Michael Brantley and José Altuve had just hit two home runs in the bottom of the eighth to make it 6-1 in Game 5 of the American League Division Series against Tampa Bay. Now Reggie Jackson, a special advisor with the Yankees, was on the telephone, saying that it looked as if the Yankees were on their way to Houston.

“This is the one everybody wanted to see, isn’t it?” Reggie said. “I know it’s the one I wanted to see.”

He was talking about Yankees vs. Astros in another American League Championship Series. He was talking about the Astros and the 110 wins they have so far (including the ALDS), against the Yankees, who have 106 of their own. The two teams went up against each other just two years ago in a memorable seven-game ALCS. Now they are set to do it again. The Astros had to work harder to get to Saturday night, because the Rays took them the distance in their ALDS after the Yankees had already swept the Twins. But now here they both are, Games 1 and 2 at Minute Maid Park this weekend.

“A couple of heavyweights,” Reggie said, but then added this: “One of them just a little more proven at this time of year.”

He meant the Astros, who beat the Yankees in the ALCS two years ago and went on to win the World Series. Even last year, they went one round further in the postseason than the Yankees did, even though they both lost to the Red Sox. Now the Astros are coming off the greatest regular season in their history, no matter how hard the Rays, tough as a tick to the end, pushed them.

“But our guys are the Yankees,” Reggie said. “And even though we haven’t won it all for a while [2009], they know this is what they sign up for when they put on the uniform. There are certain expectations here. Those expectations never change. The expectations are that we’re supposed to win, no matter how many new guys there are, no matter how long it’s been since the last World Series. There’s just things you learn here when you come here.”

His A’s teams had won three straight World Series when he signed a free-agent contract with the Yankees and joined them for the 1977 season. The Yankees hadn’t won the World Series since 1962, even if they’d just been swept in the ’76 Series by the Big Red Machine from Cincinnati. Then Reggie showed up, having famously told everybody that he didn’t need New York to make him a star, he was bringing his star with him.

He did just that, backed up all his big talk, ended the 1977 World Series against the Dodgers with three home runs on three swings of the bat in Game 6. It was the night he became Mr. October. The next year, the Yankees did it again. Now Aaron Judge and Gleyber Torres and Giancarlo Stanton will try to put their own points on the board against the Astros.

I asked Reggie what he thinks can be different this time for the Yankees against the Astros.

“There’s just a different culture,” he said. “And it starts with everything they’ve had to overcome this season. What was it, 30 guys on the injured list? I’ve never seen any baseball team have to overcome something like that. I’m not sure I ever seen a team in any sport overcome something like that, and just get to where we are right now. But these guys didn’t whine. They didn’t cry. They didn’t complain. They trusted each other and Brian [Cashman] trusted them to the point where we didn’t go get go players at the [Trade] Deadline. They had their own expectations for each other. They bought into all that next-man-up stuff, totally. And never stopped believing they were supposed to be here.”

Reggie paused and said, “The atmosphere is just different this time.”

He talked then about how DJ LeMahieu is new. He talked about Gio Urshela, who came out of nowhere to play like a star at third base. He talked about how getting Stanton back after he’d missed almost all of the season due to a couple of injuries of his own “is like we made a trade in September for a guy who not too long ago led the whole world in home runs.”

“They believe this is their time,” Reggie said.

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It takes more than belief. He knows it better than anyone, because he was one of the great winners at this time of year. The Dodgers, after losing the last two World Series, thought it was their time, too. You saw what just happened to them. You saw that everything can change, seasons can be lost, on a handful of late-game pitches the way it did at Dodger Stadium on Wednesday night. The Yankees thought it was their time two years ago when they led that ALCS against the Astros, three games to two. Then they scored a total of one run in the last two games. Last year they thought it was their time when they went back to Yankee Stadium tied at one game apiece with the Sox. Then they lost Game 3 16-1 and never recovered.

“I think all that makes you stronger,” Reggie said.

Mr. October saying that. He used to go deep at this time of year. Now another Yankee team tries to go deep into October. They try to knock out an old champ to become champs again. Reggie’s right. This is the one we wanted to see.