But Sanchez is 27 years old and under team control through 2020. He won the league E.R.A. title in 2016 and earned the Blue Jays’ only victory in that fall’s A.L.C.S. He throws a sinker, a pitch the Astros generally de-emphasize. That made Sanchez a distressed asset willing to entertain changes or build off the small signs of progress he had already made, like Charlie Morton did in Houston two years ago.

“They showed me how my stuff played and showed me how to execute it,” Sanchez said. “I think that’s the biggest thing for me — my mind always knew how to get to that point but I just never knew how to turn that into the game. Their presentation to me was very thorough in how to execute plans.”

Then again, insisted Sanchez, who has thrown more curveballs and four-seamers with the Astros, game-planning is useless without the talent to apply it. Naturally, in his first start for Houston, he fired six innings of a combined no-hitter against Seattle. Sanchez’s next start was even easier — a 23-2 rout over the Orioles. The rookie Yordan Alvarez pounded three homers and the Astros set a club record for runs scored.

“When they came calling and gave me the opportunity to start, I felt like that was perfect for me,” said Sanchez, who was worried a new team might stuff him in the bullpen. “It’s just awesome to be a part of this .”

Luhnow acquired Sanchez and reliever Joe Biagini from the Toronto Blue Jays in exchange for outfielder Derek Fisher as part of his flurry of activity just before the July 31 deadline. He also reacquired catcher Martin Maldonado from the Chicago Cubs for the utility man Tony Kemp, and he sent prospects — including the former first-round draft picks J.B. Bukauskas and Seth Beer — to Arizona for Greinke, a starter with a Hall of Fame résumé, and $24 million to help pay his salaries through 2021.

The Astros, who have been at the forefront of baseball’s analytics revolution since Luhnow took over in 2011, identify dormant skills, make supporting data easy to understand and access, and cultivate an environment in which players are assertive yet open-minded and share information.

“We push each other,” said second baseman Jose Altuve, the longest-tenured Astro (since 2011) and a former A.L. most valuable player. “We encourage each other to be the best version of the best player we can be .”