And if Dortmund is to be a challenger to Bayern Munich, displays like this are going to be needed. On Friday evening, Munich had trounced a hapless Hamburg, 5-0.

Not only did Robert Lewandowski and Thomas Müller do their thing by scoring goals for Bayern, but Douglas Costa, the club’s new $34 million winger, created some of those goals before scoring the final one with a cunning, curling low shot from his left foot.

Douglas is one of those Brazilians plucked out of his country during his teens, joining Shakhtar Donetsk when he was 19. Now 24, he left the Ukrainian club this summer, partly because of the unrest there and partly because Bayern Munich has the financial power to make offers nearly impossible to resist. Over the years, Bayern had severely weakened Borussia Dortmund by luring away the best players of its close rival.

After finishing as the runner-up to Bayern in 2013 and 2014, Dortmund ran out of gas last season after Lewandowski departed for Munich and injuries seemed to lay the entire team low at times.

Jürgen Klopp, the coach for seven years, admitted he had exhausted himself, and quite possibly his players, with the extreme demands of his high-pressure style. He left at the end of the season after the team recovered to finish seventh.

Dortmund knew where to find Klopp’s replacement. It went to Mainz, the team where Klopp cut his managerial teeth, to hire Thomas Tuchel as its new coach.

The two coaches are alike, yet different. Each stands 6-foot-4, but whereas Klopp is almost part of the action during games with his emotions laid bare, Tuchel is the calm after the storm. At least he appeared so Saturday, when he waved a finger of disapproval only after a goal was disallowed because of an offside call. Klopp, we know, would still be jumping up and down with rage over such a ruling.