Logical thinking, analytical skills, and the ability to recognize patterns are crucial in an array of fields that overlap with mathematics, including economics. But what does math (or economics, for that matter) have to do with the world’s most popular sport? Economist Ignacio Palacios-Huerta’s recent book, Beautiful Game Theory: How Soccer Can Help Economics made a splash during the last World Cup, showing how universal economic principles can be understood through soccer. Read on for his thoughts on why the language of modern economics, including behavioral economics, is mathematics.
The Role of Mathematics in my Life as an Economist
To describe the role of mathematics in my life as an economist, I first need to explain what, to me, Economics is all about. So let me take you to one of my favorite books, A Treatise of Human Nature, written almost 300 years ago by David Hume.
In the introduction Hume writes, “‘Tis evident that all the sciences have a relation, more or less, to human nature … Even Mathematics, Natural Philosophy, and Natural Religion, are in some measure dependent on the science of Man, [which is] the only solid foundation for the other sciences”. By the science of man Hume means the understanding of all facets of human nature, including preferences, senses, passions, imagination, morality, justice, and society. This science applies wherever men are making decisions, be it running public institutions or countries, as employees in firms, or as individuals investing in education, taking risks in financial markets, or making family decisions. This science of man is thus what one may initially be tempted to call Economics for, as George Bernard Shaw puts it in my favorite definition, “Economy is the art of making the most of life”.
But of course this definition is incomplete because other social sciences (e.g., sociology, history, psychology, political science) are also concerned with human behavior. So what makes Economics “different”? Here is the difference: the difference is not the subject matter but the approach. The approach is totally different, and a very mathematical one. As such, mathematics plays a critical role in the life of any economist.
Let me elaborate. Continuing with Hume, it turns out that he also anticipated our methodological approach in modern Economics: observation and logical arguments. Which can be translated as: data and data analysis (what we call econometrics), and mathematics, for mathematics is, after all, the language of logic. So in Economics, as in physics, we write down our ideas and theories in mathematical terms to make logical arguments, and then we use more math (statistical, econometrics, etc) to check whether the data appear to be consistent with the theoretical arguments. If they are, the evidence can be said to support the theory; if they aren’t, the theory needs to be refined or discarded. Yes, lots of math and related techniques provide what is our distinct “economics approach to human behavior.” It is not the subject matter but the approach that is different, and it heavily relies on mathematics.
To economists and other social scientists, mathematics has many methodological virtues: it can lend precision to theories, can uncover inconsistencies, can generate hypothesis, can enable concision and promote intelligibility, and can sort out complex interactions, while statistical and econometric analysis can organize and carefully interpret voluminous data.
None of this is obvious when you begin studying Economics (“Why should I take all this math, statistics and econometrics? Why all this pain?”). But I think most of us soon learn to appreciate that the language of modern economics is mathematics, and that it is rightly so. And this is not math for the sake of math (as in pure mathematics), but math with a purpose: modeling human behavior.
Let me conclude by saying that since the economic approach is applicable to all human behavior, any type of data about human activity can be useful to evaluate economic theories. This includes, why not, sports data, which in many ways can be just perfect for testing economic theories: the data are abundant, the goals of the participants are clear, the outcomes are easy to observe, the stakes are high, and the subjects are professionals with experience. If a theory is “correct”, sport is a good setting to check it.
So just as data involving falling stones and apples were useful to Galileo Galilei and Isaac Newton to test for the first time theories that were important in physics, data from sports can be useful in Economics to do exactly the same. As such in some of my contributions to Economics I have used math to develop theoretical models, and further mathematical tools applied to this type of data to test them.