“The ball is round, the game lasts 90 minutes, everything else is pure theory”

Abstract

We model a soccer match between two heterogeneous teams as a two-stage contest where each team chooses its attacking and defending effort for each half of the match. We characterize the optimal teams’ efforts as well as the optimal effort allocation between offense and defense. In contrast to the theoretical literature on soccer we show, for example, that the leading team may preempt its competitor in the first half. Our analysis also sheds new light on empirical studies that investigate the change in winning points on the number of ties by showing that this effect depends crucially on teams’ heterogeneity.

Competitive Balance and the Away Goals Rule During Extra Time

“…17. For this and the following proofs we omit to show that the second order conditions are satisfied: These proofs are similar to the ones in Jost (2021a).…”

“…Since the second leg is on the home court of Team 1, it benefits during extra time from its home-field advantage so that its marginal effort cost are lower than the one of Team 2. Similar to Jost (2021a) we model this home-field advantage by assuming that the marginal effort cost of Team 1 are 1 − b 1 , b 1 < 1, whereas Team 2 as the away team suffers from Team 1's home-field advantage and has marginal effort cost of 1 + b 1 . We interpret b 1 as the degree of Team 1's home-field advantage.…”

“…The present paper is the first that analyzes the away goals rule in a game-theoretical framework. Related literature on how to model a soccer match is provided in Jost (2021a). 9.…”

“…6 The aim of the present article is to discuss these arguments and the pros and cons for the away goals rule during extra time in a game-theoretical model. Our analysis builds on the papers by Jost (2021aJost ( , 2021b. In the first paper, Jost (2021a), a soccer match between two teams is interpreted as a two-stage contest, where each team chooses its attacking and defending effort for each half of the match.…”

“…Our analysis builds on the papers by Jost (2021aJost ( , 2021b. In the first paper, Jost (2021a), a soccer match between two teams is interpreted as a two-stage contest, where each team chooses its attacking and defending effort for each half of the match. 7 The present paper follows this approach and interprets teams' play during extra time as a match with two halves.…”