H]) / (1/[d.sub.H] + 1 /[d.sub.D] + \/[d.sub.L]).

In Equation (1), [Winpct.sub.hik] is home team h's winning percentage prior to game i in season k, while [Winpct.sub.vik] is visiting team v's winning percentage prior to this game. Finally, Popular is the variable of interest, a proxy for the presence of bettors with sentiment bias. The popularity of teams and the existence of bettors with sentiment bias should be reflected in data from social media and, in particular, by the difference in Facebook "Likes" for each team. Because the number of members, the general usage, and the utilization as a marketing tool by professional sport teams of the social media platform Facebook is still growing, we use the relative difference in Likes instead of the absolute difference. The share of the Facebook "Likes" for each team relative to the league average at the beginning of season k is calculated for each team. To capture the relative difference in popularity of the two teams competing in game i in season k, the variable Popular is defined as the difference in these shares of the Facebook "Likes." As this difference in Facebook "Likes" increases, we hypothesize that more bettors with sentiment bias toward the team with the larger number of Facebook "Likes"' exist in the betting market. As a robustness check, we correct the share of Facebook "Likes" for previous team success using a regression approach: all results are robust to this change.

B. Data

The data analyzed come from matches played in both European and North American team sports leagues, augmented by betting market data and information from social media. The data set for the European leagues includes every regular season game played in the domestic football leagues in England, France, Germany, Italy, and Spain over two seasons (2011-2012 and 2012-2013). Both match data and fixed decimal betting odds were gathered from http://www.football-data.co.uk. We limit our analysis odds set by the bookmaker (bet365) because odds from this bookmaker are available for all games in the European leagues in our sample. Bet365 is a UK-based bookmaker that offers on-line sports betting and casino games. Bet365, founded in 2000, reponed 2014 revenues of 1.4 billion pounds sterling from more than 14 million customers in over 200 countries.

The North-American data set contains data on regular season games for two seasons from the NBA (2011-2012 and 2012-2013) and one season from the NFL (2012-2013). Game data for these North American leagues were collected from Sports Reference. Point spreads were collected from Goldsheet. Finally, the Facebook "'Likes" popularity proxy were collected from the clubs' official Facebook pages on the same day at the beginning of each regular season, before play started, for all seven leagues in the sample.

Overall, there were 6,127 games played in the seven leagues. The most games in the sample occurred in the NBA (2,219). Four of the European football leagues contain 20 teams (England, France, Italy, and Spain). Seven hundred and sixty matches were played in these leagues; 612 games were played in the German "Bundesliga," which contains 18 teams. Two hundred and fifty-six NFL games are included into the data set because information on the number of Facebook "Likes" was only collected for a single NFL season, 2012-2013.

Table 1 contains summary statistics for each of the seven leagues. Both the mean home and away team winning percentage prior to playing the observed game was around 0.500. The average bookmaker probability for a home win ranges between 44.9% for France's Ligue 1 and 46.8% for Spain's La Liga. Table 1 contains also the absolute difference of the share of Facebook "Like." The mean of this difference is quite similar in all five European football leagues lying between 8.0% (France) and 9.4% (Spain). The minimum is around zero for all leagues, while the maximum ranges from 41.8% for the French league and 59.6% for the Italian league. In the North American leagues, the average point spread was -3.194 in the NBA and -2.428 in the NFL. meaning that the home team was just over a three point favorite to win the games in the NBA and about a 2.5 point favorite in the NFL, respectively. Furthermore, the home team covered 49.5% of the time and 1.7% of the NBA games in the sample were a push. In the NFL, approximately 46.1% of the games were covered by the home team, while only 0.8% of the games were a push. Compared to the European football leagues, the maximum values of the absolute difference in Facebook "Likes" share are lower for the NBA with 27.4% and remarkably lower for the NFL with only 9.6%. Also the standard deviation of this measure is lower for the North American leagues with 2.4% and 6.9% compared to the European leagues ranging from 11.8% to 19.2%. This might lead to the assumption that the distribution of team popularity is more skewed to the most popular teams in the European football leagues compared to the NBA and NFL.

C. Analysis of Wagering Prices

Table 2 contains estimated coefficients and robust standard errors for the OLS estimator applied to Equation (1) using data from each of the top five European domestic football leagues. The estimates of the fixed effects parameters included in Equation (1) are suppressed for simplicity, but they are available upon request from the authors. The number of observations is lower than the overall number of games played in the league since no winning percentage prior to the game can be observed for each team's first game of the season.

Equation (1) explains between 55% and 76% of the observed variation in the implied bookmaker probabilities. All estimated coefficients are significantly different from zero at the 1% level and the estimated signs are the same across all leagues. The estimated parameters for the home team's winning percentage prior to the game indicate that an increase in home team strength increases the implied home win probability (decreases the bookmaker odds on a home team win) for each match. Furthermore, as expected, the stronger the away team--measured by its winning percentage prior to the game--the lower is the implied bookmaker probability for a home win, other things equal.

Our variable of interest is Popular, the difference in the share of Facebook "Likes" for a given team relative to the league total at the beginning of each regular season. For example, if in the 2011-2012 season Manchester United had 42% of all Facebook "Likes" in the English Premier League and Arsenal accounted for 17%, then Popular is equal to 25 for a match at Old Trafford between Man U and Arsenal; if Arsenal are the home team in this match. Popular would be equal to--25.

From Table 2, in the case of the English Premier League, for every one percentage point increase in the difference in Facebook "Likes" in favor of the home team, the bookmaker probability of a home win increased by 0.6 percentage points, implying that the odds on a home team win decreased. Results from matches in other European leagues show a similar pattern. Bookmakers adjust the betting odds based on the relative popularity of the teams competing in a given match when popularity is measured by the difference in fans' attachments expressed on Facebook, holding constant the quality of the teams playing in the match. This result can be interpreted as evidence that investor sentiment is present in the big five European football leagues and that bookmakers adjust the odds on matches to account for this.

Forrest and Simmons (2008) reported evidence consistent with bookmakers increasing the odds on wagers on home team wins for popular teams in Spanish and Scottish football; Franck, Verbeek, and Nuesch (2011) reported similar results for English football. The results in Table 2 suggest bookmakers offer less favorable odds on bets on more popular teams to win at home; the implied home win probability increases for more popular teams, which is consistent with lower bookmaker odds on a home win. One reason for the different results is that our data come from the 2011 and 2012 seasons, 5 years later than the data analyzed by Franck, Verbeek, and Niiesch (2011) and 8 years later than the data analyzed by Forrest and Simmons (2008); either bookmaker behavior or the composition of the pool of bettors on football matches changed in the intervening period. The model of bookmaker behavior developed by Franck. Verbeek, and Nuesch (2011) predicts that bookmakers could increase or decrease prices offered to bettors with sentiment bias, depending on how sensitive these bettors are to price changes; in the presence of large numbers of price insensitive bettors with sentiment bias, bookmakers increase the price. The number of price insensitive bettors in this market could have increased over time, or the alternative popularity measure used here may better reflect the presence of price insensitive bettors with sentiment bias than previously used attendance-based proxy variables.

Table 3 contains OLS regression results for Equation (1) using data from two major North American leagues. All parameter estimates are significant at conventional levels. Since the point spread reflects the perspective of the home team, decreases in the point spread mean that the home team is a bigger favorite (the point spread moving from home team -7 to home team -9 means the home team is stronger) or a smaller underdog (the point spread moving from home team +3 to home team +1 means the home team is stronger). The estimated coefficient on the home team's winning percentage prior to the game suggests that an increasing home team winning percentage decreases the point spread. The positive and significant sign on the variable isolating the effect of the away team's winning percentage prior to the game indicates that the home team becomes a smaller favorite (bigger underdog) the stronger the away team is.

The estimated coefficients on the popularity variable are negative in both leagues, indicating that, for every one percentage point increase in the difference in the share of Facebook "Likes," the point spread favors the home team by additional 0.1 points in betting on NBA games and 0.6 points in betting on NFL games. Again, the results show evidence that bookmakers adjust point spreads based upon the relative popularity of the two competing teams. Bettors with sentiment bias appear to exist in betting markets for NBA and NFL games. Like in football betting in Europe. U.S. bookmakers offer higher prices--a favored home team is a stronger favorite, and must win by more points for a bet on that team to win--to bettors with sentiment bias. Again, in the context of the model developed by Franck, Verbeek, and Nuesch (2011), this suggests the presence of price-insensitive bettors with sentiment in this market, or that the Facebook "Likes" proxy reflects the presence of such bettors.

D. Analysis of Bet Outcomes

The results in the previous section suggest that prices set in sports betting markets (bookmaker probability based on decimal betting odds for European leagues and point spreads for North American leagues) reflect both the relative strength of the teams in the game as well as the popularity of the teams, measured by the difference in the shares of Facebook "Likes" of the two teams. To determine how the changes in prices identified in the previous section influences the likelihood of a bettor winning a bet placed on team i, the following regression model is estimated:

(3) [hwin.sub.hvik] = f ([bookprob.sub.hik], [Popular.sub.hvk])

where h indexes home teams, v indexes visiting teams, i indexes games, and k indexes seasons. The dependent variable is an indicator variable equal to one if the home team won match j in season k. [bookprob.sub.hik] is the probability of a home win based on the bookmaker odds on the match. We estimate this model using OLS, commonly called the linear probability model (LPM). We correct the standard errors for heteroscedasticity and checked to make sure that no predicted values fell outside the 0-1 interval. According to Forrest and Simmons (2008), the hypothesis of efficiency stipulates the odds quoted by the bookmaker should reflect all available information relevant to the outcome of the game (i.e., relative strength of the teams, which team is playing at home). The coefficients on the variable Popular should, therefore, be zero.

The parameters of Equation (3) could alternatively be estimated using the probit estimator. While the cumulative distribution function (CDF) of the LPM and probit function are equivalent for probabilities around 0.5, they differ in the tails. The CDF for the LPM is a linear function of probabilities, while the probit function increases at a decreasing rate as probabilities near 1.0. The former may represent a better approximation for betting odds as match outcomes approach certainty. Additionally, although the probit model might fit the conditional expectation function more closely than the LPM, this matters little with respect to marginal effects (Angrist and Pischke 2008, 107) in which we are interested. Estimating the parameters of Equation (3) with the probit estimator generates similar results to those in Table 4.

Table 4 contains the results from the LPM estimator for the European football leagues. Results in Table 4 indicate the bookmaker odds appear to contain all relevant information about the outcome of football matches in these leagues. The difference in popularity, in terms of the difference in number of Facebook "Likes" does not explain bet outcomes.

Bets on NFL and NBA games use point spreads, which requires a different approach than the one used for fixed odds betting common in Europe. For the NFL and NBA we estimate the regression model:

(4) [Coverh.sub.vik] = f ([Winpct.sub.hik], [Winpct.sub.vik], [Popular.sub.hvk])

where, again, h indexes home teams, v indexes visiting teams, i indexes games, and k indexes seasons. The dependent variable Cover is an indicator variable equal to one if a bet on the home team j in season k won. We estimate Equation (4) using the LPM correcting for heteroscedasticity and predicted values outside the 0- 1 interval. Table 5 does not reveal any significant parameter estimates for the two North American major leagues. Thus, even though the OLS regressions for these leagues showed evidence that bookmakers adjust the point spreads based upon the existence of bettors with sentiment bias in these two betting markets, the probit results indicate that this bias does not have an influence on the probability of a wager winning. The betting market for these two North American sports appears to be efficient in this sample. Sauer (1998) discussed other evidence consistent with this result.

E. Robustness Checks

One possible concern with the variable Popular is that the number of Facebook "Likes" used to construct this variable is related to the on-field success of teams. Recent research by Perez (2013) found higher rates of new Twitter followers related to increases in on-field success of Spanish football clubs. As a result, there is a concern that Popular may be correlated with the equation error term, [[epsilon].sub.hvik]. To address this issue, an OLS regression model is estimated for each team (i) in each season (s) where the dependent variable is Facebook "Likes" for the team and the explanatory variable is the record or number of points for the team in the previous season

[Likes.sub.is] = [alpha] + [beta][succes.sub.is-1] + [[epsilon].sub.is].

The residual from this OLS model reflects the number of Facebook "Likes" not explained by the on-field success of the football club. The residual "Likes" were used to calculate an alternative popularity measure. Franck and Nuesch (2012) used this approach to account for past success on a popularity measure based on press coverage of German football players. For each league, Equations (1) and (3) are estimated with the variable Popular equaling the difference in the residual "Likes" for each team in the observed game. The results are consistent with the results reported in the tables above for the seven professional leagues in both Europe and North America. (4)

IV. CONCLUSIONS

Previous research found evidence of sentiment bias sports betting markets for the English Premier League (Franck, Verbeek, and Nuesch 2011), Spanish "Primera Division" and Scottish Premier League matches (Forrest and Simmons 2008) in Europe, and NBA games (Feddersen, Humphreys, and Soebbing 2016) in North America. These papers assumed the existence of investor sentiment in betting markets is reflected in differences in attendance or capacity utilization at home games. Feddersen, Humphreys, and Soebbing (2016) identified several limitations of attendance-based proxies and use data on all star game voting to construct an alternative proxy for team popularity in the absence of availability of the according social media data. This article uses information on Facebook "Likes" collected for teams participating in European football leagues and North American major leagues over several seasons. Our analysis is among the first to use social media data, a broader measure of team popularity that avoids many of the problems associated with using attendance data, to capture the presence of investor sentiment.

Based on results from OLS and LPM regression models of the determination of prices and bet outcomes, we develop evidence suggesting the popularity of teams, based on the number of Facebook "Likes," influenced prices set by bookmakers. The results indicate bookmakers adjust prices in proportion to the number of bettors with sentiment bias, and that bettors with sentiment bias are offered less favorable odds or point spreads. In terms of the model of bookmaker behavior developed by Franck, Verbeek, and Niiesch (2011), this implies that the sentiment biased bettors in these markets are price insensitive. The bet outcome analysis suggests that this adjustment in prices cannot be exploited by bettors since sentiment-related price adjustment increases generates small increases in the probability of winning a bet. These results are robust to controlling for the effect of teams' on-field success on social media followers and Facebook "Likes."

For example, the results in Table 3 suggest that in an NFL game between a popular team, one with substantially more Facebook "Likes" than its opponent, the more popular team would be favored by about 0.5 points more than it would be in a game involving another team with the same number of Facebook "Likes." The results in Table 4 indicate that bets on popular teams are not more likely to win than bets on unpopular teams. So the half point change in the point spread does not represent an inefficiency that increases winnings for bettors with sentiment bias; the prices affected by sentiment bias are still efficient.

These results support the predictions of the model developed by Franck. Verbeek, and Niiesch (2011) and raise interesting questions about the operation of bookmakers. The fact that bookmakers reduce the odds on bets on home team wins to bettors with sentiment bias implies an increase in bookmaker profits. An increase in bookmaker profits would be the case if offering more favorable prices leads more fans of these teams to participate in betting, thus generating imbalanced betting on popular teams (Feddersen, Humphreys, and Soebbing 2016). Paul and Weinbach (2008) reported evidence of unbalanced betting on NBA games while Humphreys (2010) showed unbalanced betting on NFL games led to higher bookmaker profits than balanced betting. Although a bet placed on a team associated with sentiment bias is not more likely to win, betting volumes, and thus bookmaker profits, could be affected by sentiment bias. A full assessment of the effect of this "shading" of lines and betting odds on bookmaker profits requires data on bet volume, but we currently lack access to available data. Flepp, Niiesch, and Franck (2016) analyzed sentiment bias and betting volume data on over/under betting in football, but little research has analyzed betting volume on game or match outcomes. Further research should also focus on betting volumes and not just betting odds or point spreads to better understand the effects of sentiment bias in betting markets. ABBREVIATIONS CDF: Cumulative Distribution Function LPM: Linear Probability Model NBA: National Basketball Association NFL: National Football League OLS: Ordinary Least Squares

doi: 10.1111/ecin.12404

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SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

Appendix S1. Detailed robustness results

Feddersen: Associate Professor, Department of Environmental and Business Economics, University of Southern Denmark, Esbjerg, Denmark. Phone 45-6550-1597. Fax 456550-1091, E-mail af@sam.sdu.dk

Humphreys: Professor, College of Business & Economics, West Virginia University, Morgantown. WV 265066025. Phone 304-293-4092, Fax 304-293-2233, E-mail brhumphreys@mail.wvu.edu

Soebbing: Assistant Professor, School of Tourism and Hospitality Management. Temple University, Philadelphia, PA 19122. Phone 780-492-7308, Fax 780-492-2222, E-mail brian.soebbing@temple.edu

(1.) See Edelman (2012b) for additional information on the use of data from social media in economic research.

(2.) Retrieved from: http://www.facebook.com/help/ 131263873618748/?q=Like&sid=OPOJmFTevPsrjBwzO.

(3.) Flepp, Ntiesch, and Franck (2016) analyzed bet volume on bets on the number of goals scored in football matches, but not bets on match outcomes.

(4.) Results of these regressions can be found in Appendix S1. Supporting Information. TABLE 1 Summary Statistics Mean SD Min Max England (N = 760) Home team wpct 0.498 0.184 0.000 1.000 Away team wpct 0.478 0.195 0.000 1.000 Prob home win 0.456 0.185 0.079 0.844 Prob away win 0.293 0.163 0.037 0.776 Ab. val. Popular 8.411 11.842 0.000 42.140 Spain (N = 760) Home team wpct 0.506 0.189 0.000 1.000 Away team wpct 0.508 0.197 0.000 1.000 Prob home win 0.468 0.185 0.041 0.900 Prob away win 0.285 0.170 0.028 0.855 Ab. val. Popular 9.407 19.150 0.000 51.652 France (N = 760) Home team wpct 0.493 0.178 0.000 1.000 Away team wpct 0.502 0.170 0.000 1.000 Prob home win 0.449 0.139 0.124 0.825 Prob away win 0.271 0.117 0.050 0.652 Ab. val. Popular 8.044 12.307 0.000 41.800 Germany (N = 612) Home team wpct 0.502 0.199 0.000 1.000 Away team wpct 0.486 0.197 0.000 1.000 Prob home win 0.451 0.162 0.063 0.856 Prob away win 0.296 0.146 0.045 0.781 Ab. val. Popular 8.197 14.571 0.008 53.479 Italy (N = 760) Home team wpct 0.499 0.180 0.000 1.000 Away team wpct 0.516 0.190 0.000 1.000 Prob home win 0.452 0.156 0.063 0.821 Prob away win 0.278 0.137 0.055 0.803 Ab. val. Popular 9.010 16.863 0.001 59.572 NBA (N = 2,219) Home team wpct 0.499 0.186 0.000 1.000 Away team wpct 0.501 0.187 0.000 1.000 Point spread -3.194 6.126 -17.500 15.000 Ab. val. Popular 4.625 6.880 0.000 27.426 NFL (N = 256) Home team wpct 0.485 0.251 0.000 1.000 Away team wpct 0.517 0.249 0.000 1.000 Point spread -2.428 6.151 -18.000 15.500 Ab. val. Popular 2.765 2.451 0.004 9.555 TABLE 2 OLS Regression Results--European Leagues ENG ESP FRA Home team wpct 0.3329 *** 0.1701 *** 0.2737 *** (0.0437) (0.0359) (0.0340) Away team wpct -0.3164 *** -0.2546 *** -0.1614 *** (0.0420) (0.0398) (0.0338) Popular 0.0061 *** 0.0055 *** 0.0050 *** (0.0004) (0.0002) (0.0003) Observations 717 718 725 [R.sup.2] 0.686 0.759 0.526 GER ITA Home team wpct 0.2392 *** 0.2573 *** (0.0287) (0.0419) Away team wpct -0.1493 *** -0.3447 *** (0.0306) (0.0398) Popular 0.0059 *** 0.0029 *** (0.0002) (0.0002) Observations 577 720 [R.sup.2] 0.689 0.547 Notes: Table contains OLS results explaining observed variation in prices offered by bookmakers to bettors. The dependent variable is the implied home win probability from the bookmaker odds. Robust standard errors shown in parentheses. * p <.05, ** p <.01, *** p <.001. TABLE 3 OLS Regressions Results--U.S. Major Leagues NBA NFL Home team wpct -1.737 *** -0.938 *** (1.048) (1.962) Away team wpct 1.848 *** 1.057 *** (1.035) (1.732) Popular -0.115 *** -0.606 *** (0.010) (0.088) Observations 2,181 240 [R.sup.2] 0.661 0.541 Notes: Table contains OLS results explaining observed variation in prices offered by bookmakers to bettors. The dependent variable is the point spread on each game. Robust standard errors shown in parentheses. * p<.05, ** p<.01, *** p<.001. TABLE 4 LPM Regression Results--European Leagues ENG ESP FRA Prob home win 1.0514 *** 0.8970 *** 1.0282 *** (0.1195) (0.1610) (0.1536) Popular 0.0003 0.0018 -0.0005 (0.0015) (0.0013) (0.0015) Observations 760 760 760 [R.sup.2] 0.158 0.158 0.077 GER ITA Prob home win 0.9720 *** 0.9445 *** (0.1780) (0.1347) Popular 0.0013 0.0010 (0.0015) (0.0010) Observations 612 760 [R.sup.2] 0.124 0.102 Notes: Table contains OLS results explaining observed variation in bet outcomes. The dependent variable is an indicator variable equal to one of a bet on the home team to win the match was successful. None of the predicted values from the regression model fell outside the (0,1) interval. Robust standard errors shown in parentheses. * p<.05, ** p<.01, *** p<.001. TABLE 5 LPM Results--U.S. Major Leagues NBA NFL Home team wpct -0.0607 -0.1121 (0.0587) (0.1285) Away team wpct -0.0569 0.1179 (0.0586) (0.1303) Popular 0.0011 -0.0073 (0.0013) (0.0086) Observations 2,181 240 [R.sup.2] 0.001 0.011 Notes: Table contains OLS results explaining observed variation in bet outcomes. The dependent variable is an indicator variable equal to one of a bet on the home team to win the match was successful. None of the predicted values from the regression model fell outside the (0.1) interval. Robust standard errors shown in parentheses. * p <.05, ** p <.01, *** p <.001.