How to win the cup pool?

Dear investors, The 2022 Fifa World Cup, the biggest football event and passion for Brazilians, starts next Sunday (11/20), and with that, many groups have organized sweepstakes that reward participants who are most accurate in the results of the cup. For the participants, the question that remains is how to win the cup prize pools? Is there any strategy that allows you to increase the chances of winning? At first, it is intuitive to imagine that those who have more chances are those with deep knowledge of football, who watch the games and follow the news that allow a detailed view of the strengths and weaknesses of each team. But that is not true! While specific football knowledge can help when used properly, the most important thing is to use the correct methodology for making predictions. This is valid not only for football, but also for several other subjects, including investments. With the right methodology, anyone can win, from those who are just learning which teams will participate in the World Cup, to those who closely follow every game and have been waiting anxiously for this moment. About the methodology The strategy discussed in this memo is presented in detail in the book “Superforecasting: The Art and Science of Prediction”, a book released in 2015 and written by Philip Tetlocke Dan Gardner. In this book, the authors present the results of “The Good Judgment Project”, a project that analyzed the accuracy rate of different people in different types of predictions, covering topics ranging from “How likely is there to be a terrorist attack in Europe in the next 3 months?” to “What is the chance of Arctic glaciers increasing next year?”. The results of the project are quite amazing. According to the authors, ordinary people using correct methodologies had higher 30% success rates than experts with access to confidential information. For those interested, Ártica's management team recorded a podcast that summarizes the ideas contained in the book in more detail. The podcast is available on our Spotify and Youtube channels. where to start Returning to the subject of the bubble. First, it's important to point out that there are several types of pool, and each one has different scoring rules. In the discussions of the next paragraphs, we assume a simple lottery, in which the person who matches the highest number of results wins more points. To begin with, the first step is to define a baseline, or base rate. The base rate consists of observing similar events that occurred in the past and analyzing the most frequent results. For coin games, the base rate is that 50% of flips are heads, and 50% tails. For unbiased dice, the base rate is that the probability of landing on a given number is 1/6. For football games, the calculation of the base rate consists of observing the historical results of football games and analyzing the most common scores. For this, we present the two graphs below that show the history of scores in the premier league (main football championship in England) and in world cups. Graph 1 – Most common premier league scores (1888-2014)¹

Graph 2 – Most common scores in world cups (1930-2018)

What becomes clear after looking at these two graphs is that the distribution of scores is incredibly concentrated. Both in the premier league and in world cups, the most common scores are: 1×0, 2×1, 2×0 and 1×1. Therefore, the baseline for any forecast should come from these scores. It's a lot of fun to risk a 5-0 guess and get it right, but those kinds of scores just don't happen! If your goal is to win the pool, focus on low scores. Make adjustments from the baseline Having drawn the baseline, it is possible for those with greater knowledge to deviate a little (not much!) and risk a guess that they consider more likely, depending on the difference in quality of two teams. If one team is much better than the other, the participant can risk a score of 2×0 instead of 1×0 or 2×1. If the teams have very close levels, the guess could be 1v1. Another adjustment that can be made is to consider that the scores have been thinner in recent decades. Premier league data shows that, until the 1970s, the average of goals per game was between 3.0-3.5. After 1970 until today, that average has remained at ~2.5 goals per game. In other words, the most elastic scores are even rarer nowadays than the graphs above suggest (points for the 1×0!). It is not clear what the reasons for this reduction are, but it is possible that they have to do with the professionalization of the sport, and with rule changes (possibility of substitution, yellow and red cards, etc.). It is important to emphasize that, even if the participant follows the best practices, there is no guarantee that he will win the pool. Good practices allow you to increase the chances of hitting the scores, but the results still depend on luck. The greater the number of participants, the greater the chance that a participant who does not follow any rules, and who guesses several unlikely outcomes, will get lucky and end up winning. An unlikely score like 4×1 for example, which occurs in about 3% of games, is expected to be seen 2 times in the cup (considering a total of 64 games). It is impossible to know which 2 games these are, but the participant who guesses correctly increases his chances of winning (even if the best strategy is not to guess 4×1 for any game). Good luck to everyone in your pools!