So far, the Jays have. At the time of the Tulowitzki deal, which had been brewing since last off-season, the Blue Jays were underachievers. Their record was 50-50, seven games behind the Yankees in the American League East despite having the best run differential (118 after Thursday’s win).

But after Tulowitzki put on the uniform July 29, homering in his Jays debut, Toronto won eight of its next nine games to move into the second A.L. wild-card spot. The Blue Jays are also four and a half games behind the Yankees, the team Toronto will visit this weekend in the Bronx.

As well as the Yankees are playing this season, confidence is surging in Toronto and across Canada, especially because this weekend’s games are the first of 13 left between the teams, providing ample opportunities for the Blue Jays to whittle away the deficit.

“I’d like to say,” outfielder Jose Bautista said, “that the inclination for me to feel optimistic about our chances, with our additions and some of the stuff that’s going on over there with injuries and lack of performances, that if I was a betting man, I would bet on us.”

Bautista, who hit a thundering grand slam against the Twins on Wednesday, is still at the core of a lineup that is stacked with right-handed power. Even before the trades, Toronto had scored more runs than any other team, and its on-base plus slugging percentage was the highest in the majors.

But now Tulowitzki is leading off. Third baseman Josh Donaldson, who was brought over from the Oakland Athletics in an off-season trade, bats second and is the Jays’ hottest hitter, with five home runs in his last seven games. He had 29 home runs and 29 doubles after Thursday’s series finale with the Twins, which the Blue Jays won, 9-3.