1. 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 1 Incentives in Tournaments with Heterogeneous Agents: Empirical Evidence from the German “Bundesliga” Bernd Frick and Joachim Prinz University of Paderborn bernd.frick@notes.upb.de joachim.prinz@wiwi.uni-paderborn.de Oliver Gürtler University of Bonn oliver.guertler@uni-bonn.de

2. Structure of the Presentation 1.Motivation 2.Related Literature 3.The Model 4.Data and Hypothesis 5.Estimation and Empirical Findings 6.Summary and Implications 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 2

3. 1. Motivation (I) -Tournaments are an important element of firms’ incentive systems: -Promotion tournaments are used to identify the most talented employee(s) -“Bonus pools” are offered to motivate the most productive em- ployee(s). -Theory suggests that tournaments can be effective only if the con- testants are homogeneous. In tournaments with heterogeneous par- ticipants the underdog will soon recognize that he has no chance to win and will, therefore, reduce his effort. The favorite’s best respon- se is to reduce his effort, too. Thus, the incentive effects of tourna- ments are likely to “disappear” … 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 3

4. 1. Motivation (II) The design of tournaments -prizes are fixed in advance and independent of absolute performan- ce - a player receives the winner’s prize not by being good, but by being better than the other player -the level of effort of each player depends on the size of the potential increase in his wage -since the optimal amount of effort is not infinite, there is a limit to the prize spread. -The average prize money must be high enough to attract contest- ants to enter the tournament in the first place 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 4

5. 1. Motivation (III) -larger prize spreads not only induce higher effort levels, but may also result in a “rat race” -collusion is less likely, if the number of contestants is high as an agreement to slack off is difficult to enforce -the higher the noise in the tournament (“luck”, production uncertain- ty and measurement error), the lower the level of effort -the more important luck is in determining the winner, the larger the spread has to be -tournaments serve a sorting function as well as an incentive function 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 5

6. 1. Motivation (IV) -advantage of using relative performance as measure of effort -lower measurement costs -elimination of the effect of luck on reward Problem to be addressed in our empirical analysis -efforts suffer when heterogeneous contestants compete with each other. Effort has the largest effect on changing the probability of winning when the contestants are of similar ability. If ability differs among contestants, then both the less able and the more able tend to slack off. 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 6

7. 1. Motivation (V) -to maintain high levels of effort, it is important to group contestants so that, at least at the outset, participants feel they are (more or less) evenly matched with those against whom they will directly compete for the tournament prize. -when contestants are (too) heterogeneous not even a highly skewed prize money distribution will motivate well, because contestants who feel that they have no chance of winning the tournament will give up early. - Our paper is the first to test this hypothesis in the context of a pro- fessional team sports league, the German “Bundesliga”. 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 7

8. 1. Motivation (VI) “It is difficult to observe the effects of tournament-like pay structures on effort because in cases where tournaments are used, neither effort nor output is easily observed. If effort or output could be observed easily, then the case for using a relative performance- based incentive scheme would be diminished. There is, however, one arena in which output is easily measured and in which the tournament pay structure is explicit – professional sports” (Lazear 1998: 241). 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 8

9. 2. Related Literature 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 9 Author(s) and Year of Publication DataFindings Ehrenberg and Bognanno (1990) GolfBetter player are motivated by other good players; weaker players are demotivated by the presence of good players. Lynch (2005)Horse RacingThe farther away the next opponent is, the smaller the effort level of the respective jockey. Lynch and Zax (2000)Middle- and Long-Distance Running Tournaments do not have incentive effects, but only selection effects. Frick and Klaeren (1997)Marathon (Men and Women) If contestants are homogeneous, additional bonus pay- ments induce higher effort levels, if the are heteroge- neous, bonus payments do not work at all.. Sunde (2003)Tennis (Men)In matches with heterogeneous players the underdog exerts more effort. Lallemand, Plasman und Rycx (2005) Tennis (Women)In matches with heterogeneous players the weaker athlete is less motivated.

10. 3. The Model (I) N (1)y i = Σ e ij + a i + ε i i=1 (2)U i = U(I i ) - C(e i ) (3) Prob {Σ e 1j + a 1 + ε 1 > Σ e 2j + a 2 + ε 2 } = Prob {ε 2 - ε 1 < Σ e 1j - Σ e 2j + a 1 - a 2 } =: G(Σ e 1 - Σ e 2 + a 1 - a 2 ) 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 10

11. 3. The Model (II) (4)EU 1j = U(w 2 ) + G(Σ e 1j - Σ e 2j + a 1 - a 2 ) (U(w 1 ) – (U(w 2 )) – C(e 1 ) and (5)EU 2j = U(w 2 ) + [1 - G (Σ e 1j - Σ e 2j + a 1 - a 2 )] (U(w 1 ) - U(w 2 )) - C(e 2j ) 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 11

12. 3. The Model (III) δEU 1j (6) ________ = g (Σ e 1j - Σ e 2j + a 1 - a 2 ) * (U(w 1 ) - U(w 2 )) - C´(e 1j ) = 0 δe 1j δEU 2j (7) ________ = g (Σ e 1j - Σ e 2j + a 1 - a 2 ) * (U(w 1 ) - U(w 2 )) - C´(e 2j ) = 0 δe 2j (8)g (a 1 – a 2 ) * (U(w 1 ) – U(w 2 )) = C´(e) 02.12.2015 12 Bernd Frick, Oliver Gürtler, Joachim Prinz

13. 3. The Model (IV) Result 1: The optimal level of effort of both contestants is strictly decreasing in |a 1 - a 2 | 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 13

14. Figure 1 Talent Difference and Optimal Effort Level Effort Level Talent Difference 02.12.2015 14 Bernd Frick, Oliver Gürtler, Joachim Prinz

15. 4. Data and Hypothesis (I) 756 matches played in the seasons 1998/99 (n=144), 1999/2000 (n=306) and 2000/01 (n=306) Match and referee characteristics as well as betting odds (Oddset) - age of referee - body mass index - FIFA-referee (0=no; 1=yes) - goals scored by home and away team - attendance - score after 45 minutes 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 15

16. 4. Data and Hypothesis (II) We use two different, yet related measures of heterogeneity of the contestants: HET 1 = |ODDS_H – ODDS_A| HET 2 = |ODDS_H 2 - ODDS_A 2 | The larger the heterogeneity between the two competing teams (HET), the smaller the “intensity” of the match, i.e. the smaller the number of cards (CARDS). 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 16

17. Figure 2 Number of Disciplinary Sanctions (I) Number of Matches Number of Yellow Cards and Total Number of Cards 02.12.2015 17 Bernd Frick, Oliver Gürtler, Joachim Prinz

18. Figure 3 Number of Disciplinary Sanctions (II) Number of Matches Number of Yellow / Red and Red Cards 02.12.2015 18 Bernd Frick, Oliver Gürtler, Joachim Prinz

19. Figure 4 Kernel Density Estimate of HET 1 and HET 2 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 19

20. 5. Estimation and Empirical Findings (I) The model is of the following general form: CARDS = α 0 + α 1 AGE + α 2 AGE 2 + α 3 BMI + α 4 FIFA + α 6 H_G + α 7 A_G + α 8 ATT + α 9 ATT 2 + α 10 HTS + α 11 DER + α 12 HET + ε Count data model controlling for unobserved referee-specific effects (Negbin Model with Random and Fixed Effects). 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 20

21. Table 1 Intensity Measures 02.12.2015 21 Bernd Frick, Oliver Gürtler, Joachim Prinz

22. Table 2 Control Variables 02.12.2015 22 Bernd Frick, Oliver Gürtler, Joachim Prinz

23. Table 3 Betting Odds 02.12.2015 23 Bernd Frick, Oliver Gürtler, Joachim Prinz

24. 5. Estimation and Empirical Findings (II) 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 24

25. 5. Estimation and Empirical Findings (III) 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 25

26. 6. Summary and Implications (I) -Using a unique data set from the top tier in German professional football we demonstrate that the effort levels of the two teams in a single match are significantly lower when the teams are heteroge- neous. -Our measure of “match intensity” is the number of disciplinary sanc- tions, the measure of heterogeneity is the (squared) difference in the respective betting odds. -So far, we have looked at “destructive efforts” only. In further re- search we will, of course, also look at “constructive efforts”. 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 26

27. 6. Summary and Implications (II) -Next steps include -International comparison with data from the other four top lea- gues in Europe (England, Italy, France and Spain) -Adding controls for the market values of the teams at the start of the respective season. 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 27

28. Literature Chevalier, J., and G. Ellison (1997): Risk Taking by Mutual Funds as a Respon- se to Incentives. Journal of Political Economy, 105, pp. 1167-1200 Clark, D. and C. Riis (2001): Rank-Order Tournaments and Selection. Journal of Economics, 73, pp. 167-191 Kräkel, M. and D. Sliwka (2004): Risk Taking in Asymmetric Tournaments. Ger- man Economic Review, 5, pp. 103-116 Lazear, E. (1998): Personnel Economics for Managers, New York: Wiley Lazear, E. and S. Rosen (1981): Rank-Order Tournaments as Optimum Labor Contracts. Journal of Political Economy, 89, pp. 841-864 Schotter, A. and K. Weigelt (1992): Asymmetric Tournaments, Equal Opportu- nity Laws, and Affirmative Action: Some Experimental Results, in: Quarterly Journal of Economics, 107, pp. 511-539 02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 28