Mexico finished far behind the United States in the two rivals’ World Cup qualifying group — and made the tournament only because the United States scored late in a match it did not need to win.

How did the United States get repaid for its generosity? By being placed in a far more difficult group than Mexico, because of the luck of the draw. Mexico now seems in a better position than the United States to advance to the Round of 16.

Mexico, in fact, is the luckiest team in the entire 32-team tournament, according to our analysis of the bracket. Its first-round grouping is easier than 99 percent of its potential groupings. Mexico (the 19th-ranked team) has been placed with Brazil (ranked fourth and the tournament’s host), Croatia (20th) and Cameroon (50th). Two teams from each group advance to the Round of 16.