I. INTRODUCTION

Rank-order tournaments are a popular field of research in both labor economics and sports, because not only are tournaments part of people's everyday lives, but tournament theory also provides several well-formulated and empirically or experimentally testable hypotheses. Theoretical considerations largely stem from Lazear and Rosen's (1981) early finding that in certain conditions, rank-order tournaments can efficiently induce greater worker effort. However, disparities in ability or the availability of intermediate information about contestants' performance or relative rankings might reduce these incentive effects (McLaughlin 1988). For example, in a two-player tournament, low probability of winning likely results in the less capable contestant reducing its efforts to avoid effort costs. The more capable competitor anticipates this reduction and decreases its effort as well. Accordingly, in asymmetric contests, incentive effects are weak. Empirical literature supports this result; however, extant studies typically do not consider within-tournament dynamics explicitly (see, e.g., Berger and Nieken 2016; Genakos and Pagliero 2012; Lynch 2005). Thus, empirical evidence of the impact of interim results on contestants' efforts is limited. This research gap is surprising, given that intermediate information defines incentives to provide effort in a tournament setting and should influence the contest organizer's actions.

"Intermediate information" describes the knowledge contestants' gain during the course of the competition about intermediate results and competitors' abilities. Information suggesting the contest is already decided can be an important determinant of effort exerted, because it determines negative incentives, similar to ex ante heterogeneity. Empirical studies of the impact of intermediate information on effort are rare at best (Casas-Arce and Martinez-Jerez 2009; Genakos and Pagliero 2012), and experimental studies usually investigate the circumstances in which it is efficient to reveal interim results. Moreover, few of these studies provide experimental or empirical evidence of their assumptions (see Aoyagi 2010; Ederer 2010; Gershkov and Perry 2009). Open questions remain, especially with respect to the incentive effects of dynamic contests (Genakos and Pagliero 2012).

In an attempt to close this gap, we use running data gathered from professional soccer players in the German Bundesliga and extensive within-game information. Detailed game-level statistics for each player's running distance and number of high-intensity runs and sprints provide proxies for effort. Focusing on the effort exerted by each player who was substituted into the game, we can disentangle incentive effects due to intermediate results from other aspects that influence effort, such as the ex ante heterogeneity of the two competing teams or the intensity of the match before the substitution. Thus, this article adds insights into the effect of interim results and ex ante heterogeneity. The results indicate strong incentive effects of intermediate results, measured as the score of the match at the time of the substitution. In support of a loss aversion effect, we find that players' effort is greatest when their team is leading by one goal, that is, when the team has the most to lose if it concedes a goal. Because potential losses are weighted more heavily than gains, effort climaxes at the point of greatest loss. In contrast with interim score effects, the results for ex ante heterogeneity are mixed and depend on the model.

The article is organized as follows: In the next section, we review literature on the effects of heterogeneity and intermediate results on performance in general and for the specific case of soccer. Then we discuss our proxy for effort, describe our dataset, and present descriptive statistics for the variables of interest. Next, we explain our empirical method and present the results of several estimations before concluding with some key implications of our findings.

II. LITERATURE REVIEW

Tournament theory suggests that distinct intermediate information should have an effect on effort similar to that of heterogeneity, and it identifies both as important drivers of effort. Most existing studies confirm these theoretical propositions, in terms of the predicted impacts of both heterogeneity and intermediate results, as we specify in the next sections.

A. Impact of Heterogeneity on Effort

Studies of asymmetric tournaments can be classified as experimental and empirical, as well as according to whether their focus is firms or sports. For example, Bull, Schotter, and Weigelt (1987) experimentally investigate incentive effects in tournaments and find that in asymmetric contests, the effort levels of disadvantaged agents are greater than predicted by theory, but the behavior of advantaged participants accords with theoretical predictions. Schotter and Weigelt (1992) analyze the impact of affirmative action programs and equal opportunity laws, modeled as rank-order tournaments, on the efforts of heterogeneous agents. They find that the implementation of equal opportunity laws, intended to combat asymmetries and benefit disadvantaged groups, lead to higher effort levels for all subjects. In line with theory, effort is higher in settings with homogeneous contestants. In a sales setting, Backes-Gellner and Pull (2013) theoretically and empirically investigate the effect of employee heterogeneity on performance. The empirical results are highly consistent with tournament theory: Sales representatives' performance relates negatively to heterogeneity. However, the effect varies with several aspects, such as the number of prizes and participants in the tournament.

A wide range of studies involving the incentive effects of asymmetric contests uses nonexperimental field data from sporting competitions, for which detailed information about both the tournament and the contestants usually is publicly available (Kahn 2000). Frick, Gurtler, and Prinz (2008), for example, investigate the impact of ability heterogeneity on effort using data from the German Bundesliga. Their game-level analysis suggests that ex ante heterogeneity significantly reduces both teams' effort levels. Bach, Gurtler, and Prinz (2009) confirm these results with an analysis of Olympic rowing regattas, showing that more capable oars-people row faster when the heterogeneity of the starting field decreases, and underdogs always provide the most effort.

Using data from tennis matches, Sunde (2009) and Lallemand, Plasman, and Rycx (2008) analyze the effect of ability differences between the two players on effort. Sunde's results confirm that the greatest effort is exerted in homogeneous contests in support of theoretical assumptions; in contrast, Lallemand, Plasman, and Rycx (2008) find that in uneven matches, favorites (underdogs) win more (fewer) games, such that they perform better (worse). They thus conclude that ability differences exert greater influence on match outcomes than do effort differences. Brown's (20ff) empirical analysis of golf data focuses on the adverse incentive effect of superstars in tournaments--specifically, the impact of Tiger Woods on other golfers' level of effort. The author finds that the presence of Tiger Woods significantly decreases the performance of other competitors, and this negative effect is strongest for more skilled players. Finally, Berger and Nieken (2016) study handball teams and their reactions to heterogeneity and intermediate information, measured by halftime scores in matches. The intensity of the match at halftime relates negatively to the ex ante heterogeneity of the teams, though this effect appears to be driven mostly by the favored team.

B. Intermediate Information

In an experimental study, Bull, Schotter, and Weigelt (1987) also investigate the impact of information about intermediate ranks and performance on future effort provision; they find that providing information does not influence agents' effort, and Schotter and Weigelt (1992) confirm this finding with experimental data. Gurtler and Harbring (2010) analyze whether a principal's feedback policies affect agents' performance and find evidence in line with their prediction that the principal should provide information only if the agents are homogeneous. If the intermediate information indicates large differences in performance, it is detrimental to future effort.

Ludwig and Lunser (2012) experimentally determine the impact of intermediate performance information on effort in symmetric two-stage tournaments. The authors find that if contestants can observe each other's effort in the first stage, the competitor who is trailing tends to increase and the one who is leading tends to decrease effort, compared with efforts in the initial stage. The greater the observed differences in effort, however, the smaller the impact on second-stage effort. Azmat and Iriberri (2010) rely on data from a natural experiment in a high school to investigate whether feedback information about relative performance affects students' behavior. They find that students' grades increase significantly after they receive feedback information, especially among high-ability students. Their natural competitive preferences appear to prompt these students to respond to the additional information. Therefore, releasing additional information likely increases (decreases) the benefits for students who are ahead (are lagging).

Casas-Arce and Martinez-Jerez (2009) investigate the incentive effects of heterogeneity in multiperiod tournaments, both theoretically and empirically, using data from sales contests. The effect of releasing intermediate performance information appears similar to that of ex ante heterogenity, in that leading contestants reduce their effort when the distance to the closest follower increases. However, trailing competitors decrease their effort only if the distance to a higher rank is very large.

Many sports studies investigate incentive effects, but few focus on the impact of intermediate results on contestants' effort. Lynch (2005) identifies the incentive effects of horse races, noting that horse race organizers use handicaps to improve homogeneity in the starting field. The focus of that study is the closeness of the race and its impact on effort. The results show that jockeys increase their effort when the distance between them and their closest competitors is small, so interim information significantly affects their effort. Although Berger and Nieken (2016) address ex ante heterogeneity, they also investigate whether the score at the end of the first half of a handball game affects the intensity of the second half. The insignificant coefficient for the halftime score implies that additional information about a team's winning probability does not affect match intensity. We seek to advance this research stream by investigating the incentive effects of intermediate information using extensive match-level data from substituted soccer players, as we detail in Section III.

C. Intermediate Results, Marginal Utility, and Loss Aversion in Soccer

Soccer provides a specific incentive structure, due to the nonlinear distribution of points for the participants. If a team loses, it receives no points; a draw earns both teams one point; and a winning team receives three points. This reward system was implemented in 1995 to increase incentives to play more offensive-oriented matches (Moschini 2010). Additionally and unintended by the institutional changes, incentives for sabotage behavior often increase simultaneously with incentives to effort provision (Lazear 1989). The new 3-1-0 payoff scheme increased the number of fouls and yellow cards (Garicano and Palacios-Huerta 2006). In contests like soccer, games are decided by relative performance between competitors (e.g., in league play, it is irrelevant if a game's score is 3-1 or 1-0) providing incentives for constructive as well as destructive effort (Deutscher et al. 2013). At the end of a game, the difference between goals scored and goals conceded determines the teams' payoff in terms of points. During the game, the current score determines marginal gains (losses) for scoring (conceding) a goal. Table 1 displays the relationship between the intermediate score and marginal gains and losses.

Unlike golf, where par is a very salient reference point for each hole (Pope and Schweitzer 2011), soccer does not provide any such. While relative performance is as decisive as in golf, expected success in soccer is determined prior to the game by the teams' and opponents'. Still, gains and losses are not valued identically (Kahneman and Tversky 1979) by individuals. Instead, loss aversion suggests that losses are weighted substantially more heavily than gains. In the context of sports, Pope and Schweitzer (2011) find that golfers' putting performance is affected by the number of strokes they needed prior to the putt: Golfers who putt for par perform better than those who putt for birdie. Hence, "par" is a reference point with impact on future performance. In the case of soccer, intermediate information about the current score acts as this kind of reference point and therefore can have explanatory power for future effort provision. For head-to-head contests, the literature finds support of increased effort by trailing competitors. Berger and Pope (2011) find basketball teams trailing by one point at halftime to win games more often than teams ahead by one point. They point at increased motivation for teams that are behind to increase performance in the second half of games. The dataset applied for the paper at hand covers soccer. In contrast to basketball, where a team scores every few minutes, goals in a soccer match are rare events. A single goal often decides matches. Given the rareness of goals in soccer, their production costs are rather high, especially for the weaker contestant. This explains why a turn-around equilibria, where the trailing opponent increases effort (Berger and Pope 2011; Bergerhoff and Vosen 2015) is not expected to be found in our context. Instead we expect teams to enhance effort when given the chance to hold on to a lead. This suggests, first, that effort is greatest when marginal losses peak, in accordance with Table 1 for the case of [goaldiff.sub.+1], followed by [goaldiff.sub.0]. Second, marginal gains and losses might only be temporary; goals scored later during the same game can affect the number of points awarded to the teams. The dynamic structure of the game suggests that leading or trailing by a large margin further reduces incentives for effort. Third, teams have incentives to play a more defensive style of play when in the lead.

III. DATA AND DESCRIPTIVE STATISTICS

Our data cover detailed pre-, post-, and within-game information for each match of the German Bundesliga for the seasons 2011/12-2013/14. This professional soccer league comprises 18 teams, which play each other twice (once at each team's stadium) per season, resulting in 306 matches per season and 918 match observations overall. Prior to every match, the teams' coaches each choose 11 players for the starting lineups. In the course of a match, each coach may replace or substitute in up to three players. (1) Reasons for substitutions range from injuries to weak performance to tactical changes. In our dataset, substituted players get graded on average with 3.82 (on a 1 - 6 scale) as assigned by Kicker magazine, and players who remain on the pitch get graded on average with 3.58. Coaches prefer more offensive substitutions when their team is trailing, and more conservative or defensive substitutions take place when teams are leading. On average, players who do not participate in the full game provide greater effort per minute than players who are on the field for the whole time, as these players have to pace themselves more carefully.

At the match level, we have information about the performance of each player, which we use to proxy for effort exerted. This information includes the running distance and the number of sprints and intensive runs each player undertakes during the match. Our dataset contains 25,381 player-match observations for 772 players. We also gathered detailed information about the score of each match and the number of substitutions by both teams from the league's official website (www.bundesliga.de). Unfortunately, the match-level statistics per player refer to the entire time that the player is on the field, not to subperiods of the games. Therefore, we cannot estimate the incentive effect of the interim results for players who were on the starting roster at the beginning of the match, when information on the interim results does not exist and thus is of no relevance. Therefore, our analysis focuses exclusively on substituted players, who at the time they enter the game have access to important intermediate information regarding the likelihood of their team to win the respective match. Note that because of the limited number of substitutions allowed during a game, coaches usually start the game with the best lineup available. A player who starts the game exhibits a superior value compared with players substituted into the game, as indicated in monetary terms by their average of 1.09 million [euro] higher salary (transfermarkt.de). The probability of winning an ongoing match depends crucially on the goal difference at any particular time, so we use the score at the time of the substitution to measure intermediate information (see also Berger and Nieken 2016; Frick, Giirtler, and Prinz 2008).

A. Measuring Effort in Sports

Effort is perhaps an even more important variable than intermediate information, though few studies address the effort expended by individual soccer players or teams. Extensive research centers on different determinants of performance, success, or productivity of teams or individual athletes, (2) but few focus explicitly on effort, mainly because of the difficulty of measuring something that "is [often] not directly observable by the principal or the audience (including the econometrician), which constitutes the major empirical problem for testing the incentive effect" (Sunde 2009, 3200). Sports data provide manifold, extensive statistics, but the best method to measure effort is unclear (Berger and Nieken 2016), and many previously applied measures might not actually reflect it.

Some studies argue that overall team effort can be derived from the intensity of a match, which can be approximated by the number of penalties a team receives due to fouls or other rule violations. Frick, Gurtler, and Prinz (2008) use the number of penalty cards (yellow, yellow/red, and red) issued to each soccer team per match to assess match intensity and thus team effort; Berger and Nieken (2016) similarly rely on the number of 2-minute suspensions per handball match and team as a measure of "defensive effort." Although they acknowledge that such efforts also could reflect sabotage activities, they relate positively to a team's winning probability. Therefore, these authors consider the number of 2-minute suspensions as a good proxy for the intensity of a team's play. However, other studies use measures reflecting contest outcomes to analyze the incentive effects of tournaments. Frick and Prinz (2007), in a study with running data, use running times as their dependent variable; Sunde (2009) and Lallemand, Plasman, and Rycx (2008) both analyze tennis data and estimate incentive effects on the basis of the average number of games a player wins per match. Sunde notes that it is important to separate capability from incentive effects, but that this method is problematic, because effort often is unobservable. He therefore proposes a model to identify effort by separating competing players into favorites and underdogs and investigating them separately.

In all of these studies, the authors are cautious in their denotation of the variable chosen to represent effort. They estimate incentive effects rather indirectly, whether by referring to the intensity of a match and its potential relation to overall effort or by using an outcome to separate effort from ability effects subsequently.

Recent technological advancements create extensive, match-level statistics for German Bundesliga matches. These publicly available statistics cite the overall team's and individual players' performance, including running distance, number of sprints and intensive runs, duels won, passes played, and goal shots, such that they represent a compelling means to measure effort more directly. Wicker et al. (2013) were among the first to apply these statistics to establish an innovative effort measure: Using information about the number of intensive runs and the running distance per game and player to capture effort, these authors explain that this procedure is advantageous because it acknowledges that "a player can choose the level of intensive runs without touching a ball and being productive. To put it differently, an individual can reach his maximum effort independent of his level of ability" (Wicker et al. 2013, 131). They study the impact of effort on a player's market value but find that a player's salary is not affected by effort.

Similar to Wicker et al. (2013), we use running statistics to measure effort, but our goal is to test the impact of intermediate results. We distinguish three one-dimensional measures of effort: the distance covered by a player (distance), the player's number of sprints (sprints), and the player's number of intensive runs (runs) in the course of a match. Distance refers to the total running distance in a match (measured in kilometers per minute), while sprints and runs refer to the number of high-effort observations per minute. Because the function of goalkeepers differs significantly from the tasks of the other players and is largely unrelated to running, we excluded them from the analysis and consider only defenders, midfielders, and strikers. To fortify our confidence in these measures of effort, we performed a correlation analysis with three additional variables that represent player effort: touches, percentage of passes intercepted, and percentage of duels won. As shown in Table 2, the correlations are as expected, especially for distance and runs. The intermediate score varies for players who are substituted in during the course of a match, so we focus on this subsample and test the effect of the intermediate score at the time of their substitution on the effort these players exert.

B. Descriptive Statistics

In most matches (85%), coaches use the maximum substitutions allowed. Our sample contains only one match in which a coach did not substitute at all. On average, there were 2.82 substitutions per match and team, and overall, we observed 5,185 substitutions. Almost all substitutions took place in the second half of the matches; only 4.24% occurred in the first half. Most substitutions (8.81 %) take place in the 46th minute, that is, during the halftime break.

Evaluating effort by substituted players requires some constraints. First, players who enter the game during the first half might differ systematically from their second-half counterparts, because they can recover during the halftime break and put forth additional effort during the rest of the game. Excluding goalkeepers and players who were substituted in the first half reduced our dataset to 4,946 observations. For undocumented reasons, information about the distance run and the number of intensive runs and sprints was unavailable for a few cases; the final dataset thus contained 4,886 observations for the distance, 4,850 observations for runs, and 4,576 observations related to the sprints variable. There are close to eight observations per player in our dataset. Distance, runs, and sprints all depend critically on the minutes a player is in the game, so we divided these variables by the number of minutes played. Table 3 contains the descriptive statistics (per minute played) for the subsample, as well as the number of minutes these players were in the game.

On average, a substituted player ran 124 m per minute and engaged in roughly three intensive runs and one sprint every 4 minutes. Because we expect that the prospect of winning or losing a match critically affects effort, we applied the score (i.e., goal difference) at the time of the substitution as a control variable, reflecting intermediate information. We could operationalize the goal difference in one of two ways: determine the difference between the number of goals scored and conceded or generate dummy variables for each goal difference. Following the assumptions of tournament theory, we expect that a large goal difference at the time of the substitution has a negative effect on effort, irrespective of whether the team is leading or trailing. We thus used dummy variables for the respective goal differences instead of a single variable representing the goal difference.

As shown in Figure 1, most substitutions take place when the team trails by one goal. This finding is not surprising; the goal of strategic substitutions is to change the course of the game. Very few observations occur when the goal difference is greater than 3, so we pooled all observations with an absolute value of [greater than or equal to] 3.

Figure 2 shows the average running distance and the numbers of runs and sprints per minute, in relation to the goal difference at the time of substitution. For all effort measures, we find the highest values when the team is leading by one or two goals and the lowest values when the respective team is trailing or leading (cf. sprints) by 3 or more goals at the time of the substitution.

In addition to the intermediate information, we control for other aspects that might determine individual effort. For example, tournament theory predicts lower effort levels for asymmetric contests, so we controlled for ex ante heterogeneity (heterogeneity) between the two teams, which we operationalize according to betting odds (obtained from the website www.betexplorer .com). Betting odds provide a good match for the ex ante strength of teams (Berger and Nieken 2016; Deutscher et al. 2013; Frick, Gurtler, and Prinz 2008; Garicano and Palacios-Huerta 2006). We measure the heterogeneity as the absolute difference between the winning probabilities of the two teams, which can be drawn easily from the betting odds. We assume a negative impact of ex ante heterogeneity on effort.

In addition, we control for the remaining number of minutes in the game at the time of the substitution (remaining) and the number of sendoffs that the respective team undertook prior to the substitution (sendingoffs). A player who is substituted in the 46th minute must pace himself for longer than a player who enters in the 76th minute and therefore must choose a lower effort level per minute. After a dismissal, the remaining players must compensate for the loss of a player and therefore should run or sprint more (often). We hypothesize a positive impact of send-offs on the effort exerted by the remaining players. (3)

Many studies indicate a "home field advantage" in soccer (Clarke and Norman 1995; Courneya and Carron 1992; Nevill, Balmer, and Williams 2002; Nevill and Holder 1999; Nevill, Newell, and Gale 1996), such that the fraction of wins by the home team is considerably larger than its number of losses. (4) Several theories circulate about this phenomenon, such as the role of the crowd. Social support by home fans might influence players' behavior, resulting in greater effort and better performance (Schwartz and Barsky 1977). Home teams also tend to exhibit a more offensive style of play, even though a more defensive style of play produces fewer scores by visiting teams. We thus included a dummy variable to indicate whether the substituted player was a member of the away team (away). We assume a negative impact of being on the away team.

It also is necessary to control for the intensity of a match prior to a substitution, because it makes a difference if the player is substituted into a match in which both teams play defensively or with two very offensive teams. The goal difference variables cannot capture this intensity, because they indicate the difference in the number of goals scored by the two teams, not the total goals scored in a particular match, which also reflects the intensity of a match. The total number of goals scored prior to a substitution might correlate with the goal difference at the time of the substitution and the remaining minutes though, so we implemented a different indicator of intensity: effort provided by the replaced player (effort_replaced). When the replaced player has exhibited great effort, the match should be more intense than if he had exerted minimal effort. In turn, we expect a positive effect of this variable on the effort by the substituted player. The effort by the replaced player always matches the estimated effort measure: When we use distance as the dependent variable, effort by the replaced player also refers to distance, and when the dependent variable is runs, effort by the replaced player refers to runs. (5)

Finally, we included two variables to capture the match day and its squared value, because we expect dynamics to vary throughout the season. First, we expect the importance of games to increase as the season progresses. Second, toward the end of the season, games of no importance for overall rankings are more likely to occur. Therefore, we expect effort to increase throughout the season and decrease at the very end. This is equivalent to a positive impact of matchday and a negative impact of matchday2 on effort. In addition, we include team, opponent, and player dummies to control for unobserved team, opponent, and player effects. Since incentives might depend on the position in the league standing, league position is controlled for. Additionally, the 5 sequence of substitution might impact effort and is controlled for.

Table 4 contains the descriptive statistics for the control variables. The average descriptive statistics appear to be similar for the replaced and substituted players in terms of running distance; the number of runs and sprints per minute is significantly higher among substituted players.

IV. RESULTS

To test the impact of intermediate information on individual effort, we apply an ordinary least squares regression analysis. We present three models, reflecting our use of three dependent variables.

With regard to the impact of intermediate information on effort, Table 5 shows that players exert the greatest effort when their team is leading by one goal. A tied score provides the reference category ([goaldiff.sub.0]). With the exception of number of sprints, the coefficient of [goaldiff.sub.+1] is consistently highly significant and positive, in that marginal losses are highest for [goaldiff.sub.+1]. Compared with a tied score, a player runs approximately 3.5 m more per minute and provides one additional intensive run every 3 minutes when leading by one goal.

In contrast, trailing by one goal leads to significantly less effort than a balanced score or leading the match, because the marginal loss is less when trailing than for a tied score. In all models, the coefficients for [goaldiff.sub.-1] are negative and significant. For a scoring system that incentivizes offense (three points for a win, one point for a draw, and zero points for a loss), these findings suggest players' loss aversion: They care more about avoiding loss than about winning. A team that leads a match by only one goal runs the risk of losing two points if the opponent scores a single goal, and this threat constitutes a stronger incentive than the possibility of winning two more points by scoring a goal when the score is tied. The same effect should hold for the comparison of the incentive effects of a tied score with trailing by one goal: Losing one point has more value than gaining an additional point.

Intermediate information that indicates a match is virtually decided by the time of a substitution ([goaldiff.sub.[less than or equal to]-3], [goaldiff.sub.[greater than or equal to]+3]) has a negative effect, because losses (or gains) are highly unlikely. The coefficients are negative for all three models and highly significant for distance, but they are only slightly significant or insignificant for runs. Other variables affect the effort level exerted, including playing time remaining and the effort of the replaced player. The more minutes left to be played at the time of the substitution, the less effort players show per minute, because they need to economize. Results for sequence of substitution go along with these results as players who get substituted in first provide less effort per minute. The intensity of the game, as proxied by the effort of the replaced player, strongly affects the effort exerted by the substituted player, such that greater effort by the replaced players coincides with significantly greater effort by the substituted players.

For ex ante heterogeneity, we find mixed results, though the coefficient is negative in all the models. For example, it is significant and negative for runs, but it is insignificant for distance and sprints. (6)

In summary, the results for distance and runs are very similar and indicate strong effects of the intermediate results on effort. In contrast, the goal difference merely affects the number of sprints. Although the coefficients for sprints are the same as for the other two effort measures, sprinting seems to differ from running.

As stated previously, the nature of substitutions is not random, and strategic substitutions could contort the results. When ahead, teams rely on more conservative strategies that prevent the opponent from scoring (Garicano and Palacios-Huerta 2006). Our data support that notion as teams in the lead make more defensive substitutions (e.g., replace a midfielder with a defender), while trailing teams make more offensive substitutions (e.g., replace a defender with a midfielder). To determine whether the type of substitution affects the results, we undertook additional estimations. First, we ran an estimation only including "neutral substitutions," where the player substituted in plays the same position as the replaced player. Second, another regression included dummy variables for all nine possible types of substitution pattern, with all combinations of a defender, midfielder, or forward being replaced by either a defender, midfielder, or forward. The main results hold for these supplementary estimations, too. Hence, strategic substitutions apparently do not replace effort provision as an explanation of the results at hand.

Third, different styles of play by coaches certainly could drive our results. While some managers prefer a rather defensive style of play that mostly results in reduced running distances, others rely on a more offensively oriented game that in turn demands more running from their players. Estimations including manager fixed effects supported the results presented above.

Furthermore, some teams play parallel to the Bundesliga in further competitions, such as the Champions or Euro League, or the national Cup (DFB Pokal), so that these teams have a higher pressure and shorter resting periods, which might wear players out and reduce running performance during Bundesliga games. Therefore, we controlled for another set of control variables accounting for competition in the Champions or Europe League or a national Cup Competition (DFB Pokal) during the week of each Bundesliga game. Results again remain robust. At last, we controlled for the rank of the team prior to the match. Competition between teams close in the standing could be seen as crucial and are referred to as so-called six point games. Again, intermediate information on effort provision remained robust. Sixth, one additional estimation controlled for a player's average effort previous to the observation. This estimation serves as a reasonable robustness check, because average running differs substantially between players. Yet including a player's average effort in the estimation does not affect the main results of the article. (7)

The rules of soccer must be kept in mind when analyzing the results. First, as mentioned previously, coaches are allowed a maximum of three substitutions per game. Moreover, players cannot reenter the game after having been substituted. Thus, coaches usually rely on their best lineup to start the game, in contrast to other sports such as basketball, in which there is no limit on the number of substitutions. Second, sports contracts differ from those in other industries. Players are usually on short-term (1- to 5-year) contracts and are often traded during the contract period for a transfer fee to the releasing club. During the final year of their contracts, players have higher incentives to increase their effort in hopes of signing a lucrative new contract. Although extensive research addresses this "contract year phenomenon" (e.g., Buraimo et al. 2015), for the current article, information on contract length was unavailable.

Since the impact of intermediate information on effort provision is our main interest, a limitation of the results of this article lies in neglecting intermediate information that become public after a player has entered the field. As information on effort is only available for the full period a player remains on the pitch, one could not distinguish if effort provision changed after new intermediate information became available.

V. CONCLUSION

This article examines how soccer players respond to intermediate information during the course of a match, focusing on substitute players in the German Bundesliga. In an innovative approach, we measure effort as the number of runs and sprints as well as the running distance a player covers during a match. The results suggest that effort is greatest when the team is leading by one goal. In line with loss aversion, players weight potential losses more than gains. Compared with a tied score, their effort is lower when their team trails by one goal. Effort declines when intermediate information about the score indicates that the game is already decided.

Regarding the release of intermediate information, we offer the following conclusions: If a contest is already decided, it is inadvisable to give information to the contestants. Both the leader and the trailing contestant will decrease their efforts to save costs. While this sounds convincing at first, it is hardly feasible for many contests, especially soccer, where intermediate information is publicly available. Second, if contestants compete repeatedly and intermediate information is not presented for contests already being decided or only presented to the leader, the noninformation to one or both contestants serves as information that decreases their future effort. Given that contestants know the intermediate information, handicapping the dominant contestant could increase both parties' efforts. If the intermediate information instead suggests the contest is close, trailing competitors should be incentivized (e.g., bonus pay) if they can outperform the leader.

Future research could enhance our understanding of the impact of intermediate information on effort provision by analyzing settings with less restrictions embedded. Closely related would be an analysis that splits soccer games into uniform intervals (see, e.g., Deutscher and Schneemann 2015) to determine effort during those intervals for every player on the pitch and not reduce to the substitute players. While this information is not available ex post, websites provide real time running information during soccer matches. Since running information has been tracked for the previous seasons in basketball also, another field for research emerges. Here, the advantage is given by the higher variance in intermediate information, since basketball provides a significantly higher number of points per game compared to goals per game in soccer.

doi: 10.1111/ecin.12420

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SANDRA SCHNEEMANN and CHRISTIAN DEUTSCHER *

* The authors thank Stefanie Pohlkamp, who has put in work in an earlier version of the paper. Additionally, we want to thank two anonymous referees as well as Bernd Frick and the participants of his doctoral workshop for helping to significantly improve the paper.

Schneemann: Research Assistant, Department of Sports Science, University of Bielefeld, UniversitaetsstraBe 25, Bielefeld 33615, Germany. Phone +49 521 1062010, Fax +49 521 1066489, E-mail sandra.schneemann@unibielefeld.de

Deutscher: Professor for Sports Economics, Department of Sports Science, University of Bielefeld, Universitaetsstrasse 25, Bielefeld 33615, Germany. Phone +49 521 1062006, Fax +49 521 1066489, E-mail christian.deutscher@uni-bielefeld.de

(1.) Up to seven players may sit on the bench, available for substitution in the game.

(2.) Nuesch (2009) analyzes the effect of demographic diversity on team performance, measured by the final score of a match. Franck and Nuesch (2010) focus on the impact of talent disparities on team productivity and use the same dependent variable, namely, the final score of a match, represented by the goal difference. Franck and Nuesch (2011) also investigate how wage dispersion affects team productivity, using a season-level data set and measuring productivity by the ratio of achieved points at the end of a season and the maximum number of possible points. In contrast, Frick (2011) focuses not on aggregate team performance but on individual performance and tests whether the contract length affects player performance, measured by a player's average grade from Kicker in a given season.

(3.) The impact of send-offs for the opponent has no significant impact on our findings, so we exclude it from subsequent estimations.

(4.) In our dataset, 45% of the matches end with home wins, 24% with a tie, and only 30% with a home loss.

(5.) Note that there might be spillover effects from (a) other players once the substitute enters the game and (b) from the player substituted into the game on the other remaining players. Since running information is only available on full game basis, these possible spillover effects cannot be captured by the data.

(6.) Once the sample is split into favorites and underdogs, heterogeneity is negative for underdogs and positive for favorites; the results suggest that favorites tend to decrease their effort when they are more likely to win, whereas underdogs get additional motivation when the win is less likely prior to the match. This result is in line with some previous research on heterogeneous contests (e.g., Berger and Nieken 2016; Bull, Schotter, and Weigelt 1987), but contradicts other (Gill and Stone 2010).

(7.) These results are available on request.

Caption: FIGURE 1 Distribution of Goal Differences at the Time of Substitution

Caption: FIGURE 2 Average Distance, Runs, and Sprints per Goal Difference at Time of Substitution

TABLE 1

Intermediate Score, Marginal Gains, and Losses
for Scoring a Goal

Intermediate                   Points   Marginal   Marginal
Score                                    Gains      Losses

[Goaldiff.sub.[less than or      0         0          0
  equal to] - 3]
[Goaldiff.sub.- 2]               0         0          0
[Goaldiff.sub.- 1]               0         1          0
[Goaldiff.sub.0]                 1         2          1
[Goaldiff.sub.+1]                3         0          2
[Goaldiff.sub.+2]                3         0          0
[Goaldiff.sub.[greater than      3         0          0
  or equal to]+3]

TABLE 2

Correlation Matrix for Effort in Soccer

Variable                Distance    Runs    Sprints

Distance                   1
Runs                     0.625       1
Sprints                  0.385     0.721       1
Touches                  0.051     -0.081   -0.097
Percentage of passes     0.087     0.178     0.210
  intercepted
Percentage of            0.161     0.198     0.179
  duels won

Variable                Touches   Percentage of   Percentage of
                                     Passes         Duels Won
                                   Intercepted
Distance
Runs
Sprints
Touches                    1
Percentage of passes    -0.254          1
  intercepted
Percentage of            0.200        0.106             1
  duels won

Note: All correlation coefficients are significant at the
0.001% level.

TABLE 3

Descriptive Statistics: Effort Variables (per
Minute Played) and Minutes Played

Variable           Obs.     Mean    Std. Dev.   Min.    Max.

Distance (in km)   4,886   0.124      0.023     0.007   0.360
Runs               4,850   0.808      0.324     0.063   3.333
Sprints            4,576   0.277      0.169     0.021    1.5
Minutes played     4,946   20.639    12.656       1      47

TABLE 4

Descriptive Statistics: Control Variables

Variable            Obs.     Mean    Std. Dev.    Min.    Max.

Heterogeneity       4,886   0.002      0.353     -0.865   0.865
Remaining           4,886   20.736    12.705       3       47
Sendingoffs         4,886   0.049      0.222       0        2
Away                4,886   0.501      0.500       0        1
Effort_replaced     4,886   0.123      0.009     0.087    0.159
  distance
Effort_replaced     4,850   0.686      0.168     0.111    1.422
  runs
Effort _replaced    4,576   0.215      0.088     0.013    0.542
  sprints

TABLE 5

Regression Results: Fixed Effects

Dep. Variable          Model 1       Model 2       Model 3
                      Distance        Runs         Sprints

[goaldiff.sub.       -0.0086 ***   -0.0474 ***   -0.0226 **
[less than or         (0.0010)      (0.0160)      (0.0090)
equal to]-3]

[goaldiff.sub.-2]     -0.0012 *    -0.0347 ***   -0.0156 ***
                      (0.0007)      (0.0108)      (0.0060)

[goaldiff.sub.-1]      -0.0007     -0.0380 ***   -0.0164 ***
                      (0.0006)      (0.0088)      (0.0049)

[goaldiff.sub.+1]    0.0048 ***    0.0395 ***    0.0165 ***
                      (0.0006)      (0.0101)      (0.0057)

[goaldiff.sub.+2]      0.0011      0.0374 ***     0.0179 **
                      (0.0008)      (0.0125)      (0.0070)

[goaldiff.sub.       -0.0106 ***   -0.0633 ***   -0.0179 **
[greater than or      (0.0009)      (0.0150)      (0.0084)
equal to]+3]

Heterogeneity          -0.0018     -0.0678 **      -0.0260
                      (0.0018)      (0.0286)      (0.0159)

Remaining            -0.0001 ***   -0.0047 ***   -0.0023 ***
                      (0.0000)      (0.0003)      (0.0002)

Sendingoffs          0.0033 ***    0.0703 ***     0.0165 *
                      (0.0010)      (0.0152)      (0.0085)

Away                   -0.0006       -0.0134      -0.0110 *
                      (0.0007)      (0.0104)      (0.0058)

Effort replaced      0.1075 ***    0.1808 ***    0.1296 ***
                      (0.0229)      (0.0197)      (0.0212)

Matchday             0.0003 ***    0.0038 ***      -0.0008
                      (0.0001)      (0.0013)      (0.0007)

Matchday2            -0.0000 ***   -0.0001 ***     0.0000
                      (0.0000)      (0.0000)      (0.0000)

League position

Sequence of
substitution

Constant             0.1093 ***    0.7093 ***    0.2390 ***
                      (0.0053)      (0.0723)      (0.0396)

Observations            4,886         4,850         4,576

Adjusted                0.295         0.378         0.324
[R.sup.2]

Dep. Variable          Model 4       Model 5       Model 6
                      Distance        Runs         Sprints

[goaldiff.sub.       -0.0084 ***   -0.0443 ***   -0.0220 **
[less than or         (0.0010)      (0.0162)      (0.0091)
equal to]-3]

[goaldiff.sub.-2]      -0.0010     -0.0338 ***   -0.0166 ***
                      (0.0007)      (0.0110)      (0.0061)

[goaldiff.sub.-1]      -0.0005     -0.0373 ***   -0.0179 ***
                      (0.0006)      (0.0090)      (0.0050)

[goaldiff.sub.+1]    0.0049 ***    0.0387 ***    0.0153 ***
                      (0.0007)      (0.0103)      (0.0058)

[goaldiff.sub.+2]     0.0014 *     0.0409 ***    0.0190 ***
                      (0.0008)      (0.0127)      (0.0071)

[goaldiff.sub.       -0.0104 ***   -0.0591 ***   -0.0187 **
[greater than or      (0.0010)      (0.0152)      (0.0085)
equal to]+3]

Heterogeneity          -0.0013     -0.0670 **      -0.0226
                      (0.0019)      (0.0304)      (0.0169)

Remaining            -0.0001 ***   -0.0047 ***   -0.0023 ***
                      (0.0000)      (0.0003)      (0.0002)

Sendingoffs          0.0033 ***    0.0699 ***     0.0172 *
                      (0.0010)      (0.0158)      (0.0089)

Away                   -0.0005       -0.0134       -0.0097
                      (0.0007)      (0.0109)      (0.0060)

Effort replaced      0.1020 ***    0.1784 ***    0.1277 ***
                      (0.0234)      (0.0201)      (0.0216)

Matchday             0.0003 ***    0.0047 ***      -0.0011
                      (0.0001)      (0.0015)      (0.0008)

Matchday2            -0.0000 ***   -0.0001 ***     0.0000
                      (0.0000)      (0.0000)      (0.0000)

League position        0.0001        0.0006        0.0003
                      (0.0001)      (0.0012)      (0.0007)

Sequence of
substitution

Constant             0.1074 ***    0.6844 ***    0.2411 ***
                      (0.0059)      (0.0812)      (0.0446)

Observations            4,744         4,708         4,447

Adjusted                0.297         0.379         0.325
[R.sup.2]

Dep. Variable          Model 7       Model 8       Model 9
                      Distance        Runs         Sprints

[goaldiff.sub.       -0.0092 ***   -0.0534 ***   -0.0248 ***
[less than or         (0.0010)      (0.0163)      (0.0091)
equal to]-3]

[goaldiff.sub.-2]    -0.0016 **    -0.0394 ***   -0.0173 ***
                      (0.0007)      (0.0110)      (0.0061)

[goaldiff.sub.-1]     -0.0010 *    -0.0404 ***   -0.0172 ***
                      (0.0006)      (0.0089)      (0.0050)

[goaldiff.sub.+1]    0.0049 ***    0.0410 ***    0.0171 ***
                      (0.0006)      (0.0102)      (0.0057)

[goaldiff.sub.+2]     0.0013 *     0.0391 ***    0.0185 ***
                      (0.0008)      (0.0125)      (0.0070)

[goaldiff.sub.       -0.0106 ***   -0.0634 ***   -0.0179 **
[greater than or      (0.0009)      (0.0150)      (0.0084)
equal to]+3]

Heterogeneity          -0.0019     -0.0688 **     -0.0265 *
                      (0.0018)      (0.0285)      (0.0159)

Remaining            -0.0001 ***   -0.0043 ***   -0.0022 ***
                      (0.0000)      (0.0003)      (0.0002)

Sendingoffs          0.0031 ***    0.0688 ***     0.0160 *
                      (0.0010)      (0.0152)      (0.0085)

Away                   -0.0006       -0.0132      -0.0110 *
                      (0.0007)      (0.0104)      (0.0058)

Effort replaced      0.1076 ***    0.1817 ***    0.1309 ***
                      (0.0229)      (0.0197)      (0.0212)

Matchday             0.0003 ***    0.0039 ***      -0.0008
                      (0.0001)      (0.0013)      (0.0007)

Matchday2            -0.0000 ***   -0.0001 ***     0.0000
                      (0.0000)      (0.0000)      (0.0000)

League position

Sequence of          0.0011 ***     0.0112 **      0.0042
substitution          (0.0003)      (0.0054)      (0.0030)

Constant             0.1063 ***    0.6779 ***    0.2274 ***
                      (0.0054)      (0.0738)      (0.0404)

Observations            4,886         4,850         4,576

Adjusted                0.297         0.379         0.325
[R.sup.2]

Dep. Variable         Model 10      Model 11      Model 12
                      Distance        Runs         Sprints

[goaldiff.sub.       -0.0090 ***   -0.0498 ***   -0.0237 ***
[less than or         (0.0010)      (0.0164)      (0.0092)
equal to]-3]

[goaldiff.sub.-2]    -0.0015 **    -0.0381 ***   -0.0180 ***
                      (0.0007)      (0.0112)      (0.0062)

[goaldiff.sub.-1]      -0.0007     -0.0395 ***   -0.0186 ***
                      (0.0006)      (0.0091)      (0.0051)

[goaldiff.sub.+1]    0.0050 ***    0.0400 ***    0.0158 ***
                      (0.0007)      (0.0104)      (0.0058)

[goaldiff.sub.+2]     0.0016 **    0.0425 ***    0.0194 ***
                      (0.0008)      (0.0127)      (0.0071)

[goaldiff.sub.       -0.0104 ***   -0.0592 ***   -0.0187 **
[greater than or      (0.0010)      (0.0152)      (0.0085)
equal to]+3]

Heterogeneity          -0.0015     -0.0687 **      -0.0231
                      (0.0019)      (0.0304)      (0.0169)

Remaining            -0.0001 ***   -0.0043 ***   -0.0022 ***
                      (0.0000)      (0.0003)      (0.0002)

Sendingoffs          0.0031 ***    0.0682 ***     0.0167 *
                      (0.0010)      (0.0159)      (0.0089)

Away                   -0.0005       -0.0135       -0.0097
                      (0.0007)      (0.0108)      (0.0060)

Effort replaced      0.1022 ***    0.1796 ***    0.1290 ***
                      (0.0234)      (0.0201)      (0.0216)

Matchday             0.0003 ***    0.0048 ***      -0.0011
                      (0.0001)      (0.0015)      (0.0008)

Matchday2            -0.0000 ***   -0.0001 ***     0.0000
                      (0.0000)      (0.0000)      (0.0000)

League position        0.0001        0.0006        0.0002
                      (0.0001)      (0.0012)      (0.0007)

Sequence of          0.0010 ***     0.0105 *       0.0034
substitution          (0.0003)      (0.0055)      (0.0030)

Constant             0.1048 ***    0.6570 ***    0.2323 ***
                      (0.0059)      (0.0824)      (0.0453)

Observations            4,744         4,708         4,447

Adjusted                0.298         0.380         0.325
[R.sup.2]

Notes: All regressions include player, team, and opponent
dummies. Standard errors are in parentheses. Values are weighted
by number of minutes played by player. Reference category is
[goaldiff.sub.0].

* p < .1, ** p <. 05, *** p<.01.