Against All Odds? National Sentiment and Wagering on European Football

Transcription

1 Against All Odds? National Sentiment and Wagering on European Football Sebastian Braun Humboldt University Berlin Michael Kvasnicka RWI Essen February 7, 2008 Abstract National sentiment may be of non-negligible importance for individual consumption and investment decisions. Little empirical research, however, has been done to substantiate such conjectures. This paper contributes to this insufficiently researched area by studying pricing patterns on national wagering markets for international football games. Based on a unique data set of betting quotas from online bookmakers in twelve European countries for qualification games to the UEFA Championship 2008, we analyze differences in odds for win offered across countries for evidence of systematic biases in the pricing of own national teams. For several countries in our sample, we find evidence for such biases. Variations in the sign and magnitude of these deviations are shown to be explainable by differences across countries in the respective strengths of two distinct, yet potentially complimentary pathways through which national sentiment may influence wagering behavior, a perception and a loyalty bias of bettors. Keywords: Football, Home Bias, Investment, Patriotism. JEL Classification: L20, L83. This paper has benefited from comments by Ronald Bachmann, Martin Spieß, Thorsten Vogel, and participants of a research seminar at RWI Essen. All remaining errors are our own. Contact author: Michael Kvasnicka, Rheinisch-Westfälisches Institut für Wirtschaftsforschung e.v. (RWI Essen), Berlin Office, Hessische Straße 10, Berlin, Germany. 1

2 1 Introduction Consumer preferences for home country products, buy domestic campaigns, the issuing and success of war bonds, or the home equity puzzle in international financial markets suggest that home country bias may be of non-negligible importance for individual consumption and investment choices. Little empirical research, however, has been done to substantiate such conjectures. 1 This paper contributes to this insufficiently researched area in economics by studying the international football betting market, a market that is especially likely to be influenced by national sentiment. Based on a unique data set of betting quotas from online bookmakers in twelve European countries for qualification games to the UEFA Championship 2008, we analyze differences in odds for win offered across countries for evidence of systematic biases in the pricing of domestic teams. Among the extensive and growing body of literature on sports wagering, our study is the first, to the best of our knowledge, that explores betting markets across countries. 2 The online betting market in international football exhibits a number of features that make it particularly suited for analyzing the influence of national sentiment on economic behavior. First, as already noted, there appears to be a strong bonding of patriotism and sports, especially in football, the most popular sport in Europe. Second, information on the quality of national teams and odds marketed (prices offered by bookmakers) should be largely symmetric across countries, as detailed information, including statistics on past performances and expert analyzes, can be obtained online easily, quickly and at zero cost. Given our focus on online wagering, access of bettors to this source of information is furthermore warranted. Third, there is a single homogeneous good traded on this market ( outcome of a game ). Variations in prices across countries therefore cannot be caused by (potentially unobservable) differences in the respective products traded. Finally, online betting markets in Europe still appear segmented between countries, as legal constraints, language barriers, and transactions costs impede wagering abroad. 3 Segmentation of national betting markets (pools of bettors) is important for our empirical analysis. With a homogeneous product and symmetric information, prices (quotas) should be identical across countries if markets are unified. With segmented markets, however, prices may differ. They will differ in terms of the average payout per monetary unit waged, if different industry structures across countries support different markups charged by bookmakers. They will also differ in terms of relative quotas for particular outcomes of a game, if bookmakers can profitably exploit either a perception bias among bettors regarding the winning chances of their national team, or a loyalty bias 1 See, for example, Shankarmahesh (2006) for evidence on consumer ethnocentrism, or Morse and Shive (2006) on the importance of patriotism for the portfolio choices of domestic investors. 2 For a comprehensive survey of the economics literature on sports wagering markets, see Sauer (1998). 3 In a perfect unified market, competitive pressures should eliminate excess profits of bookmakers. For our sample of European countries, however, we show in Section 3 that the fixed markups charged by online bookmakers in different countries vary considerably. 2

3 that keeps bettors from wagering against their own team even under favorable odds. 4 Both type of biases reflect bettor sentiment. Empirical support for their influence on betting market outcomes has been found for various club sports at national level. 5 In theoretical models of the wagering market, however, only the misperception bias has yet been formally modeled and analyzed. This paper develops a model of wagering markets that allows for both types of biases and provides first empirical evidence on their influence on betting odds for international sport events in a crosscountry context. For several countries in our sample, we find evidence for systematic biases in the odds for win of domestic teams. Variations in the sign and magnitude of these deviations can be explained by differences in the respective strengths between countries of the perception and the loyalty bias among bettors. Overall, our empirical results provide strong evidence for a non-negligible influence of national sentiment on wagering market outcomes in Europe. The paper is structured as follows. Section 2 develops a simple theoretical model to show that it is in the interest of a profit-maximizing bookmaker faced with bettors exhibiting either a perception or a loyalty bias to shade the odds for win of the home team in a way that is informative about underlying bettor preferences. Section 3 describes the data, Section 4 presents and discusses the empirical results, and Section 5 concludes. 2 Theoretical Considerations In this section, we analyze theoretically the effects of national sentiment on quotas set by a profitmaximizing (risk-neutral) bookmaker. National sentiment is assumed to express itself in one of two ways. First, it may bias the perception of bettors regarding the winning probability of their national team (perception bias). Over-confidence in the home team is shown to unambiguously decrease the quota for its win. This result is in line with Kuypers (2000) who shows that a bookmaker is able to take advantage of committed supporters by offering them a lower payout. Second, national sentiment may induce individuals to wager - if at all - only on win for their home team (loyalty bias), an idea suggested but not formalized by Forrest and Simmons (2008). Quotas set by bookmakers will again be influenced. The direction in which odds offered are shaded by bookmakers is shown to depend on the demand elasticity of supporters. If the latter is high relative to the expected increase in the profit per unit bet, odds will be shaded in favor of rather than against committed bettors. bias, favorable odds may only result from the loyalty bias. Whereas unfavorable odds may hence potentially arise from either 4 Note that these two biases are distinct from the favorite-longshot and home field biases, which have attracted much attention in the empirical literature on sports wagering. The favorite-longshot bias refers to a tendency of bettors to overbet favorites and underbet longshots. 5 On the perception bias, see for example, the study by Levitt (2004) which explores wagering behavior on NFL games in the US. Evidence for the loyalty bias is provided by Forrest and Simmons (2008) who analyze wagering on top tier Spanish and Scottish football. 3

4 For a formal treatment and analysis of these effects, consider a football match between countries A and B and assume, for simplicity, that there are only two potential outcomes, either country A or country B wins. 6 Wagering markets are assumed to be separated between countries and served each by a single bookmaker. Bettors in both countries may hence place bets only with their respective domestic bookmaker. Information on the quality of national teams is furthermore assumed to be freely available and symmetric across countries, bookmakers, and bettors. In the absence of any national sentiment bias, quotas marketed in countries A and B would hence be identical. Given this setup, we can restrict the analysis, without loss of generality, to the pricing behavior of a bookmaker in one of the countries, say country A. The respective bookmaker in country A places probabilities a and 1 a (with 0 a 1) on the outcomes win and loss of the own national team. These probabilities translate into the corresponding so-called straight-up odds, 1 ρa 1 and ρ(1 a), where ρ > 1 represents some fixed mark-up.7 Straight-up odds are quoted based on the payout for a single bet unit. Note that the probabilities underlying the offered odds may or may not coincide with the true (subjective) probabilities of the bookmaker, which are denoted by â and 1 â, respectively. We first turn to the analysis of the perception bias. 2.1 Perception Bias In line with Kuypers (2000) and Levitt (2004), we first assume that the decision of bettors to enter the market has already been made and concentrate on how punters spread the total volume of bets on the two outcomes. 8 Let f represent the fraction of punters betting on country A and assume that the stakes in the wager are identical across bettors. The fraction increases with the ( ) 1 odds on offer and with some exogenous over-confidence parameter g [0, 1], i.e. f ρa, g with ( ) ( ) 1 f 1 ( ) > 0, f 2 ( ) > 0 and f ρa, g 1 > f ρa, 0 for g > 0. Bettors compare the probability implied by the quotas with their own subjective outcome probabilities. As the bookmaker increases the odds for win of country A, more and more bettors consider a bet on this outcome to be favorable so that f increases. The parameter g, a measure of the confidence people in country A have in their home team, biases bettors perceptions of the winning chances of their national team upwards. 9 It 6 See Kuypers (2000) for a related model that allows for three distinct outcomes. 7 Our data confirms that betting companies apply a fixed markup when setting their odds and that furthermore this markup varies considerably across countries which testifies to the validity of our assumption of nationally separated wagering markets (see Table 1). 8 By entering the market punters accept the fixed markup charged by the betting company. The simplifying assumption of a fixed betting volume can easily be relaxed by allowing for two distinct revenue functions, one for each of the two outcomes, which are linked through the quotas set by the bookmaker. Qualitative results remain unchanged. 9 In principle, one may also allow for under-confidence in the national team. However, the (rare) existing evidence suggests that supporters, if at all biased in their perceptions, over-estimate the winning chances of their own team (see Babad and Katz, 1991). 4

5 can be thought of shifting the distribution of outcome probabilities of the population. The more over-confident people are, the more bettors switch to team A for some given odds. The bookmakers expected profit on a unit bet on one of the two teams is the unit itself minus the expected payout. The latter is given by the corresponding straight-up odds multiplied by the subjective outcome probability of the bookmaker. To obtain total profits per-unit bet, the (perunit) profit generated by a bet on one of the two teams has to be weighted by the fraction of the total betting volume that is waged on that country. Summing up across the two outcomes yields: ( 1 â ) ( ) ( 1 f ρa ρa, g â ) ( ( )) 1 1 f ρ(1 a) ρa, g. 10 (1) The bookmaker will choose a as to maximize expression (1). The corresponding first-order condition is given by: ( â ρa 2 f( ) â ) f 1 ( ) 1 ( ρ(1 a) ρa 2 = 1 â ) f 1 ( ) 1 ρa ρa â (1 f( )). (2) ρ(1 a) 2 The terms on the left-hand side of the equation represent the marginal benefits (MB) of a small increase in the probability a, while the right-hand side contains the corresponding marginal costs (M C). Since a reflects the probability for country A winning the match, an increase translates into lower odds for bets on team A. Consequently, the bookmakers expected profit for any monetary unit placed on country A rises with an increase in a, as reflected by the first term on the left-hand side. However, lower odds also induce punters to switch to team B so that expected gross profit per-unit bet on country A now applies to a smaller fraction f (first term on the right-hand side). For bets waged on team B, the findings are just reversed as the corresponding probability 1 a gets smaller. Now we can illustrate how the straight-up odds offered by the bookmaker are affected by changes in the over-confidence index g. Assuming for the moment that the bookmaker s subjective probability â is independent of g, 11 the effect of over-confidence on the probability a chosen by the bookmaker can be appreciated by taking the first derivative of equation (2) with respect to g. 12 Marginal benefits rise because the higher expected profit per-unit bet on country A now applies to a larger fraction of bettors: MB g = â ρa 2 f 2( ) > 0. (3) 10 Note that for the bookmaker to expect positive profits from bets on either of two outcomes, the chosen probability a has to fall into the interval [ â ρ, 1 1 â ]. If quotas are distorted too far, informed professional bettors could make ρ positive profits. 11 Levitt (2004) presents evidence which suggests that bookmakers are more skilled at predicting match outcomes. This finding can be explained by bookmakers being less affected in their assessment of outcome probabilities than bettors. 12 In what follows, we assume that the cross derivatives f 12 are zero. Alternatively, g may lower (increase) the responsiveness of total revenues to the odds offered by the bookmaker, i.e f 12 ( ) < 0 (f 12 ( ) > 0). The effects identified in the following are then still present but additionally the negative effect of an increase in a on f would be more (less) pronounced. 5

6 At the same time, the corresponding marginal costs decline: MC g = 1 â ρ(1 a) 2 f 2( ) < 0, (4) as lower expected profits on any monetary unit waged on country B now accrue only for a reduced fraction 1 f( ) of bettors. As it is unambiguously profitable to do so, the bookmaker will hence increase probability a and thereby reduce the straight-up odds offered for win of team A. It is straightforward to show that this result also holds when the bookmaker s subjective probability â is influenced by g as well. In fact, the bookmaker s tendency to reduce the straight-up odds for win of team A will be reinforced. In general therefore, the more confident are bettors regarding the success probability of their home team, the lower will be the actual straight-up odds. 2.2 Loyalty Bias Up to now it was assumed that punters always spread their betting stakes over the two outcomes. However, as noted by Forrest and Simmons (2008), wagering against the own team may well be unacceptable to supporters. Viewed as an act of disloyalty, supporters may just be interested in a bet on their team or none at all. 13 To formalize this idea in the present context, we assume that a fraction x of all bettors only considers betting on their national team. In this case, the potential but not the actual betting volume is fixed. Bettors committed to their national team will not bet at all if the quota for win of their team is set too low. The fraction of committed bettors, denoted by h, that are actually placing a bet on their national team is again a function of the quota on offer and - potentially - ( ) 1 the over-confidence index g, i.e. h ρa, g with h 1 ( ) > 0, h 2 ( ) > 0. The bookmaker will then maximize the following expression: ( x 1 â ) ( ) (( 1 h ρa ρa, g + (1 x) 1 â ) ( ) ( 1 f â ) ( ( ))) 1 1 f. (5) ρa ρa ρ(1 a) ρa To see whether the loyalty bias increases the optimal a chosen by the bookmaker, consider first the optimal value a = a for which the first-order condition is fulfilled in the absence of committed bettors, i.e. for x = 0. Then by assumption the first derivative of the second part of the profit function, which refers to the objective bettors only, with respect to a equals zero. Evaluating the derivative at the point a = a therefore yields: ( ( â x h( ) 1 â ) ρa 2 ρa h 1 ( ) 1 ) ρa 2. (6) 13 Committed bettors, the authors note, might be as unwilling to switch bets to the opponent team if odds on win offered for the own team get unfavorable, as they are unlikely to switch to replica shirts of the opponent team only because these got relatively cheaper - a not altogether unreasonable possibility. 6

7 The sign of this expression and therefore also the impact of the loyalty bias on the offered quotas can not be unambiguously determined. The probability chosen by the bookmaker will increase (decrease) whenever the marginal benefits of further increases in a are larger (smaller) than the corresponding marginal losses at a = a. As before benefits materialize in form of higher expected profits per unit bet while the actual betting volume declines with a. In fact, the sign of the expression and, hence, the direction of the loyalty bias is independent of x, the fraction of committed bettors in a country. An additional perception bias among these committed bettors, however, will increase the likelihood of expression (6) being positive as: â ρa h( ) 2 = â g ρa 2 h 2( ) > 0 (7) and hence will induce bookmakers to increase the implied probability a. The same holds true for a decrease in the demand elasticity of committed bettors as measured by h 1 ( ). Summarizing our analysis of the loyalty bias, if national sentiments induce bettors to wager, if at all, only on win for their home team, then the bookmaker may profitably bias odds in favor of rather than against committed bettors. More favorable odds on win for domestic teams, if indeed observed in the data, therefore provide conclusive evidence for a loyalty bias of domestic bettors. In such a case, bettors need not necessarily be free of perception bias. But any over-confidence on their part would have to be very weak. If, in contrast, odds on win for domestic teams are found to be less favorable, national sentiment in the form of either or both a perception and loyalty bias may sign responsible. While biases, however signed, in the probabilities underlying straight-up odds therefore provide evidence for national sentiment to influence bettor behavior, only negative biases carry additional information on the respective strengths of the perception and loyalty bias. 3 Data We collected betting quotas from online bookmakers in twelve European countries for qualification games of national football teams to the UEFA European Championship The bets considered are simple bets on home win, tie, and away win (respectively, quota 1, quota 0, and quota 2). Quotas for games were collected online in the morning of a qualification round in random order across countries to avoid potential sampling bias due to systematic early or late recording. Online bookmakers for the twelve countries considered were primarily selected from members of the European Lotteries and Toto Association which is composed of State Lottery and Toto companies established in Europe. 14 For each country, a bookmaker was chosen that operated online and offered simple home win, tie, and away win bets. If none of the members of a country met 14 See 7

8 these conditions, we selected a large private online bookmaker from the internet. Throughout this process, we disregarded bookmakers who operated via subsidiaries in more than one European country Table 1 describes our final dataset, which covers betting quotas on 218 qualification games from 12 European countries in 6 qualification groups, sampled online between November 2006 and November Table 1: countries, bookmakers, and summary statistics Country: Betted Games: 1/Markup: Name Bookmaker Group Total Home Away Mean St.d. (1) (2) (3) (4) (5) (6) Bulgaria eurofootball.bg Czech Republic eurotip.cz Denmark danskespil.dk England skybet.com France fdjeux.com Germany sportwetten-gera.de Italy match-point.it Netherlands toto.nl (De Lotto) Norway norsk-tipping.no Slovenia sportna-loterija.si Spain miapuesta.com Sweden svenskaspel.se Note: denote countries for which the respective bookmaker is state run. (1): qualification group of betting country; (2): total number of games for which betting country has complete triplet (win, tie, loss) of quotas; (3),(4): number of home and away games of betting country; (5): average expected payout per monetary unit waged when quotas reflect true probabilities; (6): standard deviation of average expected payout to bettors. As can be seen in column (2) of Table 1, no bookmaker offers bets on all games. Indeed, for only 107 games do all twelve bookmakers in our dataset offer quotas. For each country, we observe a total of eight to nine home and away matches (columns 3 and 4), i.e. matches in which the national team takes part. Table 1 also documents that markups differ significantly across bookmakers (column 5), but do not vary across games for a particular bookmaker (column 6). 18 These findings support our assumptions of nationally separated online betting markets and a constant bookmaker markup. 15 For Germany, we had to drop the state-run online bookmaker Oddset from our sample, as its online betting service was temporarily discontinued during the observation period. 16 The choice of an English bookmaker poses some problems since its service is likely to be taken up also by Scots which do not share much sympathy with the English national team. However, the English are by far in the majority among potential bettors in the United Kingdom. Nevertheless, the estimates for the national sentiment bias in England should be taken with some caution. Dropping England from our dataset does not affect the results for the other countries. 17 Starting the research project only after the qualification had started, we did not record the first 5 qualification rounds. Our sample, however, covers 71% of all qualification games. 18 For a given match, the markup can be calculated as the sum of the inverse quotas. If quotas reflect the true outcome probabilities, the expected payout per monetary unit waged is then given by the inverse of the mark-up, as reported in column (5). 8

9 4 Results To investigate whether or not bettors behavior in different countries is subjected to a national sentiment bias of one type or the other, we consider two endogenous variables in the following regression analysis, the probability of win for the home team (a H ) and the probability of win for the away team (a A ). These probabilities are calculated from the quotas bookmaker j offers on match i as the inverse of the quota for the respective outcome, adjusted for the markup ρ ij, i.e. a k ij = 1 ρ ij quota, where k = {H, A}. We regress the probabilities a H k ij and aa ij on a set of interaction ij terms of betting country identifiers and dummies for home, respectively away game status. These indicate whether or not the country of a bookmaker j participates as home or away team in match i. In addition, we control for betting country and game fixed effects. Game fixed effects capture all relevant information on the objective winning chances of teams on the day of a game (recall that quotas have been sampled in the morning of a qualification round). If information is indeed symmetric across countries, we should be able to account for most of the variation in probabilities in the data (and indeed we are, as shown below). As not all countries offer bets on all games, we will use three estimation samples for each outcome variable to gauge the influence of potential sample selection bias. The first, or Total Sample, includes all games for which at least one betting country offers quotas (218 games). The second ( Restricted Sample I ) includes all games for which at least six betting countries offer quotas (208 games), and the third ( Restricted Sample II ) all games for which at least nine betting countries offer quotas (189 games). 19 outputs are reported in Tables 2 and 3. The main regression As is evident from Table 2, we can explain most of the variation in the odds of win for home teams. Our set of game identifiers primarily signs responsible for this, which testifies to the validity of our identifying assumption that information on objective winning chances of teams is symmetric across countries. Of primary importance for the purpose of our analysis, however, probabilities for home win implied by quotas offered appear systematically biased in several countries when it is their respective national team that has the home game. Following our theoretical analysis, this suggests that in these countries bettors behavior is indeed influenced by national sentiments. Biases, however, are not uniform, either in sign or magnitude. In Bulgaria, Denmark, and Italy, the bias is positive, in France, Slovenia, and Sweden, it is negative. Among the former, the bias is most pronounced in Bulgaria and Denmark (approx. +5%), among the latter it is largest in Sweden (approx. -4% each). Results are remarkably consistent across estimation samples in terms of the sign, magnitude, and statistical significance of estimated coefficients. 20 Potential sampling 19 Sample sizes decline significantly if this minimum threshold is further increased. Only for less than half of all games covered in our data (107 games) do all twelve betting countries offer quotas. 20 Only for Slovenia, does the estimated coefficient, although unchanged in size, turn insignificant in the third estimation sample. 9

10 Table 2: ols estimates for winning probability in home games End. var: probability win home team Covariates Total Sample Restr. Sample I Restr. Sample II Home Game Bulgaria Czech Republic Denmark 4.8 England France (1.2) Germany Italy 2.0 (1.2) Netherlands 1.9 Norway (1.2) Slovenia Spain Sweden Away Game x Country yes yes yes Country dummies yes yes yes Game dummies yes yes yes N R Note:,, denote statistical significance at the 10%, 5%, and 1% level. Standard errors in parentheses. Total Sample: at least 1 obs. per match; Restr. Sample I: at least 6 obs. per match; Restr. Sample II: at least 9 obs. per match. Base group: betting countries not participating in a game. bias due to non-coverage of particular games by bookmakers, if indeed present at all, hence appears negligible. Following our theoretical discussion in Section 2, the empirical finding of a downward bias in the probability for home win in France, Slovenia, and Sweden suggests that national sentiment in these countries primarily express itself in terms of committed bettors that only consider betting on the home team if at all (loyalty bias). Bettors in these countries do not - or only to a very limited degree - overrate the winning chances of their home team. We also know from our theoretical analysis that the fraction of committed bettors ceteris paribus increases in absolute terms the magnitude of the bias. This suggests, given our regression results, that the loyalty bias is likely to be more pronounced in Sweden than it is in Slovenia. The positive biases found for Bulgaria, Denmark, and Italy can, following our formal treatment, be explained with reference to both types of biases. Bettors may only consider bets on their home team and / or overrate the winning chances 10

11 Table 3: ols estimates for winning probability in away games End. var: probability win away team Covariates Total Sample Restr. Sample I Restr. Sample II Away Game Bulgaria Czech Republic Denmark 4.0 England 0.4 France 0.1 Germany 1.0 Italy 0.1 Netherlands 1.3 Norway 0.5 Slovenia 0.4 Spain Sweden Home Game x Country yes yes yes Country dummies yes yes yes Game dummies yes yes yes N R Note:,, denote statistical significance at the 10%, 5%, and 1% level. Standard errors in parentheses. Total Sample: at least 1 obs. per match; Restr. Sample I: at least 6 obs. per match; Restr. Sample II: at least 9 obs. per match. Base group: betting countries not participating in a game. of their national team in home games relative to the chances as they are on average marketed in countries not participating in a game. If the loyalty bias were generally negative in sign, however, bettors perceptions of the winning chances of their national team would have to be significantly upward biased for a positive bias in the odds for win for the domestic team to be in the interest of a profit-maximizing bookmaker. In this case, the magnitude of the bias in the odds for win is again informative about the respective strengths of the two biases. Specifically, both the fraction of committed bettors and the level of over-confidence will ceteris paribus increase the degree to which odds are biased. Rerunning the same regressions, but now with the probabilities for win in an away game as implied by quotas set, we get results that are qualitatively identical for countries exhibiting the largest upward, respectively downward bias in home games (Table 3). Specifically, in Bulgaria and Denmark (Sweden) implied probabilities for win of the home team are again biased upwards (downwards), 11

12 albeit to a lesser degree. However, there are also some differences. Italian (French and Slovenians) bettors, who in home games are faced with less (more) favorable odds for win of the own team, are not confronted with such biases in away games of their national team. This may point to a greater importance of national sentiment biases in home games. In addition, for Spain an upward bias is observed in away but not in home games. 21 Table 4 summarizes the qualitative findings of our baseline regressions in concise form. Entries along its main diagonal are comprised of countries that display consistent patterns in the direction of sentiment bias in both home and away games of their national team. Eight out of twelve countries in our sample, and hence the majority, belongs to this group. The remainder (off-diagonal entries) are countries in which probabilities for win of the national team are biased upwards or downwards in home or in away games, but not in both. Overall, we find evidence for systematic biases in the rating of own national teams in seven out of the twelve countries in our sample. Incidences of a positive bias outnumber incidences of a negative bias. As argued, the latter can be attributed to a loyalty bias among bettors while the former may be the result of either or both a perception and loyalty bias. Table 4: summary of results from baseline regressions Away Game Positive Bias Home Game Negative Bias Objective Positive Bias Bulgaria, Denmark Italy Negative Bias Sweden France, Slovenia Objective Spain Czech Republic England, Germany Netherlands, Norway Note: Objective denotes countries who do not differ statistically significant in their odds for win of their domestic team from odds on the same outcome as on averaged marketed in countries not opposing these countries. Spain (the Netherlands) only exhibit a barely insignificant positive (negative) bias in home games. Note that the biases emerging from our empirical analysis are different from (and hence cannot be explained by) a major bias investigated in the literature on sports wagering, the favorite-longshot bias according to which favorites tend to be overbet and longhots underbet. Nor do they reflect mere home team advantage, as it is differences across bookmakers in the odds for a particular outcome of a specific game that we consider. Biases also neither resemble simple patterns of overall country performance in the qualification to the Euro Odds on win for the Swedish team, for instance, have been unfavorable in Sweden, but the team safely qualified as second best in its group. English bettors, in contrast, appeared not to exhibit any sentiment bias, although their national team did not qualify for the Euro finals in Austria/Switzerland. Estimated biases 21 Note, however, that the estimated positive coefficient for Spain in home games is only barely insignificant at the 10% level. 12

13 also do not fit a simple national-private bookmaker divide. Among the countries with a positive sentiment bias, there are both countries with state-run bookmakers (Bulgaria and Denmark) and countries with private bookmakers (Italy and Spain). A negative bias, in contrast, can only be found in countries with state-run bookmakers (France, Slovenia, Sweden), and among countries that do not exhibit any bias at all, again both state-run (Netherlands and Norway) as well as private bookmakers (Czech Republic, England, and Germany) can be found. We checked the robustness of our results to changes in both regression specification and estimation sample. None changed our results materially. Checks of the former type included the clustering of standard errors at game level, the inclusion of country-specific time trends across qualification rounds, and the use of identifiers for games of teams that are in the same group as the respective betting country. Changes in the latter dimension included the restriction of the estimation sample to games in which at least one of the betting countries participated, to games not involving teams in the same qualification group as the betting country unless the latter itself represents the home or away team, and to games for which quotas are offered by all twelve betting countries. The already noted near statistically significant positive (negative) bias for Spain (the Netherlands) in home games in our baseline regressions at times turns significant, while the weakly statistically significant positive (negative) bias for Italy (Slovenia) in home games occasionally turns insignificant, although only barely (p-values then mostly fall in the range of ). virtually unchanged throughout. 22 Results for away games are 5 Conclusion This paper has provided a theoretical treatment of how national sentiment, in the form of either a perception or a loyalty bias, may bias across countries odds for win of own national teams in sports competitions. Furthermore, based on a unique data set of online betting quotas from twelve European countries for qualification games to the UEFA European Championship 2008, we analyzed differences in odds for win offered across countries for evidence of systematic biases in the pricing of own national teams. Several countries are found to exhibit such biases, some positive, and some negative. Biases, moreover, appear to be more frequent in home than in away games. Countries with positive biases (Bulgaria, Denmark, Italy, and Spain) outweigh in number countries with negative biases (France, Slovenia, and Sweden). For the former group, national sentiment of bettors in the form of either or both a perception and loyalty bias may explain observed deviations in odds marketed. For the latter, in contrast, bettors must be subject to a loyalty bias. Overall, our empirical results provide strong evidence for a non-negligible influence of national sentiment 22 The respective regression output of these robustness checks can be obtained from the authors upon request. 13

14 on wagering market outcomes in Europe. References Babad, E. and Y. Katz (1991), Wishful thinking Psychology, 21, against all odds, Journal of Applied Social Kuypers, T. (2000), Information and efficiency: an empirical study of a fixed odds betting market, Applied Economics, 32, Levitt, Steven D. (2004), Why are gambling markets organised so differently from financial markets?, The Economic Journal, 114, Morse, A. and S. Shive (2006), Patriotism in your portfolio, Mimeo, University of Notre Dame. Sauer, R. (1998), The economics of wagering markets, Journal of Economic Literature, 36(4), Shankarmahesh, Manesh (2006), Consumer ethnocentrism: an integrative review of its antecedents and consequences, International Marketing Review, 23, Strumpf, K. (2002), Illegal sports bookmakers, Mimeo, Department of Economics, University of North Carolina. 14