Elsevier

European Economic Review

Volume 100, November 2017, Pages 412-427
European Economic Review

First in first win: Evidence on schedule effects in round-robin tournaments in mega-events

https://doi.org/10.1016/j.euroecorev.2017.09.006Get rights and content

Abstract

The order of actions in contests may have a significant effect on performance. In this study, we examine the role of the schedule in round-robin tournaments with sequential games between three and four contestants. Our empirical analysis, based on soccer FIFA World Cups and UEFA European Championships, and on two Olympic wrestling events, reveals that there is a substantial advantage to the contestant who competes in the first and third matches. Our findings are in line with the hypothesis that winning probabilities in multi-stage contests with sequential games are endogenously depending on the schedule of contests as predicted by game-theoretical models. We also discuss possible ways to reduce the effect of the schedule.

Introduction

The effect of possible future actions on current performance in sequential contests is a standard object of interest in game theory. Such effects are usually shown by backward induction (Aumann, 1995, Klumpp and Polborn, 2006, Sheremeta, 2010, Groh et al., 2012; among many others). According to this procedure, every agent deduces backward from the end of a situation to determine a sequence of optimal actions. In most studies backward induction is studied in laboratory settings (Palacios-Huerta and Volij, 2009, Ryvkin, 2011, Deck and Sheremeta, 2012).2 The laboratory setting is chosen, because it is quite challenging to identify the causal effects of different orders of actions in real-life situations, mostly because in the majority of cases there is uncertainty about the exact order of future actions, tasks and the related opponents. In this paper, in order to overcome these obstacles, we take advantage of two real-life contests with high rewards in which all contestants have full information about future actions and previous outcomes.

Moreover, in one of the contests analysed in this paper, the treatment and the control groups were determined via explicit randomisation, which simplifies credible causal inference substantially (Manski, 1995). Although in the second type of contests there is a deviation from randomisation, we observe the factors underlying the deviation from randomness and control for them in the empirical analysis.

We ask a simple question: Does the order of actions affect the probability of success? In other words, we analyse whether the probability of success depends on the schedule of the contest. More specifically, we investigate whether the order of matches in the group stage of important sporting events affect the probability to qualify for the next stage. To that end, we study two very different sports. The first is an individual sport, wrestling, where the groups in the Olympic tournaments are composed of three wrestlers. The second is a team sport, soccer, where the groups in the FIFA World Cup and the UEFA European Championship are composed of four teams. These group stages are organized as round-robin tournaments in which each contestant (individual or team) competes against all the others in sequential games.3

It is important to note that applying data from professional sports, where contestants have strong incentives to win, has several advantages. First, it eliminates possible scepticism about applying behavioural insights obtained in a laboratory to real life (Hart, 2005, Levitt and List, 2008, Palacios-Huerta and Volij, 2009). Second, (professional) sports contests involve high-stake decisions familiar to agents. Third, they provide an opportunity to observe and measure performance as a function of heterogeneity in abilities and prizes, for example. Fourth, in each point of time, round-robin settings provide the contestants with complete information on the future order of games and the state of the tournament. Thus, according to Kahn (2000), sports data is unique in that no other setting provides researchers with such detailed information about those theoretically important issues.4

As already mentioned above, for wrestling, we observe random contests that occurred in the Greco-Roman and freestyle wrestling Olympic tournaments in Sydney 2000 and in Athens 2004. Our results indicate that a wrestler who competes in the first and the third matches has a significantly higher probability to win the group than the other contenders have. The advantage of such a favourable schedule on the qualifying (success) probability is approximately 10%-points.

For the case of soccer, we utilized data on all the group stages from all the FIFA World Cups and UEFA European Championships from 1996 to 2014. These tournaments are the most prestigious soccer tournaments that involve the best soccer nations.5 Our econometric analysis is based on propensity score matching to remove possible confounding. It reveals a large and significant first mover advantage. We find that a team that plays in the first match of each round, namely in the first and the third matches, has a higher probability to qualify for the next stage than the other teams. The effect of this schedule on the qualifying probability is on average 17%-points, which is relatively large. The results are robust to different specifications as well as to controlling for possible confounders such as teams’ rankings, home advantage, seeding, rest hours and distances between cities in which the matches took place.

Our results are in line with a recent theoretical study of Krumer et al. (2017). They modelled each match as an all-pay contest. Based on backward induction analysis and given their setting, they showed that in round-robin tournaments among three or four symmetric contestants, there is a first-mover advantage driven by strategic effects arising from the subgame perfect equilibrium. More specifically, they found that a contestant who competes in the first and third matches has the highest probability to win the first match as well as the entire round-robin tournament.6 The intuition behind their result is that a contestant who competes before the others has an advantage because winning an early game affects the continuation value of winning and losing of other contestants. As a result, a contestant who competes first has on average a higher continuation value of winning than the other contestants.

Several alternative explanations of our result include asymmetry in fatigue or psychological states that may stem from the schedule during the tournament. We nevertheless find that a wrestler or a soccer team that competes in the first and the third matches has a significantly higher winning probability already in the first match when contestants are supposed to be symmetric with regard to fatigue or psychological states. A possible mechanism behind this result, as described by Krumer et al. (2017), is that, for example in the specific three contestants’ case, a contestant who competes in the first and third matches has a positive probability that his opponent in the third round lost his previous match. However, a contestant who competes in the first two matches has to compete in both rounds against contestants who still have not lost a single match. This allocation creates an asymmetry in the continuation values of winning already in the first game, such that even in the asymmetric case a weaker contestant may have the highest probability to win the contest and the dominant contestant's probability is considerably lower if he does not compete in the first and the third matches (Krumer et al., 2016). Therefore, even in the a priori symmetric case, a win in the first game changes contestants’ continuation values of winning, whether they compete against the winner in the next round or not. As a result, a contestant who competes in the first and the third matches has a higher continuation value of winning and a higher probability to win the contest than his or her opponents do.

For wrestling, we also investigate the results along the path of each contestant during the tournament. We compare the results obtained with the theoretical predictions of Krumer et al. (2017). We find that in six out of seven possible cases, the theoretical model correctly predicts the identity of the wrestler who has the higher probability to win.

This paper also contributes to the literature on the effect of scheduling on individual and team performance in competitive environments. Although our findings are in line with certain theoretical predictions of models dealing with the strategic allocation of effort, we cannot rule out additional psychological motives that may affect performance in tournament settings. Previous studies highlighted the possible role of different psychological motives on performance driven by scheduling, such as memory related issues (De Bruin, 2005, Page and Page, 2010) or psychological momentum (Krumer, 2013, Cohen-Zada et al., 2017). In addition, the round-robin structure may create an asymmetry in interim rankings, because some competitors may have a different number of games at different stages of the tournament. This in turn may create ahead-behind asymmetry which leads to an advantage for one of the contestants (Apesteguia and Palacios-Huerta, 2010, Genakos and Pagliero, 2012, Palacios-Huerta, 2014, Genakos et al., 2015, González-Díaz and Palacios-Huerta, 2016).

In any case, our results, obtained in two different sport settings, increase the evidence for the claim that winning probabilities are endogenously determined as they depend on the structure of the particular contest. Therefore, our findings also have implication for contest design in general, since we show that in the usual round-robin structure the probability of success depends on the schedule. This may raise questions about alternative tournament structures in which success or failure only depend on players’ innate abilities and not on the schedule. Such alternatives are relevant to tournaments with a round-robin structure. This in particular applies to mega-events, such as the FIFA World Cup, the UEFA European Championship and the Olympic Games whose economic, cultural and political significance is enormous. For example, 3.6 billion viewers around the globe watched the 2012 London Olympic Games and 3.2 billion viewers watched the 2014 FIFA World Cup.7 Not surprisingly, the outcomes of these mega-events have a large effect on various important aspects of life. For example, the World Cup qualification match between El Salvador and Honduras was a build-up for the so-called “Football War” between the two countries in 1969. Russia initiated the annexation of Crimea three days after the most successful sports event for Russian athletes ever, the 2014 Winter Sochi Olympic Games. Furthermore, Edmans et al. (2007) found that a loss in the World Cup leads to a next-day abnormal lower stock return in the losing country.

Finally, note that one possible interpretation of our results is that the round-robin structure is intrinsically unfair. This is because the choice of effort and as a result the probabilities of qualifying for the next stage depend on the schedule. However, Konow (2003) suggested that “differences owing to birth, luck and choice are all unfair and that only differences attributable to effort are fair” (p. 1207). In this case, if players choose to allocate efforts in a strategic way, the claim about unfairness of the round-robin structure may be arguable. Nevertheless, in the concluding remarks we discuss possible ways to mitigate or even eliminate the effect of the schedule on the qualifying probabilities.

The remainder of the paper is organized as follows: Section 2 describes the theoretical framework of the round-robin tournaments. The description and the empirical results for wrestling are presented in Section 3. Section 4 describes the settings and the results for soccer. Finally, in Section 5 we offer concluding remarks.

Section snippets

Theoretical framework of round-robin tournaments

A round-robin tournament is a multi-stage tournament in which the number of contestants is n > 2. If n is even, then in each of the (n1) rounds, n2 games take place, and if n is odd, there will be n rounds with n12 games in each round, with each contestant resting in one of the rounds.

Description of the setting

For round-robin tournaments with three contestants, we found a unique case where contestants were allocated into groups randomly with one winner who qualified for the next stage to compete for the medals. This case occurred in two wrestling Olympic tournaments in Sydney 2000 and Athens 2004. According to the Official report of the XXVII Olympiad Sydney 2000 Olympic Games (Sydney Organising Committee for the Olympic Games, 2001): "…Wrestlers were paired off for each round according to the

Soccer tournaments

In addition to the wrestling case, which is an individual sport, we present another interesting setting that involves teams, where one team is always a first mover, which may affect other contestants’ valuations. Among others, this case appears in group stages of mega-events such as the soccer FIFA World Cups and UEFA European Championships.

Conclusion

The goal of game theory is to understand and predict what should happen in strategic environments (Kreps, 1990). However, in most cases, the reality is too complicated and does not allow matching the real-world data to the theoretical predictions. In this study, we use a unique opportunity to test the theoretical prediction of the first mover advantage that arises from a subgame perfect equilibrium. In a randomised group stage of three contenders in wrestling, whose settings resemble the

References (44)

  • R.M. Sheremeta

    Experimental comparison of multi-stage and one-stage contests

    Games Econ. Behav.

    (2010)
  • J. Apesteguia et al.

    Psychological pressure in competitive environments: evidence from a randomized natural experiment

    Am. Econ. Rev.

    (2010)
  • M.R. Baye et al.

    The all-pay auction with complete information

    Econ. Theory

    (1996)
  • H. Bodory et al.

    The Finite Sample Performance of Inference Methods For Propensity Score Matching and Weighting Estimators

    (2016)
  • S.J. Brams et al.

    Making the rules of sports fairer

    SIAM Rev.

    (2017)
  • W.B. De Bruin

    Save the last dance for me: Unwanted serial position effects in jury evaluations

    Acta Psychol.

    (2005)
  • E. Dechenaux et al.

    A survey of experimental research on contests, all-pay auctions and tournaments

    Exp. Econ.

    (2015)
  • C. Deck et al.

    Fight or flight? Defending against sequential attacks in the game of siege

    J. Conflict Resolut.

    (2012)
  • A. Edmans et al.

    Sports sentiment and stock returns

    J. Financ.

    (2007)
  • L. Garicano et al.

    Favoritism under social pressure

    Rev. Econ. Stat.

    (2005)
  • C. Genakos et al.

    Interim rank, risk taking, and performance in dynamic tournaments

    J. Polit. Econ.

    (2012)
  • C. Groh et al.

    Optimal seedings in elimination tournaments

    Econ. Theory

    (2012)
  • Cited by (0)

    This paper is a substantially revised version of “First in first win: evidence on unfairness of round-robin tournaments in mega-events,” SEPS, University of St. Gallen Discussion Paper no. 2016-11, July 2016. The paper was presented at the 20th annual meeting of the AK Sportökonomie 2016 in Tübingen, Oligo 2017 workshop in Moscow and in Contests: Theory and Evidence 2017 Conference in Norwich. We thank participants as well as editor and three anonymous referees for helpful comments and suggestions. The usual disclaimer applies.

    1

    Michael Lechner is also affiliated with CEPR, London, CESIfo, Munich, IAB, Nuremberg, IZA, Bonn, and RWI, Essen.

    View full text