02.12.2015 Bernd Frick, Oliver Gürtler, Joachim Prinz 1 Incentives in Tournaments with...

18.04.23 Bernd Frick, Oliver Gürtler, Joachim Prinz 1

Incentives in Tournaments with Heterogeneous Agents:

Empirical Evidence from the German “Bundesliga”

Bernd Frick and Joachim PrinzUniversity of Paderborn

[email protected]@wiwi.uni-paderborn.de

Oliver GürtlerUniversity of Bonn

[email protected]

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


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” …


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


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


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.


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”.


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).


2. Related Literature


Author(s) and Year of Publication

Data Findings

Ehrenberg and Bognanno (1990)

Golf Better player are motivated by other good players; weaker players are demotivated by the presence of good players.

Lynch (2005) Horse Racing The 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.

3. The Model (I)

N

(1) yi = Σ eij + ai + εi

i=1

(2) Ui = U(Ii) - C(ei)

(3) Prob {Σ e1j + a1 + ε1 > Σ e2j + a2 + ε2} =

Prob {ε2 - ε1 < Σ e1j - Σ e2j + a1 - a2} =:

G(Σ e1 - Σ e2 + a1 - a2)


3. The Model (II)

(4) EU1j = U(w2) + G(Σ e1j - Σ e2j + a1 - a2) (U(w1) – (U(w2)) – C(e1)

and

(5) EU2j = U(w2) + [1 - G (Σ e1j - Σ e2j + a1 - a2)] (U(w1) - U(w2)) - C(e2j)


3. The Model (III)

δEU1j

(6) ________ = g (Σ e1j - Σ e2j + a1 - a2) * (U(w1) - U(w2)) - C´(e1j) = 0 δe1j

δEU2j

(7) ________ = g (Σ e1j - Σ e2j + a1 - a2) * (U(w1) - U(w2)) - C´(e2j) = 0 δe2j

(8) g (a1 – a2) * (U(w1) – U(w2)) = C´(e)

18.04.23 12Bernd Frick, Oliver Gürtler, Joachim Prinz

3. The Model (IV)

Result 1:

The optimal level of effort of both contestants is strictly decreasing in |a1 - a2|


Figure 1Talent Difference and Optimal Effort Level

Effort Level

Talent Difference


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


4. Data and Hypothesis (II)

• We use two different, yet related measures of heterogeneity of the contestants:

• HET1 = |ODDS_H – ODDS_A|

• HET2 = |ODDS_H2 - ODDS_A2|

• 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).


Figure 2Number of Disciplinary Sanctions (I)

0 1 2 3 4 5 6 7 8 9 10 11 130

20

40

60

80

100

120

140

160

180

Numberof Matches

Number of Yellow Cards and Total Number of Cards


Figure 3Number of Disciplinary Sanctions (II)

Number of Matches

Number of Yellow / Red and Red Cards


Figure 4Kernel Density Estimate of HET1 and HET2


01

23

4D

ensity

0 .2 .4 .6HET

HET_1 HET_2

5. Estimation and Empirical Findings (I)

• The model is of the following general form:

CARDS = α0 + α1 AGE + α2 AGE2 + α3 BMI + α4 FIFA +

α6 H_G + α7 A_G + α8 ATT + α9 ATT2 + α10 HTS +

α11 DER + α12 HET + ε

• Count data model controlling for unobserved referee-specific effects (Negbin Model with Random and Fixed Effects).


Table 1Intensity Measures

Variable Mean Min Max YELLOW Number of yellow cards per

match 4,21 0 10

YELLOW / RED Number of yellow/red cards per match

0,16 0 3

RED Number of red cards per match 0,10 0 2 CARDS Total number of cards 4,48 0 13 CARDSw Weighted total number of cards

per match CARDS = ((yellow * 1) + (yellow/red * 3) + (reds * 5))

5,23 0 23


Table 2Control Variables

AGE Age of Referee 38,25 29 46 HEIGHT Size of Referee (in m) 1,84 1,75 1,96 WEIGHT Weight of Referee (in kg) 78,1 68 90 BMI Body Mass Index (kg/m2) 22,8 19,8 23,8 H_G Goals scored by home team 1,71 0 6 A_G Goals scored by away team 1,15 0 10 ATT Attendance 31532 5000 76000 DERBY Match is a derby (for example

Schalke vs. Dortmund) 0,04 0 1

HTS Goal difference at half-time 0,81 0 5


Table 3Betting Odds

Variable Mean Min. Max. ODDS_H Odds of home win 1,89 1,15 4,45 ODDS_A Odds of away team 3,35 1,45 8,55 ODDS_D Odds of draw 2,91 2,55 4,20


5. Estimation and Empirical Findings (II)


Model 1 (HET_1) Model 2 (HET_2) Variable NEGBIN-RE NEGBIN-FE NEGBIN-RE NEGBIN-FE

HET_1 -0,61261 (-4,46)***

-0,59884 (-4,44)***

/ /

HET_2 / / -0,81508 (-4,54)***

-0,79800 (-4,52)***

McFadden_R2 0,032 0,011 0,033 0,011 Wald χ2 22,18*** 21,61** 22,88*** 22,33*** Hausman-Test 1,46+ 1,38+ N of Cases 756 756

5. Estimation and Empirical Findings (III)

NEGBIN_RE Variable YELLOW YELLOW /

RED RED

HET_2 -0,57073 (-3,25)***

-2,11440 (-2,48)***

-0,59788 (-0,57)+

McFadden_R2 0,056 0,098 0,023 Wald χ2 16,43* 17,24** 8,48+ LL -1561,25 -342,79 -258,82 N of Cases 756 756 756


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”.


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.


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: WileyLazear, E. and S. Rosen (1981): Rank-Order Tournaments as Optimum Labor

Contracts. Journal of Political Economy, 89, pp. 841-864Schotter, 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


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