From Galileo to penalty shootouts: data, economics and human behaviour
Ignacio Palacios-Huerta,
Professor of Managerial Economics and Strategy, LSE.
Ignacio Palacios-Huerta is Professor of Managerial Economics and Strategy in the Department of Management at LSE. His research mainly focuses on identifying and studying novel questions concerning individual and aggregate human behaviour, including strategic behaviour in competitive settings, human preferences, incentives and human capital, among others.
As the FIFA World Cup reaches its closing stages, Professor Palacios-Huerta discusses the relationships between human behaviour, economics and football.
Your book Beautiful Game Theory: how soccer can help economics was a huge success when it was published in 2014 ahead of the last World Cup. Did you expect it to be so well received by a sport that has historically been slow to embrace a data-based approach?
I was a bit surprised to be honest. I thought it would do well among academic economists and students, and it did, but I was not sure among sports people. I think its success shows that even though football is the last major sport to embrace a data-based approach, it is also a sport in which there is a huge demand for any type of approach that might provide some new competitive advantages, especially approaches that have already worked and are working well in other sports.
What can football do for economics?
Let me give you an analogy. You may recall that stones falling from towers in Pisa and Florence sparked fundamental insights for Galileo Galilei (1564–1642) in his tests of the theory of gravity and others. Those stones contributed to providing the empirical evidence necessary to evaluate a number of theories in physics for the first time.
Just as data involving stones were useful in physics, data from football and other sports can be useful for economics. As a social scientist, they can be helpful in generating novel insights into human behaviour and human decision-making. As my dear mentor at the University of Chicago, Gary Becker (Nobel Prize in Economics 1991) repeatedly emphasised:
What most distinguishes economics as a discipline from other disciplines is not its subject matter but its approach. The economic approach is applicable to all human behaviour.
This general applicability means that in fact any type of data about human activity is potentially useful to evaluate economic theories. And sports are in many ways the perfect laboratory to do this, for a number of reasons. There is an abundance of readily available data, the goals of the participants are often uncomplicated (score, win, enforce the rules), and the outcomes are extremely clear. The stakes are typically high, and the subjects are professionals with experience.
And so, if one of the attractions of spectator sports is to see occasionally universal aspects of the human struggle in stark and dramatic forms, their attraction to economists is twofold: First, to illustrate economic principles in interesting ways and, second, and much more important, to give us a chance (sometimes) to provide the first clean empirical evidence on different theories of human behaviour.
Analytics
"Analytics can also be useful for the sports industry more generally, ranging from clubs to the international federations which design rules and competitions. For example, my work has led to the introduction of a different and fairer ordering of kicks in penalty shootouts to make sure that two identical teams should have the same chance to win."
How do data and maths inform football?
Data and maths (let’s call it “analytics”) in football is the rigorous application of data and scientific method to inform decisions and maximise the chances of winning as many games as possible. This could be via talent identification and development, player selection (buying and selling), in-game decision-making, or in the design and analysis of plays. But I want to emphasise that analytics is distinct from “statistics” or “data,” which I see as just collections of observations about the game which may or may not be useful to anyone.
Examples I have been directly involved with are decision making in penalty kicks (in 2010 I worked for Holland in the World Cup Finals in South Africa, in 2008 for Chelsea in the Champions League Final),optimal decision making in corner kicks, talent identification, and even which goal to attack in a U-shaped stadium (something that was estimated to be worth around two points (€2 million) in the case of Athletic Club de Bilbao in Spain’s La Liga.
Analytics can also be useful for the sports industry more generally, ranging from clubs to the international federations which design rules and competitions. For example, my work has led to the introduction of a different and fairer ordering of kicks in penalty shootouts to make sure that two identical teams should have the same chance to win.
As a slightly different example, I participated in the design of an “algorithm” to move 36,000 season ticket holders from one old stadium to a brand new stadium (again in Athletic Club de Bilbao), assigning seats to fans in a fair way so that they can be together with friends and families. Incidentally, this problem is very similar mathematically to the “matching problems” studied by Alvin Roth (Nobel Prize in Economics 2012), though here we do not have to match, say, donors and recipients of kidneys but to match seats for fans with their friends and families in an optimal manner.
Speaking of algorithms, Sabermetrics (the ‘Moneyball’ approach) revolutionised the sport industry in the US. Various football clubs have tried to adapt it, with varying degrees of success. But many remain sceptical: is it an imperfect fit for football?
There are basically two things that make football quite different to other sports:
1. It is more complex in many dimensions. For instance, it is more dynamic, with more strategies, fewer repetitions of the same plays, and more players involved; and
2. The number of games played each year is actually not very large, and the number of goals in a game is small. These factors mean that the advantages gained via analytics are more difficult to detect. But make no mistake, they are
there. With small samples characterised by high variance, you have to consistently apply analytical methods and be a bit lucky in order to reap the benefits of analytics in the short run.
Are these reasons to be sceptical that it might not work? Well, I think it is exactly the opposite. I remember a sports consultant called Tray Causey talking about people who work in big tech firms in the world facing tremendously complicated problems with thousands of variables and up to billions of users every day. How often do they say that their problems are too complicated for analytics? Zero. Quite the opposite — the problems are so complicated that you must use analytics. The idea that football is somehow “special” in this regard and should be left exclusively to “intuition” is preposterous on its face and wouldn’t be taken seriously in any other industry.
How does a professor of economics end up analysing 11,000 penalty kicks?
This comes back to my book and one of my first influential articles in economics. I began collecting data on penalty kicks in 1997 and continue to collect them today. To me there was an important unresolved question in economics that had remained open for more than 50 years: can humans behave in a strategically optimal way when using mixed strategies?
Recall the movie A Beautiful Mind, Oscar recipient for Best Picture in 2001. It portrays the life and work of John F. Nash Jr., who received the Nobel Prize in Economics in 1994. Perhaps you would think that after a movie and a Nobel Prize, the theories of Mr. Nash must have been solidly established and empirically validated on countless occasions. Right? Well, not quite. A subset of his theories deals with how people should behave in strategic situations that involve what are known as “mixed strategies,” that is, choosing among various possible strategies when no single one is always the best when you face a rational opponent.
The beauty of penalty kicks is the following: data from this specific play (the penalty kick) is really perfect to provide the first complete test of a fundamental theorem in game theory: the Minimax Theorem (the Nash Equilibrium for mixed strategies in zero-sum situations). This is in short why I have studied so many penalties…
If you are curious, it turns out that most professional players in the top leagues in the world play as the Nash Equilibrium predicts, but not all. They choose the frequencies of their strategies in a way that make their pay-offs statistically identical across strategies and do so in a way that is essentially random (whereas most of us, inexpert humans, are bad at behaving randomly even if we try). This, according to Nash theory, is what should happen, and this is what happens. I was very pleased with these findings as this empirical evidence was considered to be a major breakthrough among economists in game theory.
Your work has led to the trialling of a new penalty shootout model in certain competitions. How does this structure compensate for unfair advantage?
A penalty shootout is a sequence of penalty kicks (typically five), taken in a perfectly alternate way by two teams, say A and B, to decide the winning team where competition rules require one team to be declared the winner after a drawn match. That is, they follow the order A B A B A B … and this is randomly decided with a coin flip.
As a result of looking at so many penalties, I noticed that in penalty shootouts something unexpected happens: the order matters! The first-kicking team (A) wins significantly more often than the second-kicking team; the ratio is about 60-40. (Intuitively, in every pair of penalties the first-kicking team is given a greater chance to be leading, simply because it kicks first, whereas the second-kicking team is given a greater chance to be lagging simply because it kicks second). And this leading/lagging asymmetry matters for performance, helping the team with a greater chance to be leading (A).
To mitigate as much as possible this effect, while preserving that kicks be taken sequentially (rather than simultaneously), the idea is that in the first pair we do A B, then reverse the order in the second pair, B A. Hence the first four kicks would be ABBA. And then repeat: ABBA-ABBA-ABBA-… This is a simple order, easy to implement, that improves the fairness of the shootout as it reverses the leading/lagging asymmetry. You may have noted that this new order for football is not new elsewhere – another sport that uses it to great effect is tennis, in tie-breaks.
I was very pleased to see that the world governing body FIFA, and the International Federation Board (IFAB), have started trials with this new ordering in various youth European and World Championships. I expect that my ABBA order will be adopted worldwide soon, as a way to improve the fairness of the world’s most popular sport.
On that note, the FIFA World Cup in Russia has now entered its final stages. If the semi-finals and final were to go to penalties, what would your observations be, based on data?
First, some advice: be prepared for both in-game penalties and for penalty shoot-outs!
An in-game penalty (in favour or against your team) typically had a 25% chance of happening – and, as we have seen so far in this World Cup, whether through the introduction of VAR or not, it is higher at around 50% as of today.
In the knockout phases there is a 20-25% chance of a game ending with a penalty shootout. For instance, there were 4 shootouts in 16 games in the last World Cup – and there have been three already in Russia from eight second round games. (When you consider that three of the last six winners had to win a shootout to become world champions, you can see that penalties are no minor events.)
Also, be aware that under the current ABAB kicking-order system, as mentioned earlier, there is the 60-40 advantage to kicking first in a shootout – even though the first three shootouts in this extraordinary tournament to date have favoured the team kicking second. (My sense is that most teams already know this, and in fact the three winners of the referee's coin toss have chosen to kick first; if not, read Chapter 5 in my book for empirical evidence from 1,000+ shootouts.)
So, if you win the coin toss, choose to kick first. A 60-40 advantage is not a 100-0, so there are no guarantees, but that extra 20% is still very significant.
"So, if you win the coin toss, choose to kick first."
"A 60-40 advantage is not a 100-0, so there are no guarantees, but that extra 20% is still very significant."
Ignacio Palacios-Huerta,
Professor of Managerial Economics and Strategy, LSE.
