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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.

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