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An Analysis of Loss Aversion and Reference-Dependent Preferences in the NFL

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An Analysis of Loss Aversion and Reference-Dependent Preferences in the NFL Splitting the Uprights: An Analysis of Loss Aversion and Reference-Dependent Preferences in the NFL Patrick Burke - 11373350 August 2017 Abstract Critics of behavioral literature maintain that behavioral biases and nonstandard preferences disappear in competitive markets. In this analysis1, the goal is to assess whether loss aversion and reference dependent preferences persist in the National Football League (NFL). Models with reference-dependent preferences around a fixed reference point imply that players would exert additional effort to avoid falling into the loss domain. This paper provides suggestive evidence that NFL kickers exhibit these tendencies, using field goal attempts in the 2015 and 2016 seasons. Kickers improve their performance when they are kicking while their team is losing. As their teams fall further behind in a game, kicker performance increases - suggesting that they slightly exhibit reference-dependent preferences around a tie game. University of Amsterdam MSc Economics: Behavioural Economics and Game Theory MSc ECO - 15 ECTS 1, I would like to thank my thesis supervisor Arthur Schram for guidance and support during the process of writing this thesis. Statement of Originality This document is written by Patrick Burke who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents. Table of Contents 1. Introduction 2. Institutional Background 2.1 American Football and the National Football League 2.2 Field Goals 3. Literature Review 3.1 Prospect Theory and Loss Aversion 3.2 Prospect Theory in Sports 4. Methodology 4.1 Conceptual Framework 4.2 Data 4.3 Empirical Strategy 5. Results 5.1 General Results 5.2 Initial Regression 5.3 Second Regression 5.4 Third Regression 5.5 Discussion of Results & Limitations 6. Conclusion 7. Appendix 8. References Summary of Tables and Figures Figures Figure 1: NFL Field Dimensions (Appendix) Figure 2: Prospect Theory – Loss Aversion around Reference Point Figure 3: Prospect Theory – Field Goals applied to Reference Point Figure 4: Field Goal Attempts by Quarter (Appendix) Figure 5: Predicted Probabilities of Field Goals by Distance Figure 6: First Regression - Margins – Predicted Probability by Score Margin Figure 7: Second Regression – Margins – Predicted Probability: Winning Vs. Losing Figure 8: Third Regression – Margins – Predicted Probability: Score Margin (5 Groups) Tables Table 1: NFL Field Rules (Appendix) Table 2: Predicted Probability of Field Goals by Distance (Appendix) Table 3: Summary Statistics Table 4: Regression and Score Margin Variable Summary Table 5: Field Goals by Distance Table 6: Field Goal Success and Average Distance – Winning, Losing, Tied Domains Table 7a: Initial Regression – Score Margin as Continuous Variable (Odds Ratios) Table 7b: Initial Regression – Score Margin as Continuous Variable Coefficients (Appendix) Table 8: Second Regression – Effect of Score Margin on Likelihood of Field Goal – Winning vs. Losing – Odds Ratios (Appendix) Table 9: Third Regression - Effect of Score Margin on Likelihood of Field Goal – Five Groups - Odds Ratios (Appendix) Table 10: Summary of Predictions "I hate to lose more than I love to win." -Jimmy Connors, former #1 ranked tennis player in the world 1. Introduction Behavioral economics has provided researchers the tools to analyze markets, games, and models while taking psychological underpinnings into account. Due to the emergence of this field, a substantial amount of literature has demonstrated ways in which agents consistently violate classical economic theory (Camerer, Loewenstein, and Rabin, 2004). While these violations may have implications in the real world, most behavioral anomalies have been observed solely in laboratory experiments. Even the most renowned behavioral economists believe that the primary challenge for the field is extending these findings from the lab to the field (Levitt and List, 2008). Critics of the decision bias literature argue that behavioral biases are likely to disappear in competitive markets with high stakes, and experienced agents. “Individual behavior converges to the neoclassical prediction as experience intensifies...These results provide initial evidence consistent with the notion that market experience eliminates market anomalies” (List, 2003). However, recent works have shown that there is now considerable evidence that biases persist in the field outside of the laboratory (Goldman, 2016; Lien and Zheng, 2015). In their paper, Prospect Theory: An Analysis of Decision Under Risk, Kahneman and Tversky (1979) propose a recurring violation of the normative model of rational choice: loss aversion2. Simply put, losses loom larger than gains. Taking elements from Prospect Theory and extending them to the National Football League (NFL), this paper examines whether reference-dependent preferences and loss aversion persist in this competitive market. The core focus of the analysis is on field goals, a set kicking play that earns the offensive team three points if the kick is successful. Kickers would perform better when they are losing compared to winning if they are loss averse. Also, their performance would vary around the reference point of a tie game - better kicking as their team falls further behind, 2 Many would argue that loss aversion is not a bias but a characteristic of one’s preferences. This paper does not take sides on such issue – and views loss aversion as an element of Prospect Theory. and worse kicking as their team’s lead increases. Studying reference points and loss aversion in sports has advantages. The highly quantified nature provides clear reference points to observe behavior. Using nearly 2,000 field goals attempts from the 2015 and 2016 seasons, this study found for every 1-point increase in the score margin (the score difference between the kicking team and the opponent), the probability that a field goal is successful decreases by 1.5%. Also, kicks attempted when losing the game had up to a 4.2% higher predicted probability of success than a similar field goal while winning. Kickers performed best when losing by a large margin3. The probability of a successful kick was lowest when the team was winning by a large margin, consistent with loss aversion and reference-dependent preferences. Overall, the results suggest that with a larger dataset - and minor adjustments to the model - there may be concrete evidence that loss aversion and reference-dependent preferences persist in the NFL. While this study only finds suggestive evidence of loss aversion in kickers, it does contribute to the existing literature on loss aversion around a reference point in a high stakes market. Some recent theoretical work on reference points has conceptualized expectations as reference points - however, given the difficulty of testing these preferences, there has not been extensive work to test this theory (Abeler, 2011). Outside of the laboratory, it is hard to make a reliable inference about loss aversion since pinning down a reference point can prove to be problematic (Goldman, 2016). This study extends research on reference points and loss aversion by utilizing the zero- sum nature of the NFL to establish a fixed reference point where it is easy to split the space of outcomes into losses and gains. The rest of this thesis proceeds as follows: Section II provides background on the NFL and the role of field goals. Section III introduces previous literature on Prospect Theory, loss aversion, reference points and applications of these elements in the world of sports economics. Section IV provides the conceptual framework, predictions, and defines variables within the data set. Section V gives the results - from initial summary statistics of the kicks to testing the three 3 Large margin considered to be 11 or more points in this paper. 10 points is a scoring margin that is within a field goal and touchdown. 11 points or more implies that more than one touchdown is needed. predictions. Section VI concludes. The appendix contains materials cited throughout the main paper, followed by the references. 2. Institutional Background 2.1 American Football and the National Football League The National Football League (NFL) is the elite men's professional American football league in the world. It is made up of 32 clubs which are split into two conferences: the American Football Conference (AFC) and the National Football Conference (NFC). Each of these conferences has four divisions -North, East, South West - consisting of four teams. Teams are allowed a maximum of 46 active players on the roster. These 32 clubs play against each other for a total of 16 games during the 17-week regular season which spans from the first week of September to the week after Christmas. The 12 teams with the best record advance to the post- season tournament to compete for the Super Bowl - the championship game (NFL). The NFL is a competitive, high stakes market with experienced agents. Players are some of the top performing athletes in the world and competition is fierce as players vie for positions on the rosters and depth charts. Although kickers are not involved in the physicality of the game as much as other players - their performance is vital to winning games. Each team typically has one field goal kicker. Therefore, there is a fine line between job stability and being replaced by another kicker. As NFL coaching legend Buddy Ryan put it, “Football kickers are like taxi cabs. You can always go out and hire another one.” Incentives are high in the NFL; the average salary of kickers is about $1.4 million dollars per year4. NFL games are divided into four 15-minute quarters. The team with the most points at the end of regulation is the winner. If the score is equal at the end of the 4th quarter, the two teams will play an additional 10-minute period.
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