The Argentine superstar Lionel Messi once said: "In football ... talent and elegance mean nothing without rigor and precision."
The firm used machine learning to run 200,000 models, mining data on team and individual player attributes, to help forecast specific match scores. Goldman then simulated 1 million variations of the tournament to calculate the probability of advancement for each squad.
The tournament bracket below shows how Goldman sees the World Cup unfolding. Note that the numbers next to each nation — which dictate whether it advances over its opponent — represent the predicted, unrounded number of goals scored in each possible iteration of the tournament, based on machine-learning results applied to countless scenarios.
"We are drawn to machine learning models because they can sift through a large number of possible explanatory variables to produce more accurate forecasts than conventional alternatives," a group of strategists from Goldman's international research team wrote in a client note.
Here are the key takeaways from Goldman's data:
With all of that established, football (soccer) remains a highly unpredictable sport, with many more variables in play than even Goldman could assess. That is why the authors of the report offer this disclaimer at the end:
"We capture the stochastic nature of the tournament carefully using state-of-the-art statistical methods and we consider a lot of information in doing so," they said. "But the forecasts remain highly uncertain, even with the fanciest statistical techniques, simply because football is quite an unpredictable game. This is, of course, precisely why the World Cup will be so exciting to watch."
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