Despite it’s name, the field of game theory has had for a long time a somewhat weaker relationship with sports and games in general – although it has always been more advanced than other fields in economics with regards to its closeness to sports and games. In its early days, game theory was mostly occupied with big and more serious topics than sports and games, such as industrial organization in economics, wars and other military issues in political sciences. The reason behind this development in the early days of game theory might be due the fact that this field kind of been developed through turbulent times of World War II and Cold War – for example (e.g.) „prisoner’s dilemma“ within the nuclear arms race between USA and Russia (back then USSR).
Lately though there has been some development in the game theory within other fields, like sports and games, especially football, books like "The economics of football" (2001) and "Soccernomics" (2012) are good starting points into the subject. While these books generally inquire help from economics to explain football’s issues, Apesteguia and Palacios-Huerta (2010) (and Palacios-Huerta (2014)) gives priority to illustrate how football can help economics (the other way around).
Table of Contents
1. Introduction
2. Literature Overview
3. Causal Effect, Identification and Randomization
3.1. Modeling Causal Effect and Randomization
3.2. Conclusion
4. Binomial Regression
4.1. Linear Probability Model
4.2. Non-Linear Models
4.2.1. Probit
4.2.2. Logit
4.2.3. Conclusion
5. The Data-sets, Variables and it’s Statistics
6. Regressions
7. Conclusion
Research Objectives and Focus
This paper aims to empirically replicate the findings of Apesteguia and Palacios-Huerta (2010) to determine if there is a psychological advantage for the team that shoots first in a penalty shootout, potentially leading to a higher win probability.
- Application of binomial regression using the statistical software R.
- Evaluation of potential improvements and model specifications beyond original research.
- Analysis of the impact of various factors like home field, past team experience, and competition type.
- Discussion of causality, randomization, and identification within the context of penalty shootouts.
- Critical review of existing literature and debate regarding data consistency and selection bias.
Excerpt from the Book
3.1. Modeling Causal Effect and Randomization
Let D ∈ {0, 1} denote the treatment indicator, defining YiD as the outcome a certain observation i has had, with Yi1 as being subjected to the treatment and Yi0 as not. Therefore, the difference between both outcomes, Yi1 − Yi0, would yield the treatment effect that this certain observation i experienced. Furthermore, lets define X as a set of observed characteristics.
Now, ex-ante both potential outcomes are defined, but at the moment an observation i decides to take the treatment (or not), one of the two outcomes is revealed, but the other outcome stays unobserved, which then make the calculation of the actual treatment effect for the observation i impossible (Yi1 − Yi0), since either one or the other outcome value for i is unknown.
This fact hinders the observation and calculation of the treatment effect for the observation i. Well, one could achieve a good approximate to the treatment effect value of i, by calculating the expected average of the treatment effect a certain treated group from the same (drawn) population (distribution) of i, and this can be defined as the Average Treatment Effect of the Treated (ATT).
Summary of Chapters
1. Introduction: Outlines the research objective to empirically investigate if starting a penalty shootout provides a psychological advantage using binomial regression.
2. Literature Overview: Reviews existing studies on penalty shootouts, highlighting the initial findings of an advantage for the starting team and subsequent academic debates.
3. Causal Effect, Identification and Randomization: Explains the theoretical foundations of causal inference, focusing on how treatment effects are identified through randomization.
4. Binomial Regression: Discusses the methodology for regressing binary dependent variables, covering the Linear Probability Model as well as Probit and Logit models.
5. The Data-sets, Variables and it’s Statistics: Presents the dataset used for the analysis, including descriptive statistics of kicks and shootouts across different competitions.
6. Regressions: Details the empirical results of various logit models, testing the significance of the first-mover advantage while controlling for additional variables.
7. Conclusion: Summarizes the study's findings, acknowledges data limitations, and discusses potential reforms to the penalty shootout system to ensure greater fairness.
Keywords
Game Theory, Penalty Shootouts, Binomial Regression, Logit Model, Causal Effect, Randomization, Psychological Advantage, FIFA, Sports Economics, Empirical Analysis, Treatment Effect, Data Consistency, Selection Bias, Statistical Software R, Winning Probability
Frequently Asked Questions
What is the primary objective of this research paper?
The paper seeks to empirically verify whether teams that start a penalty shootout enjoy a psychological advantage that increases their probability of winning the match.
What are the core thematic areas covered in the study?
The study centers on sports economics, specifically applying econometric methods like binomial regression to game theory applications in football penalty shootouts.
Which specific research question does the author address?
The research question is whether the team starting the penalty shootout has a statistically significant higher probability of winning compared to the team shooting second.
What scientific methods are utilized for the analysis?
The author uses binomial regression, specifically the Logit model estimated via Maximum Likelihood Estimator (MLE), and discusses causality and identification strategies like randomization.
What is the focus of the main body of the work?
The main body bridges the theoretical framework of causal effects with the empirical application of logit regressions, including detailed dataset analysis and model testing.
Which keywords best characterize this research?
Key terms include Game Theory, Penalty Shootouts, Logit Model, Causal Effect, Randomization, and Sports Economics.
How does the author handle potential bias in the regression models?
The author addresses potential omitted variable bias by incorporating various control variables, such as home-field advantage and team experience, and by performing joint significance tests like the Wald-Test.
What does the author conclude regarding the 'first-mover advantage'?
The results generally support the existence of a first-mover advantage, consistently showing that starting teams win roughly 60% to 67% of shootouts depending on the model specification.
- Citar trabajo
- Felipe Mannshardt Oliveira (Autor), 2016, Unfairness in Penalty. Modeling the Psychological Advantage of Starting the Shootouts, Múnich, GRIN Verlag, https://www.grin.com/document/356898
