Who said that math is it boring? These days, mathematics researchers and thesis students from the Faculty of Exact Sciences/UBA They study and enjoy applying the tools of mathematics and computer science to one of the greatest passions of Argentines: soccer. As they have been doing since 2018, They are calculating with scientific methods (and not by mere intuition) the chances that the national team and those of other countries have of winning the Copa América, which this year is being played on North American soil.. So far, the results of millions of computer simulations show a clear advantage for the “Albiceleste”. But there is no room for celebration yet because – as we know – sometimes “things happen”.
According to this ranking, Argentina, which is already in the quarter-finals, is in first place with a 46.41% chance. It is followed in second place by Brazil, with 15.51%; Colombia, with 12.14%; Uruguay, with 10.49% and the United States, with 7.21%.. On the other hand, the national team has a 99.82% chance of being the leader of its group, an 83.58% chance of being a semi-finalist and a 70.28% chance of reaching the final. According to this ranking, it is most likely that there will be a Cup until the end. All results can be consulted at https://301060.exactas.uba.ar.
“To develop this tool we take into account the matches played by the different teams that compete in the Copa América from 2014 to today,” he explains. Ivan Monardo, “almost a graduate” in Mathematics who is in charge of the site, in which around 15 specialists from different disciplines participated. In addition, we include some other countries that faced these teams several times, such as Trinidad and Tobago, for example. And from those matches we use data on when the match was, what the result was, if any were local and for what competition (a World Cup, a friendly, a qualifying round). Once we have them, What we do is calculate the attack and defense power of each of these teams. We assign a score to each match. ‘weight’ which is a combination of different factors, such as how long ago it was played (if it was last week, it will have more importance than one from four years ago) and in what instance (If it is from a World Cup it will have a higher score than a friendly).”
As matches are played, scientists upload the results and recalculate the attack and defense strengths, which change slightly“As we attach a lot of importance to the date, the most recent matches played have a slightly greater impact than the older ones,” Monardo explains. Today, Argentina has already qualified for the quarter-finals and that also increases its chances of becoming champion. On the other hand, our team could only face the strongest teams in the final. So, beyond being the best team, the one with the best attack and defense coefficients, due to how the team is set up, fixture, Their chances of reaching the final increase and their probability of being champion is also quite high,” he added.
In accordance with This instrument, The other strong teams in the championship are Brazil, Colombia, Uruguay and USA, among which only one will be a finalist. Argentina should face one of them in the final, while the others eliminate each other. “Of those four, in almost all the simulations one reaches the final – highlights Monardo – but none of them have a very high probability because they would all face each other before reaching that stage.”
This tool was put to the test at the World Cup 2018, the 2019 and 2021 Copa América and the World Cup held in Qatartwo years ago.
“What we do is simulate the games [millones de veces en la computadora] –explains the mathematician–. You could imagine as if you were tossing a coin that has a certain weight for the favorite team based on these attack and defense powers, and we simulate each match between the different teams. We write down in each one what instance they reach, we repeat [esa operación] a million times and then we count, for example, how many times Argentina reached the final. That allows us to calculate the empirical probabilityNow, whether he is a champion is a little more difficult to test, so to speak, because there is only one. It’s like if I had a dice, the probability that if I throw it in the air a number from one to four will come up is 4/6, 66%. But if I roll it once and it comes up a five, it’s not that I was wrong: a number from one to four was much more likely to come up, but [la probabilidad de que saliera el 5 no es nula]. It’s the same with the champion. The Copa America is played only once and anyone can win. What we say is that if it were played many times, we would expect Argentina to win more or less half of the time. What we can check a little more are the individual matches. Since we have many matches, we can better calculate the correct predictions. And it works quite well. If we have that in 10 matches the favorite has a 60% chance of winning, in more or less six of those ten matches we get it right, that is, the favorite wins.
As scientists explain, and it becomes more and more evident every day, “mathematics is everywhere”: in health, in finance and in supermarket shopping. And football is no exception: it must be used to count goals, order the league table or calculate the averages of the relegation. Among its most complex applications, there are others that the researchers have already addressed, such as putting together a fixture further efficient or develop a model to obtain probable results.
It is clear that science is not at odds with enjoyment. But MAlthough it may seem like a game, these types of simulations are used in other areas. As Pablo Groisman, director of the Data Science program at the same faculty, explains in one of the sections of the site, a model is not reality, but a mathematical object to explain it and predict the future in some way, it is used in contexts of uncertainty and can be more or less precise. And Just as this methodology uses historical data on converted goals to train probabilistic models, if one were to replace the idea of team with ‘municipality’ and goals with floods, data scientist Andrés Farall once explained, one could train models that calculate what the probability of these events occurring in the future to guide aid to different jurisdictions.
