Beautiful Football, Beautiful Economics
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Beautiful Football, Beautiful Economics Ignacio Palacios‐Huerta London School of Economics Ikerbasque Foundation for Science at UPV/EHU X Congreso Iberoamericano de Economía del Deporte Barcelona, June 2019 RESUMEN EJECUTIVO • El enfoque económico es aplicable a todo el comportamiento humano. • Esto significa que cualquier tipo de datos acerca de la actividad humana es potencialmente útil para evaluar teorías económicas. • Y el deporte es, en muchos aspectos, un laboratorio perfecto para tratar de obtener intuiciones novedosas sobre la manera en la que los humanos tomamos decisiones y, en general, sobre el comportamiento humano. • Así pues, más allá del atractivo de los deportes como espectadores, su atractivo para los economistas es que los deportes pueden en ocasiones proporcionar la evidencia empírica necesaria para demostrar por primera vez la validez (o no) de distintas teorías económicas. • Este campo relativamente reciente de la ciencia económica está recibiendo una importante atención entre la literatura especializada. En esta charla se presentan distintos estudios que, tomando como base esta perspectiva, utilizan datos procedentes del deporte (en especial del futbol) para ayudar a la ciencia económica. Part I How Football Can Help Economics Part II … and viceversa: How Economics Can Help Football Part I: How Football Can Help Economics Galileo Galilei 1564‐1642 Sir Isaac Newton 1642‐1727 Galileo and Newton didn’t care aboutfruitsorstones… … they cared about the laws of the universe Thesameistrue in Economics: We do not care where the data comes from We care about good and unique data! “What distinguishes economics as a discipline from other disciplines is not its subject matter but its approach. The economic approach is applicable to all human behavior” Gary S. Becker (Nobel Economics 1991) This means that any type of data about human activity is potentially useful to evaluate economic theories. Sports are in many ways the perfect laboratory for testing economic theories: • There is an abundance of available data. • The objectives of the participants are often clear (e.g., score, win, enforce the rules). • The outcomes are extremely clear. • The stakes are typically high. • The subjects are professionals with experience. “If one of the attractions of sports is to see occasionally universal aspects of the human struggle in stark and dramatic forms, their attraction to economists is to illustrate universal economic principles in interesting and tractable ways” (Rosen and Sanderson, 2001). and “to test and even develop economic theories for the first time.” (Palacios‐Huerta, 2014). Examples: Chapters 1. Pelé Meets Von Neumann: Mixed strategies (in the field) 2. Vernon Smith Meets Messi: Mixed strategies (in the lab) 3. Lessons for Experimental design 4. Neuroconomics: Mixed strategies (in the brain) 5. Psychological Pressure in Competitive Situations 6. The Efficient Market Hypothesis in Financial Markets 7. Social Pressure as a determinant of Corruption 8. Incentives and effort 9. The economics of fear 10. Overcoming Emotions 11. Discrimination in Labor Markets Nash, von Neumann and the Penalty Kick John Nash (1950) generalizes the Minimax Theorem first proven by John von Neumann (1928): “every strategic situation has at least one equilibrium”. In some sense, it was surprising that the key cornerstone theorem in Game Theory, the Minimax Theorem was not verified with real data from human behavior until … 2003! With what data? With data from penalty kicks in football! A penalty in theory: i\j L R L πLL , 1 – πLL πLR , 1 – πLR R πRL , 1 ‐ πRL πRR , 1 ‐ πRR A penalty in reality: i\j kL 1 − kL gL 58, 42 95, 5 1 − gL 93, 7 70, 30 If we solve for the “equilibrium”: 100 100 pgR pgL 94.10 93.10 71.22 59.11 50 50 Prediction: 38,54% 0 1 0.3847 0.5 kL Frequencies predicted by the Nash equilibrium for kickers K 100 100 pkL pkR 94.10 93.10 71.22 59.11 50 50 Prediction: 41,99% 0 0.5 1 gL Frequencies predicted by the Nash equilibrium for goalkeepers G When we compare the theoretical predictions with the real life data (≈11.000 penalties), what do we find? gL 1 − gL kL 1 − kL . Frequencies Nash Equilibrium predicts: 41.99% 58.01% 38.54% 61.46% Frequencies observed in reality: ??? ??? ??? ??? When we compare the theoretical predictions with the real life data (≈11.000 penalties), what do we find? gL 1 − gL kL 1 − kL . Frequencies Nash Equilibrium predicts: 41.99% 58.01% 38.54% 61.46% Frequencies observed in reality: 42.31 ??? ??? ??? When we compare the theoretical predictions with the real life data (≈11.000 penalties), what do we find? gL 1 − gL kL 1 − kL . Frequencies Nash Equilibrium predicts: 41.99% 58.01% 38.54% 61.46% Frequencies observed in reality: 42.31 57.69 ??? ??? When we compare the theoretical predictions with the real life data (≈11.000 penalties), what do we find? gL 1 − gL kL 1 − kL . Frequencies Nash Equilibrium predicts: 41.99% 58.01% 38.54% 61.46% Frequencies observed in reality: 42.31 57.69 39.98 ??? When we compare the theoretical predictions with the real life data (≈11.000 penalties), what do we find? gL 1 − gL kL 1 − kL . Frequencies Nash Equilibrium predicts: 41.99% 58.01% 38.54% 61.46% Frequencies observed in reality: 42.31 57.69 39.98 60.02 Apples do not know the Law of Gravity, but they follow it … Apples do not know the Law of Gravity, but they follow it … … Football players do not know the Nash equilibrium, but they follow it On what Economics do for Football, for example: • Champions League Final 2008 in Moscow (Chelsea‐Manchester United), Soccernomics. • World Cup Final 2010 in South Africa (Holland‐Spain). • World Cup 2018 in Russia (England‐Colombia) • Champions League Final 2019 (Liverpool‐Spurs) • Nations League 2019 (England‐Switzerland) Vernon Smith Meets Messi in the Lab Locating Nash in the Brain From Neuroscience … … to Neuroeconomics Risk aversion Discounting (patience) Uncertainty aversion Backward induction (level k) Time inconsistency Where are “mixed strategies” located in the brain? Recall that these strategies require: 1. Equality of payoffsacrossstrategies 2. Randomization We scanned the brains of people playing a “penalti game” (London, Toledo) 1. Equality of payoffs across strategies z=22 y=30, 42, ‐ x= Activity in the left inferior prefrontal cortex related significantly to the ability to equate payoffs (as measured by the p‐value). Neural activity in this prefrontal region correlated with performance: higher activity in participants who more effectively succeeded in equating payoffs. 2. Randomization z=26 y=46, x=22, A contralateral, right inferior prefrontal region related to the ability to generate random sequences of choices. Neural activity in these regions was correlated with the performance score testing for the randomness of choices using the p‐value of the runs test. Neuroeconomics Goals and Incentives: Determining the exact location of the neural activity driving the different behavior and emotions may have gigantic applications in the near future (years?, decades?) Psychological Pressure in Dynamic Competitive Environments A beautiful setting: A penalty shoot‐out 1. Strictly competitive (zero‐sum) 2. Leading/lagging randomly determined 3. Professionals, high stakes, no role for risk (binary outcomes), etc Does it matter which team starts? Is it 50‐50? Are there psychological effects that make it different from 50‐50? First kicking team Second kicking 60.6 % team 39.4 % Period 1970‐2013 in all major national and international club and national team competitions (World Cup, European Cup, Champions League, national cups, etc). The coin plays a very important role: it assigns a 60‐40 = 20% greater chance to the team that kicks first. Question: What can we do to minimize the “unfair” role of the coin? Two teams: A y B Actual order: A B A B A B A B A B A B ‐? ? Two teams: A y B Actual order: A B A B A B A B A B A B ‐B A Two teams: A y B Actual order: A B A B A B A B A B A B BA ? ? ? ? Two teams: A y B Actual order: A B A B A B A B A B A B BA B A AB Two teams: A y B Actual order: A B A B A B A B A B A B BA B A AB ? ? ? ? ? ? ? ? Actual order: A B A B A B A B A B … A B BAB A AB BA AB A B BA … Note: This is a well known sequence in the natural sciences known as Prouhet‐Thue‐Morse. Hmmm... but this sequence is quite complicated. A simplification: Why not reverse A B only once and then repeat it? A B BA‐A B BA‐A B BA‐... Do you know any sport that uses this sequence? A B BA‐A B BA‐A B BA‐... Yes, tie‐breaks in tennis! • Note 1: In tennis ABBA generates … 50‐50! Alex Krumer et al (2018) • Note 2: Ongoing trials with ABBA in various UEFA, FIFA and EFL tournaments. The result so far? 34 shoot‐outs: 17‐17 • Note 3: ¿to what extent are emotions malleable? • Very difficult to study: both “rational” and “irrational” components. • The rational component may perhaps respond to incentives (if large enough). • But, is this 60‐40 “malleable”? • An interesting case in Argentina in 1988‐89: during the league, after a tied game teams had to play a penalty shoot‐out to get 1 extra point. First Second kicking kicking team team 49.5% 50.5% Nobel in Economics 2013 Theory and Empirics of Efficient(?) Financial Markets The theory of Efficient Financial Markets basically says: The price of an asset incorporates fully and immediately all the relevant news. That is, there are no delays and no partial adjustments: E(Pt+1/It)= Pt + θt con θt ~ N(0,ζ) Implications ‐ It is not possible to beat systematically the market ‐ You are compensated exclusively by the risk you take (things can go well or things can go badly).