HOUSTON — All year long, the narratives of the Houston Astros and the Yankees have been intertwined. Entering the season, both were among the favorites to win the World Series. As they plowed through their schedules, quickly emerging as the best teams in their league, a collision in the best-of-seven American League Championship Series — which begins Saturday night at Minute Maid Park — seemed inevitable.

“I heard it from Day 1,” Astros Manager A.J. Hinch said.

Then the Yankees decided not to upgrade their pitching staff at the July 31 trade deadline, banking on improvement from within, while the Astros pulled off several deals — including one that added the 2009 Cy Young Award winner Zack Greinke to a starting rotation that already had Justin Verlander and Gerrit Cole. At that point, a more direct question arose: How would one strategy compete with the other?

“Let’s find out,” Brian Cashman, the Yankees’ longtime general manager, said then.

The Yankees discovered that their formula of a powerful offense, stout relief pitching and a solid but unspectacular starting rotation was enough to win 103 games and the A.L. East. Their hitting proved worthy in a first-round division series against the Minnesota Twins, and so did their pitching, holding the Twins — the best home run-hitting team in history — to only seven runs.